The peer-reviewed study collected data for 62 days and was published in the New Journal of Physics in June 2026. The investigation targeted a theoretical proposal developed in the 1960s by Hungarian physicist Frigyes Károlyházy. His model suggests that spacetime is continually rippling with tiny fluctuations.

These fluctuations could progressively disturb quantum superpositions and prevent macroscopic objects from remaining in the combinations of distinct states imagined in Schrödinger’s cat thought experiment. The idea has since been revived, refined and reformulated by researchers seeking to understand the relationship between general relativity and quantum physics. The experiment tested a generalized version of that model rather than every gravity-induced decoherence proposal.

Although the predicted spacetime fluctuations cannot be observed directly, the model links them to a possible electromagnetic signature. If the fluctuations exist, they should cause charged particles to jiggle and accelerate randomly, leaving trails of electromagnetic radiation. The signal expected from this process is extremely faint and can be hidden by electromagnetic background from sources such as cosmic rays.

The researchers therefore searched for radiation with the signature predicted by the generalized Károlyházy model, rather than attempting to measure spacetime fluctuations directly. The Gran Sasso National Laboratory, operated by Italy’s National Institute for Nuclear Physics beneath 1.4 kilometers of rock, provided the setting for the search. The underground site is described as one of the quietest environments on Earth for detecting extremely rare physical phenomena.

Its natural shielding suppresses environmental electromagnetic radiation that could obscure the effect sought by the team. The location made it possible to collect data in a low-background setting, although the absence of a detected signal applies specifically to the model and experimental conditions tested. The detector was built around a coffee-mug-sized piece of high-purity germanium crystal, enclosed by layers of copper and lead shielding.

Over the 62-day measurement period, the team collected data, subtracted the expected background radiation and searched the remaining measurements for a signal matching the model’s prediction. No such signal was detected. In this setting, the absence of the predicted radiation is the experimental finding itself: it constrains the generalized Károlyházy model rather than supporting the existence of the proposed gravitational mechanism.

The study is an experimental test of a specific theoretical hypothesis, not an observation of decoherence in a macroscopic object and not a direct measurement of gravity’s role in the transition from quantum behavior to classical reality. Its scope is also limited to the generalized model, the predicted radiation signature and the sensitivity achieved by the germanium detector, shielding and analysis. A null result cannot exclude models that predict different observable effects or signals outside those conditions.

The result therefore narrows the experimental search while leaving the broader question of a gravitational link with decoherence unresolved. “This absence of a signal is itself a major scientific result,” said Catalina Curceanu, a member of the Foundational Questions Institute and director of research and spokesperson for the VIP Collaboration at the National Laboratory of Frascati of the National Institute for Nuclear Physics. She said the experiment rules out one of the oldest and most natural gravity-induced decoherence models, bringing researchers one step closer to understanding the interplay between gravity and quantum mechanics.

In that sense, the study changes a speculative possibility into an experimentally constrained proposal. The theoretical context extends beyond the particular model that was excluded. Károlyházy’s proposal rests on the idea that there is a fundamental limit to the precision with which an object’s position can be specified and length can be measured.

According to Kristian Piscicchia, a quantum physicist at the Enrico Fermi Research Center/INFN/VIP and the experimental lead on the study, this feature has become a common thread in many contemporary approaches to uniting quantum physics and gravity, including string theory and loop quantum gravity. The Gran Sasso experiment illustrates how a specific consequence of such a theory can be tested without directly observing the complete theory. Curceanu described the broader experimental development in similarly measured terms.

“Precision experiments are now reaching a level of sensitivity where they can test ideas that, until recently, belonged almost exclusively to the realm of theoretical speculation,” she said. “As sensitivity improves, the boundary between theory and measurement continues to move, opening new possibilities for discovering the fundamental principles that govern our universe.” The result therefore extends the reach of laboratory inquiry into a question often treated as belonging entirely to theory, while retaining the specific limits imposed by the search for a predicted radiation signal. The paper, “Experimental exclusion of a generalized Károlyházy gravity-induced decoherence model,” was authored by Nicola Bortolotti, Kristian Piscicchia, Alessio Porcelli, Matthias Laubenstein, Simone Manti, Antonino Marcianò, Federico Nola and Catalina Curceanu.

It appeared in New Journal of Physics, volume 28, article 064511, on 19 June 2026. The research was supported by the Foundational Questions Institute through its Consciousness in the Physical World program.

Subject of Research: Experimental testing of gravity-induced quantum decoherence

Article Title: What kills Schrödinger’s cat?

Article References: What kills Schrödinger’s cat?. Original publication (Bibliographic details unavailable.)

Image Credits: AI Generated

DOI: Not provided

Keywords: quantum decoherence, gravity-induced decoherence, Károlyházy model, quantum gravity, Gran Sasso, underground experiment, germanium detector, spacetime fluctuations, general relativity, kills, Schr, dinger

The theoretical framework begins with the one-particle irreducible effective action for the Standard Model coupled to gravity. Vacuum-to-vacuum diagrams in this framework generate temperature-dependent corrections to the cosmological constant. At leading order, the corrections scale with the fourth and second powers of temperature, so the effective cosmological constant can be written schematically as Λ = Λ1 + Λ2a⁻⁴ + Λ3a⁻² + …, where a is the cosmic scale factor. The associated density parameters ΩΛ2 and ΩΛ3 resemble radiation and curvature in their scale-factor dependence, but the study assigns them a different physical origin. Standard radiation is the energy density of physical particles such as photons and relativistic neutrinos, whereas the new parameters summarize off-shell vacuum-bubble contributions from Standard Model fields and, in the complete framework, gravitons.

Heavy fields are central to that distinction. The Higgs boson, top quark, and electroweak gauge bosons have masses far above the recombination-era temperature and do not behave as ordinary relativistic radiation at those temperatures. Nevertheless, virtual vacuum bubbles can contribute to the finite-temperature effective action. The paper describes two equivalent ways of organizing these terms: as time-dependent shifts in the effective cosmological-constant sector, or as quantum corrections to the effective equation of state of the early-Universe plasma. The numerical analysis is independent of which of these interpretations is preferred, because the same T⁴ and T² terms enter the background expansion rate. The new components are treated as spatially homogeneous, background-only effects in the approximation studied; no separate perturbation equations are added for them, unlike for standard radiation, baryons, cold dark matter, or curvature.

To implement the proposal, the authors modified the Cosmic Linear Anisotropy Solving System, or CLASS, which evolves a specified cosmological model and calculates observables including cosmic microwave background power spectra. The eight parameters explored were ΩΛ2, ΩΛ3, the dimensionless Hubble parameter h, physical baryon density ωb, physical cold-dark-matter density ωcdm, scalar amplitude As, spectral index ns, and optical depth τreio. The modified Hubble parameter included the ordinary matter contribution together with terms proportional to ΩΛ2 and ΩΛ3. At the level used in the study, ΩΛ2 and ΩΛ3 alter the homogeneous expansion history but do not source perturbations. The authors also report numerical checks indicating that ΩΛ3 is not redundant with curvature density, despite their similar appearance in the Hubble expression, because curvature enters the action and perturbation equations as a geometric quantity whereas ΩΛ3 originates in a quantum correction to the cosmological-constant sector.

The first stage of the numerical search consisted of broad scans over the eight-dimensional parameter space, producing tens of millions of points, followed by increasingly focused searches in regions that yielded small Euclidean distances to a theoretical Planck 2018 CMB spectrum. The reference file was an unbinned, noise-free theoretical spectrum sampled at integer multipoles and did not include a covariance matrix. The authors therefore used a deterministic comparison rather than a conventional Bayesian likelihood, describing the procedure as an iterative form of trial and error rather than a substitute for formal statistical inference. They reported that adding tools such as Cobaya or MontePython increased the runtime by a factor of six to eight, while their external script could rank spectra almost immediately once CLASS had calculated them. The data collection alone took more than three months, making computational efficiency central to the search strategy.

Artificial neural networks were then used to approximate the otherwise unavailable function connecting cosmological parameters to distance from the Planck curve. Separate networks were trained for the seven-parameter and eight-parameter populations. Each had four hidden layers of 16 neurons, with rectified linear activation functions, and received standardized inputs so that parameters with very different numerical scales could be processed more effectively. The networks were trained using the Adam optimizer with a learning rate of 0.001 and mean squared error loss. The main datasets contained 459,912 points for the seven-parameter model and 335,985 for the eight-parameter model. Despite having fewer samples and a coarser grid, the eight-parameter population had a smaller average distance to the 2018 Planck result, and its test loss converged more closely to its training loss than the seven-parameter model’s.

Repeated training provided a measure of variability in the neural-network estimator. Across 500 independent replications of the eight-parameter fitting procedure, with each model trained for 1,000 epochs, the test mean squared error had a median of 0.55 and an empirical 95% confidence interval from 0.31 to 1.14. A larger run produced a global average test mean squared error of 4.95 for a combined dataset of 795,897 points. The distance function ranged from 0 to 1,491, and the source cautions that not every digit in the theoretical Planck file carries statistical significance. These statistics characterize how accurately the neural networks reproduced the calculated distance surface. They are not probability distributions for the cosmological parameters and do not quantify uncertainty in the underlying finite-temperature theory.

Two optimization schemes searched the learned distance functions. Broyden–Fletcher–Goldfarb–Shanno optimization, using numerical gradients derived from the neural-network surrogate, found a minimum distance of 29.24 in the eight-dimensional model, compared with 32.09 in the seven-dimensional model. The corresponding eight-parameter values were ΩΛ2 = −2.069 × 10⁻⁸, ΩΛ3 = 0.00430, h = 0.6752, ωb = 0.02240, ωcdm = 0.1196, As = 2.1007 × 10⁻⁹, ns = 0.9660, and τreio = 0.05424. An artificial-network-guided stochastic simulated-annealing run, using random-walk Metropolis–Hastings transitions, converged to a slightly lower distance of 28.8111. Its values were ΩΛ2 = −2.061 × 10⁻⁸, ΩΛ3 = 0.00425, h = 0.6762, ωb = 0.0223, ωcdm = 0.1196, As = 2.1 × 10⁻⁹, ns = 0.9664, and τreio = 0.056. These are best-fit coordinates under the study’s distance metric, not posterior means or confidence-limited parameter estimates.

Feature-ablation experiments indicated that ΩΛ2 helped the neural networks reproduce the fine structure of the Planck spectrum. In an analysis restricted to the 5,000 points with the shortest distances, removing ΩΛ2 increased the average test mean squared error by approximately 25%, with 50-fold cross-validation used to construct confidence intervals for predictive performance. A global leave-one-out analysis also found that removing ΩΛ2 caused a larger error increase than removing some established cosmological parameters, although the large-scale shape of the curve remained primarily controlled by the conventional parameters. The investigators interpreted the negative ΩΛ2 estimates as consistent with dimensional regularization in their renormalization procedure. The sign is therefore a feature of the model, parameterization, and renormalization choice rather than an observationally established property of quantum gravity.

Several limitations restrict how the result can be interpreted. The authors explicitly characterize the work as a phenomenological model-building exercise, not a first-principles derivation of finite-temperature hydrodynamics from the Standard Model coupled to gravity. Their present approach couples the one-particle irreducible effective action to a separately specified hydrodynamic sector, leaving the full separation between on-shell kinetic content and off-shell vacuum contributions as an open theoretical task. The adopted T⁴ and T² expansion is not uniformly appropriate for every combination of field mass and cosmic temperature. For a heavy field, a low-temperature treatment may be required, and its leading contribution can scale as T⁶/m², implying an additional term such as ΩΛ4a⁻⁶. The framework also omits more complete in-medium effects, including Debye screening and collective excitations. Follow-up work would need a larger parameter set, formal Bayesian inference, thermal expansions that change appropriately across cosmic history, and tests against CMB polarization data. The defensible conclusion is thus a computationally promising improvement in fitting within a specified phenomenological model, not a detection of finite-temperature quantum corrections or a solution to the Hubble tension.

Subject of Research: Phenomenological analysis of finite-temperature quantum-gravity corrections to cosmological parameters and the Planck CMB spectrum

Article Title: Stochastic analysis of finite-temperature effects on cosmological parameters by artificial neural networks

Article References: Hatefi, A., Hatefi, E., & Park, I. Y. (2026). Stochastic analysis of finite-temperature effects on cosmological parameters by artificial neural networks. The European Physical Journal C, 86(10), Article 1203. https://doi.org/10.1140/epjc/s10052-026-16214-w

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16214-w

Keywords: finite-temperature cosmology, quantum gravity, cosmological constant, Planck CMB spectrum, artificial neural networks, CLASS Boltzmann code, vacuum energy, Hubble tension, stochastic optimization, Stochastic, analysis, finite-temperature

The proposal examined in the analysis involves two massive particles prepared in spatial superpositions and passing through separate interferometers. Gravitational interactions between the particles generate relative phases, and the resulting state can contain entanglement if gravity can mediate coherence between the two quantum systems. The authors consider two arrangements: paired Stern–Gerlach interferometers, where spatial path separation is created through a deviation angle, and paired Mach–Zehnder interferometers, where each particle travels through horizontal and vertical arms. These are theoretical proposals; the study does not report an observation of gravitationally induced entanglement.

Previous analyses have often assumed that the interferometers are much longer than they are wide. Under that condition, the horizontal portions of the trajectories are treated as the dominant source of gravitational phase, while the vertical or inclined segments are neglected. The new calculations show that this approximation is not always safe. When the omitted portions make a substantial contribution, the calculated phase difference can differ markedly from the simplified prediction. In some parameter regimes, the additional contribution cancels the phase difference associated with entanglement, turning an expected signal into a null result. In other regimes, it increases the signal beyond the earlier estimate.

The gravitational phase is obtained by integrating the particle mass multiplied by the gravitational potential acting on it, with the result divided by the reduced Planck constant. In the Stern–Gerlach configuration, the exact expressions combine a horizontal contribution with an integral over the inclined separation segment. They reduce to the usual horizontal-arm approximation when the path separation is small, but logarithmic terms associated with the inclined trajectory become increasingly important as the geometry changes. This means that the full shape of the interferometer enters directly into the phase difference used to predict entanglement, rather than acting only as a minor correction to the long-arm approximation.

Entanglement in the idealized setup is quantified with concurrence, a measure for a two-qubit state. For the state considered in the analysis, concurrence reduces to four times the product of the two beam-splitter amplitudes multiplied by the absolute value of the sine of half the relevant phase difference. Balanced 50:50 beam splitters simplify the expression to the absolute value of that sine. The measure consequently oscillates between zero and one: odd multiples of the phase difference give maximal concurrence, while even multiples give no concurrence. Experimental detection would not require the largest possible value, but geometry that places the phase difference at a zero would erase the entanglement predicted by the model.

With the particles’ total travel distance held fixed, the Stern–Gerlach geometry has a best-performing region rather than one universally optimal shape. The deviation angle should approach a right angle, while the path-separation fraction must be selected according to the normalized distance between the two devices. The rescaled phase first increases as the separation fraction grows, reaches a maximum at an intermediate value and then declines. The optimal fraction also increases with normalized device separation, so a geometry that is optimal at one distance is not necessarily optimal at another. Practical designs are also constrained by non-gravitational forces such as van der Waals interactions, which can dominate when the devices are brought close together.

The Mach–Zehnder analysis reaches the same central conclusion through a different path geometry. Its key parameter is the vertical-arm length divided by the total path length. For a normalized device separation of 0.2, the calculated optimum occurs near a vertical-arm ratio of 0.10 and yields a rescaled phase of approximately 0.20. At a ratio of 0.38, the induced phase becomes effectively negligible. When the normalized separation is 0.5, the preferred vertical-arm ratio shifts to approximately 0.23, with a smaller rescaled phase of around 0.07. As the devices become more widely separated, the optimal design approaches a square configuration in which the vertical and horizontal arms have equal lengths.

The practical implication is that the vertical portions of an interferometer cannot automatically be treated as incidental routing details. They can supply a substantial part of the phase difference on which the proposed entanglement signal depends, and their contribution can either reinforce or cancel the effect attributed to the horizontal arms. Within the assumptions of the analysis, the first design step is to minimize the separation between devices, subject to experimental constraints, and then tune the arm geometry for that particular distance. The rescaled phase also contains the common factor κ = Gm₁m₂/(ℏv), so the analysis isolates geometry while recognizing that particle mass and speed remain relevant to the absolute signal.

The broader experimental obstacles remain formidable. The source estimates that massive quantum systems in the approximate range of 10⁻¹⁴ to 10⁻¹² kilograms, prepared in spatial superpositions at relatively short separations, are required for gravitationally generated phases to become appreciable. Matter-wave interferometry has been demonstrated with complex molecules of approximately 10⁻²¹ kilograms, well below that range. Coherence must also survive throughout the particles’ transit, while the gravitational signal must be distinguished from molecular scattering, thermal photons, thermal vibrations, gravitational-field nonuniformities, nearby masses, Casimir–Polder forces, electrostatic charging and magnetic interactions. The proposed environment would therefore require ultra-high vacuum, cryogenic conditions, electromagnetic shielding and stringent vibration isolation.

The study is a theoretical analysis with no associated experimental dataset or code. It does not demonstrate gravitational quantum entanglement, show that a simplified model has already distorted a completed measurement or establish that an optimized apparatus can meet the required sensitivity. Its narrower result is that exact trajectory geometry can change the predicted phase and concurrence: neglecting non-horizontal path segments can produce incorrect expectations, and particular geometries can remove the predicted entanglement altogether. For experimental programs still working to prepare larger coherent masses and suppress competing interactions, the calculations identify interferometer shape as one controllable factor in estimating whether a measurable gravitationally induced entanglement signal is present.

Subject of Research: Theoretical optimization of dual-interferometer geometry for gravitationally induced quantum entanglement

Article Title: The role of geometric analysis in interferometer design and optimization for gravitational quantum entanglement

Article References: Maleki, A. (2026). The role of geometric analysis in interferometer design and optimization for gravitational quantum entanglement. The European Physical Journal C, 86(10), Article 1189. https://doi.org/10.1140/epjc/s10052-026-16455-9

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16455-9

Keywords: quantum gravity, gravitational entanglement, interferometer geometry, Stern–Gerlach interferometry, Mach–Zehnder interferometry, gravitational phase, quantum coherence, experimental optimization, role, geometric, analysis, interferometer

The alternative model in question is holographic dark energy, an idea born from the holographic principle of quantum gravity, which suggests that the information content of a region of space is bounded by its surface area rather than its volume. In the influential formulation proposed by Miao Li in 2004, the energy density of the vacuum is set by the square of the future event horizon, the largest horizon accessible to a future observer, divided by a constant called c. That single parameter c controls everything: for values below one, the dark energy density grows with time, the universe eventually enters a phantom regime in which the expansion accelerates ever faster, and the cosmos may end in a so-called Big Rip, a finite-time catastrophe in which galaxies, stars, atoms and ultimately spacetime itself are torn apart. Measuring c precisely is therefore not academic hair-splitting; it is a probe of how the universe ends.

Unfortunately, the simplest holographic model has run into trouble with modern data. Recent analyses of DESI DR2, which maps the three-dimensional clustering of millions of galaxies through baryon acoustic oscillations, the fossil sound waves of the primordial plasma, showed that a single fixed value of c cannot simultaneously satisfy the constraints from baryon acoustic oscillations, type Ia supernovae and the cosmic microwave background, the relic radiation of the Big Bang. The dark energy community has therefore been exploring minimal extensions of the model, and one of the most natural is to let dark matter and dark energy exchange energy. Such interacting dark energy scenarios have a long pedigree, partly because a coupling between the two dark components could explain the coincidence problem, the puzzling fact that the densities of dark matter and dark energy are comparable today despite evolving so differently over cosmic history.

The new work introduces what the authors call a density-triggered interaction. In their model, the energy transfer rate Q is proportional to 3H times a coupling function xi times the product of the dark matter and dark energy densities divided by their sum, where H is the Hubble expansion rate. The crucial novelty is that the coupling is not constant: it is suppressed at early times by a switch function that depends on the scale factor, effectively staying near zero before some transition epoch and switching on afterwards. Baryons, the ordinary matter we can observe directly, are strictly conserved and take no part in the exchange. This design protects the early universe from unwanted contamination while allowing the dark sectors to talk to each other during the late, accelerating era.

Getting the cosmology right, however, demands unusual care, and here the study makes its most instructive technical point. Even if the instantaneous coupling vanishes before recombination, the epoch when the cosmic microwave background was released, the accumulated effect of the interaction does not. The authors show that the interaction rescales the pre-recombination dark matter density by a factor smaller than one, and this modified early-time density must be consistently propagated into the computed acoustic scale, the damping scale and the drag-epoch redshift, the quantities that connect a model to CMB data. Doing this properly turns out to be decisive for the final answer.

The authors confronted the model with an unusually broad data combination: measurements of the expansion rate H(z) from cosmic chronometers, passively evolving galaxies whose ages can be dated from their stellar populations; the DESI DR2 baryon acoustic oscillation measurements; three separate supernova compilations, namely Pantheon+, the Dark Energy Survey five-year sample and the Union3 collection; and compressed CMB distance priors distilled from the Planck satellite’s final release. The parameter inference was carried out with Markov chain Monte Carlo sampling, and the competing models were compared with information criteria including the Akaike and Bayesian information criteria, which penalize models for extra free parameters.

The result for the full data combination is striking: instead of a well-defined measurement of the coupling strength, the data deliver only a lower bound, xi zero greater than 0.30 at 95 per cent confidence, sliding along a degeneracy between the coupling and the present-day matter density. Within that allowed region, the best fit improves on the non-interacting holographic model by a change in chi-squared of minus 8.4, so the coupling is genuinely preferred over the simpler version of the model. Yet the coupling leaves the holographic parameter essentially untouched: c comes out at 0.652 plus or minus 0.020, compared with 0.647 plus or minus 0.018 without the interaction. Because c remains comfortably below one, the model still predicts a phantom-like dark energy and the Big Rip fate survives the interaction unscathed.

The story takes a twist when the authors also let the switch scale, at which the interaction turns on, float freely. Allowing this extra freedom improves the fit further, but only by pushing the switch to the boundary of its prior range, where more than half of the present-day dark matter has been converted from dark energy. That is a regime in which the model behaves in ways that many cosmologists would consider physically suspect, effectively manufacturing dark matter out of the vacuum energy at a prodigious rate. A preference that appears only at the edge of an allowed range, rather than at an interior best-fit point, is a classic warning sign that the improvement may reflect parameter freedom rather than genuine physics.

Even more cautionary is the methodological finding at the heart of the paper. When the CMB shift parameter, a compressed summary of the acoustic peaks, is evaluated using the present-day matter density instead of the correctly rescaled early-time density, the data appear to deliver a highly significant preference for the coupling. The authors identify this as a spurious effect: an inconsistency in how the theory is mapped onto the observable, not evidence for new physics. The lesson generalizes far beyond holographic dark energy. In an era when extensions of the standard model are routinely tested against compressed CMB summaries, any interaction that alters the early-time matter budget must be propagated consistently through every derived quantity, or the statistics will happily reward an error with a false detection.

Where does this leave the holographic idea? Within the holographic family, the density-triggered coupling is mildly favored, and the improved fit is real as far as it goes. But the bigger picture is unforgiving: every holographic model considered remains statistically disfavored relative to plain Lambda-CDM, and none of them, interacting or not, relieves the Hubble tension, the persistent disagreement between the expansion rate measured locally from supernova-calibrated distances and that inferred from the early universe. The DESI DR2 era has sharpened the questions rather than settling them, with hints of evolving dark energy tantalizing the field while the humble cosmological constant continues to defend its title. For now, the universe’s two dark components may be whispering to each other through a density-triggered channel, but the data say the conversation is quiet, the holographic endpoint of cosmic history still looms, and lambda, improbably, remains the answer to beat.

Subject of Research: Observational constraints on an interacting holographic dark energy model with a density-triggered dark matter coupling, tested against DESI DR2 BAO and complementary cosmological data.

Article Title: Density-triggered interacting holographic dark energy: joint constraints from DESI DR2 BAO and complementary cosmological probes

Article References: K.R., T., & S.K., N. (2026). Density-triggered interacting holographic dark energy: joint constraints from DESI DR2 BAO and complementary cosmological probes. Astrophysics and Space Science, 371(10), Article 122. https://doi.org/10.1007/s10509-026-04658-1

Image Credits: AI Generated

DOI: 10.1007/s10509-026-04658-1

Keywords: dark energy, holographic dark energy, DESI DR2, baryon acoustic oscillations, cosmic microwave background, type Ia supernovae, cosmic chronometers, dark matter, interacting dark energy, Lambda-CDM, Hubble tension, Big Rip

A new theoretical study by Salvatore Capozziello and Giuseppe Meluccio, published in The European Physical Journal C, argues that the answer lies beneath geometry itself. The authors show that all three members of the geometric trinity, along with a broad family of extended gravitational theories, can emerge from a single pre-geometric framework in which spacetime has no metric at all, no notion of distance, angle or even causality. In this picture, curvature, torsion and non-metricity are not fundamental features of the fabric of spacetime. They are emergent properties, arising when a deeper gauge symmetry is spontaneously broken at what is expected to be an energy scale near the Planck length.

The starting point is a formulation of gravity that resembles the Yang-Mills gauge theories underpinning the Standard Model of particle physics. In ordinary metric-affine theories of gravity, the gravitational field is described by two independent sets of variables: the spacetime metric, or equivalently the tetrad fields, and the affine connection that tells observers how to transport vectors from point to point. Pre-geometric gravity, by contrast, begins on a four-dimensional differentiable manifold stripped of any metric structure. The fundamental degrees of freedom are the components of a gauge potential associated with the (anti-)de Sitter group, and the dynamics are governed by an additional Higgs-like field, in direct analogy with the Higgs mechanism that gives elementary particles their masses.

The crucial event in this framework is spontaneous symmetry breaking. A real Higgs-like field acquires a nonzero vacuum expectation value along a direction in an internal five-dimensional space, and this process reduces the fundamental gauge symmetry of spacetime from the de Sitter group SO(1,4) or the anti-de Sitter group SO(2,3) down to the Lorentz group SO(1,3). The components of the gauge field that contain the broken internal direction become the tetrads from which the spacetime metric is constructed, while the surviving components become the spin connection of the Lorentz group. In earlier work, notably a proposal by Frank Wilczek dating back to 1998, it was shown that when the fluctuations of the Higgs-like field are frozen out at low energies, this mechanism yields precisely the Einstein-Hilbert Lagrangian of general relativity, complete with a cosmological constant term and correctly identified Planck mass.

What remained unexplored, Capozziello and Meluccio point out, was the fate of the affine connection in this emergent phase, and whether more general gravitational actions could be reconstructed. Their paper addresses both gaps. First, the authors derive the gauge-fixing conditions on the pre-geometric gauge potential that generate the different affine connections used across the metric-affine landscape. The Levi-Civita connection of general relativity, the unique torsionless and metric-compatible connection on a pseudo-Riemannian manifold, emerges from a specific combination of the pre-geometric field components and their first derivatives. The Weitzenböck connection of TEGR, which is flat and metric-compatible, arises from the strikingly simple condition of setting the pre-geometric spin connection components to zero. The coincident gauge of STEGR, in which the affine connection vanishes altogether, likewise follows from a corresponding pre-geometric constraint.

Second, the authors construct pre-geometric versions of the actions of the geometric trinity. The Einstein-Hilbert action based on the Ricci scalar R can be obtained from the Wilczek Lagrangian supplemented by an additional term proportional to a pre-geometric volume-like quantity, with a suitable choice of coupling constant cancelling the emergent cosmological constant. The TEGR action, built on the torsion scalar T, emerges from a pre-geometric Lagrangian assembled from three carefully defined scalars that, after symmetry breaking, reproduce the quadratic combinations of the torsion tensor appearing in the torsion scalar. Notably, the antisymmetrisation of spacetime indices in these constructions ensures that no second-order time derivatives of the Higgs-like field appear, keeping the theory free of the Ostrogradsky instabilities that plague many higher-derivative theories.

The non-metricity case demanded the most ingenuity. Unlike curvature and torsion, non-metricity is not defined through the spin connection of the Lorentz group, which is antisymmetric in its internal indices, but through that of the general linear group, which admits a symmetric part. This means the pre-geometric gauge potential cannot be that of the (anti-)de Sitter group at all; it must be generalised to a broader symmetry, which the authors argue should be the five-dimensional general linear group GL(5). A further subtlety arises from group theory: the 25 generators of GL(5) do not decompose neatly into the 16 generators of GL(4) plus translations alone, but also include dual translation generators and a dilation generator. The authors show that a specific gauge-fixing condition, setting certain components of the gauge potential to zero, eliminates the unwanted degrees of freedom and allows the exact recovery of the STEGR Lagrangian based on the non-metricity scalar Q, with an emergent Planck mass identified in terms of the pre-geometric coupling constants and the vacuum expectation value.

Perhaps the most far-reaching result is that the construction generalises well beyond the trinity. The authors provide pre-geometric Lagrangian densities whose spontaneous symmetry breaking yields f(R), f(T) and f(Q) theories, as well as combined f(R,T,Q) theories in which f is a sufficiently smooth function of all three geometric invariants. Every pre-geometric action discussed is gauge invariant, generally covariant and background independent. In this sense, the metric-affine framework and the pre-geometric framework are shown to be fully compatible, with pre-geometry supplying a single unifying physical source for all the geometric notions that previously appeared as independent starting points.

The implications for quantum gravity could be significant. Pre-geometric theories are formulated in a Yang-Mills style on a manifold without a metric, exactly at the energy scale where general relativity is expected to break down, and the gauge choices of the emergent geometric theories are revealed to be gauge-fixing conditions on a single gauge potential rather than constraints on two independent variables. The authors argue this makes pre-geometric theories, in a sense, more natural than their metric-affine counterparts. There are also potential phenomenological signatures: pre-geometric theories like the Wilczek model possess three degrees of freedom rather than the two of a massless graviton, with the additional scalar degree of freedom excitable only in an ultra-high-energy regime near the Planck scale. Deviations from general relativity associated with this field could in principle be falsifiable, and the authors suggest the extra dynamics might even cure the ultraviolet divergences of geometric origin that afflict the emergent theories.

The study also connects to a broader classification scheme, dubbed the eightfold way of gravity, in which metric-affine theories are organised by the number of nonzero geometric invariants they involve. Special relativity corresponds to none, the geometric trinity to exactly one, theories such as Einstein-Cartan gravity to two, and the most general metric-affine theories to all three. Viewed through this configuration space, the new results indicate that the five-dimensional general linear group could serve as the unifying symmetry group of all metric-affine theories when these are understood as emergent from pre-geometric gravity. The authors note that a full Hamiltonian analysis of these theories, an exhaustive catalogue of symmetry-breaking patterns for the non-metricity case, and possible higher-dimensional Kaluza-Klein-style extensions remain open directions for future work, with several of these topics to be treated in a forthcoming paper.

Subject of Research: The emergence of the geometric trinity of gravity from pre-geometric gauge theory via spontaneous symmetry breaking

Article Title: The pre-geometric origin of geometric trinity of gravity

Article References: Capozziello, S., & Meluccio, G. (2026). The pre-geometric origin of geometric trinity of gravity. The European Physical Journal C, 86(9), Article 1073. https://doi.org/10.1140/epjc/s10052-026-16359-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16359-8

Keywords: general relativity, geometric trinity, pre-geometric gravity, spontaneous symmetry breaking, torsion, non-metricity, teleparallel gravity, Yang-Mills gauge theory, affine connection, quantum gravity, metric-affine gravity, Higgs mechanism

The achievement matters because quantum mechanics, for all its technological triumphs, has been tested almost exclusively at scales far removed from human experience. Lasers, MRI scanners, semiconductors, and quantum computers all rest on quantum principles, yet the phenomena themselves have been demonstrated on subatomic and nanoscopic particles. Demonstrating quantum behavior in objects large enough for gravity to play a significant role has proven extraordinarily difficult, because big objects are much harder to isolate from environmental noise such as heat and vibration than tiny ones. The OIST experiment offers a new starting point for that challenge.

Professor Jason Twamley of the OIST Quantum Machines Unit framed the result as a milestone in a long-running effort. “There have been many efforts to test whether quantum mechanics holds for anything larger than a few tens of nanometers, so far without success,” he said. “Now, we have observed a classical mechanical response to a quantum force on an object that is eight to nine orders of magnitude more massive than the current state-of-the-art spin-mechanical experiments.” In other words, a purely quantum mechanical effect, the collective spin of billions of electrons, produced a measurable, classical push on an object visible to the naked eye.

The experiment rests on a clever combination of components the same team had previously proven individually. At its heart is a diamond laced with billions of nitrogen-vacancy (NV) centers, defects in the crystal lattice where a nitrogen atom sits next to a missing carbon atom. These defects trap unpaired electrons, and each trapped electron behaves as a tiny, controllable quantum magnet through its quantum spin. NV centers are prized in quantum science because they are well understood, easy to control, and possess some of the longest coherence times known, meaning they can maintain quantum superposition at room temperature far longer than most other systems.

To turn those spins into motion, the researchers periodically illuminated the diamond with a green laser. The light polarizes the NV centers into a predefined spin state, generating tiny magnetic fluctuations that push the diamond downward. The diamond itself was suspended above a magnet, connected by a carbon rod to a diamagnetically levitated graphite plate fitted with a small mirror, an assembly shielded from magnetic interference. An interferometer bounced a laser off that mirror to track the resonator’s position with picometer precision, allowing the team to detect the minuscule displacement caused by the spin force. In photographs of the setup, the diamond glows red as electrons in the NV centers are excited to higher energy states by the laser.

First author Anshuman Nayak, a PhD student in the unit, explained the strategic thinking behind the approach. “To test the quantum nature of gravity, we ultimately need to put objects with large enough masses into quantum superposition. And these objects need to be levitated in a vacuum to minimize the influence of environmental noise,” he said. “The typical approach has been to start with extremely small, levitated objects and gradually increase their mass until the effects of gravity become relevant. But levitating macroscale objects using conventional techniques, such as optical traps, has proven extremely challenging.”

That difficulty pushed the OIST team into what Nayak described as the opposite camp: going from large to small. “Just as diamagnetic levitation can lift maglev trains, it can also be used to levitate centimeter-wide objects holding diamonds, where the effect of gravity can be extremely strong, but quantum effects have not been observed,” he said. Diamagnetic levitation exploits the weak repulsion between certain materials and magnetic fields, allowing stable, contact-free suspension without cryogenics or vacuum traps. By building the platform from the top down, the researchers start with an object firmly in the gravitational regime and work toward coaxing quantum behavior out of it, rather than trying to scale a quantum system up.

The deeper motivation reaches back to questions that troubled Einstein in the final decades of his life. Gravity sits at the center of general relativity, a classical theory, yet its effects are vanishingly weak at the nanometer scales where quantum phenomena have been observed. Conversely, positional superposition, in which a particle exists in distinctly different places simultaneously until measured, has only been demonstrated at the microscopic level. Whether gravity is quantum or entirely classical, what happens to information at the center of a black hole, what dark matter and dark energy are, and whether a massive object can truly be in two places at once all remain unanswered, largely because the mathematical, theoretical, and experimental frameworks of quantum and classical physics remain disconnected.

By demonstrating a mechanical effect arising solely from quantum spin on a macroscopic object, the OIST team has created an experimental platform on which such exotic theories can be tested. “We’ve shown a large classical response from a small quantum effect,” Twamley said. “It’s no longer a question of whether such technology is possible, but of how we can refine experimental conditions to achieve quantum superposition within the regime of Einstein’s general relativity.” The path forward involves sharpening the isolation of the levitated resonator, extending coherence times, and gradually building the sensitivity needed to place the entire object’s motion into superposition, a macroscopic analogue of Schrödinger’s famous cat.

The practical payoff may arrive sooner than the philosophical one. The same platform doubles as an extraordinarily precise sensor, capable of detecting minute forces and displacements. The researchers anticipate a new class of ultrasensitive devices for hunting dark matter, detecting gravitational waves, and probing other exotic phenomena that leave only the faintest signatures. “We’re pushing the bar from nanometers to centimeters,” Twamley said. “All we need is another order of magnitude, and we can finally observe Schrödinger’s cat in real life.” For now, the spinning diamond of Okinawa stands as the largest object ever displaced by quantum spin alone, and a promising bridge between two theories that have never quite spoken the same language.

Subject of Research: Spin-force manipulation of a macroscopic levitated diamond resonator using nitrogen-vacancy centers

Article Title: First observation of quantum spins shifting a centimeter-scale object in the lab

Article References: First observation of quantum spins shifting a centimeter-scale object in the lab. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: quantum mechanics, nitrogen-vacancy centers, diamagnetic levitation, quantum gravity, macroscopic superposition, spin-mechanics, OIST, Science Advances, quantum sensors, levitated resonator, dark matter detection, gravitational waves

The conjecture itself sounds deceptively simple. In any consistent theory of quantum gravity, there must exist a charged particle whose charge-to-mass ratio exceeds that of an extremal black hole, the configuration in which electric repulsion exactly balances gravitational attraction. If no such particle existed, black holes could shed their charge while retaining their mass, leaving stable remnants that would accumulate forever and render the charge lattice of the theory incomplete. Gravity, in other words, must be the weakest force: no amount of charge can permanently shield an object from collapsing under its own weight. The original argument, put forward by Nima Arkani-Hamed, Luboš Motl, Alberto Nicolis and Cumrun Vafa in 2007, was heuristic, and physicists have spent nearly two decades hunting for independent derivations — from scattering-amplitude positivity, from the second law of thermodynamics applied to black-hole mergers, and from convexity properties of operators in dual quantum field theories.

The new work, published in The European Physical Journal C by Saeed Noori Gashti and Behnam Pourhassan of Damghan University together with İzzet Sakallı of Eastern Mediterranean University, adds a fifth route that is holographic in spirit but uses only a single piece of boundary data. The key insight is that a near-extremal charged black hole develops, at its horizon, a throat of anti-de Sitter geometry in two dimensions. Quantum mechanics on that throat is conformal — scale-invariant — and the black hole’s quasinormal modes, the damped oscillations that dominate its response to any perturbation, appear as the poles of a retarded Green’s function of this one-dimensional conformal system. A universal bound due to Shahar Hod states that the damping time of any thermal system cannot fall below the inverse of its temperature. Applied to the slowest quasinormal mode, this forces the conformal weight of the dual operator to satisfy a sharp cap.

From there, the derivation compresses into a single master formula. The charged Klein–Gordon equation for a scalar probe reduces, in the extremal throat, to a Whittaker equation whose order is precisely the conformal weight. Remarkably, only two numbers from the entire black-hole geometry survive: the AdS₂ radius, fixed by the second derivative of the metric’s lapse function at the horizon, and an electric-field parameter of the throat, fixed by the derivative of the electrostatic potential. Everything else — the mass, the charge, the asymptotic structure — cancels. The conjecture then reads, in closed form, that the charge-to-mass ratio of any charged particle must exceed the ratio of these two throat parameters. For the textbook Reissner–Nordström black hole, the two numbers coincide and the familiar threshold of unity is recovered exactly.

The real test comes when the idealised Reissner–Nordström background is abandoned. The authors first examined black holes in de Rham–Gabadadze–Tolley massive gravity, a theory that promotes the graviton itself to a massive particle. Here the massive-gravity couplings do not drop out of the bound. The extremality condition and the throat curvature respond differently to the deformation: extremality is governed by a first derivative of the metric and produces one combination of couplings, while the throat curvature is governed by a second derivative and produces another. Their difference is second order in the graviton mass, so the WGC threshold becomes a square root of the ratio of the two combinations — a small but strictly nonzero correction that strengthens the bound whenever the effective cosmological constant and linear coupling have the generic positive sign. Notably, the authors show that an earlier claim of an exact cancellation was an artefact of taking a divergent zero-temperature limit of a near-extremal expression, a limit that cannot legitimately be taken.

The second background probes the opposite direction: it deforms the gauge sector while leaving gravity untouched. Einstein–ModMax theory couples general relativity to a one-parameter family of non-linear electrodynamics that preserves both electromagnetic duality and conformal invariance, the maximal deformation of Maxwell’s equations consistent with those symmetries. In the purely electric sector, the metric remains exactly Reissner–Nordström in a rescaled field strength, so the AdS₂ radius carries no trace of the non-linearity. The entire effect enters through the charge normalisation: the conserved electric charge, defined as the flux of the non-linear displacement field, differs from the integration constant of the field strength that the probe scalar actually couples to. The mismatch is an exponential of the duality parameter, and the resulting bound is exponentially strengthened: the minimum charge-to-mass ratio grows as the exponential of half the non-linearity parameter.

That exponential result passes what the authors call the sharpest available check on the whole construction. The extremal Einstein–ModMax black hole itself has a mass equal to its horizon radius and a charge equal to the radius times the same exponential factor, so its own extremal charge-to-mass ratio is exactly the number the CFT derivation produces. The left-hand side of this coincidence comes from the Whittaker order of a probe field in the throat together with a thermodynamic inequality on relaxation times; the right-hand side is computed directly from the lapse function with no perturbation theory whatsoever. That the two calculations land on the same exponential, for every value of the duality parameter, is not something the derivation was arranged to produce — and an earlier version of the analysis, which had failed this test by a full factor of the exponential, was traced back to a charge-normalisation error and corrected.

The authors then stress-tested the framework by relaxing its three main simplifying assumptions one at a time. Allowing a small but finite Hawking temperature does not weaken the inequality, because the temperature cancels between the damping time and Hod’s bound; it merely shifts the extremal reference point that supplies the throat data, an effect linear in the sub-extremality parameter and sub-percent throughout the regime where the throat exists at all. Adding a non-minimal curvature coupling to the probe scalar multiplies the massive-gravity bound by a factor involving the Ricci scalar at the horizon, but does nothing at all in the ModMax case, where conformal invariance of the gauge sector forces the Ricci scalar to vanish identically. Higher-derivative corrections from ultraviolet completion act through shifts in the same two throat parameters, modifying the bound without changing its structure.

Perhaps most impressively, every closed form in the paper is verified twice. Symbolic computation confirms the algebraic identities exactly, and an independent numerical integration of the full radial Klein–Gordon equation — using an eighth-order Runge–Kutta scheme with the lapse function deflated to avoid catastrophic loss of precision near the double root of the horizon — extracts the conformal weight from the indicial exponents at the degenerate horizon without ever invoking the throat approximation. The two determinations agree to eleven or more digits across both models, a level of cross-validation rarely seen in swampland calculations.

The significance extends beyond the two specific backgrounds. Most existing derivations of the Weak Gravity Conjecture return only order-of-unity estimates, whereas this framework yields explicit functions of the deformation parameters — a square root for gravitational deformations, an exponential for gauge-sector ones. The open questions are tantalising: whether the dyonic branch of ModMax, where electric and magnetic pieces carry reciprocal exponentials, turns the bound into a two-charge statement; whether higher-dimensional throats acquire a dimension-dependent form; and whether the convexity, lattice-completeness and positivity methods can reproduce these specific functional forms rather than merely their magnitude. If they cannot, the black-hole throat may be telling us something about the conjecture that no other approach has captured — that gravity’s status as the weakest force is written, quite literally, in the geometry of the horizon itself.

Subject of Research: Deriving the Weak Gravity Conjecture from near-horizon AdS2 conformal quantum mechanics of charged black holes

Article Title: CFT constraints on the weak gravity conjecture

Article References: Gashti, S. N., Pourhassan, B., & Sakallı, İ. (2026). CFT constraints on the weak gravity conjecture. The European Physical Journal C, 86(10), Article 1139. https://doi.org/10.1140/epjc/s10052-026-16427-z

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16427-z

Keywords: Weak Gravity Conjecture, swampland, black holes, quasinormal modes, AdS2/CFT1, dRGT massive gravity, Einstein-ModMax, non-linear electrodynamics, quantum gravity, holography, extremal black holes, theoretical physics

The latest blow to established models came from the Atacama Cosmology Telescope. When the ACT DR6 results were combined with data from the Planck satellite, the DESI baryon acoustic oscillation measurements, and the BICEP/Keck experiment, the joint analysis shifted the best-fit value of the scalar spectral index, denoted n_s, toward larger values. This single number describes how the intensity of primordial density ripples varies across different length scales, and it is one of the most sensitive probes of inflationary physics. The new measurement, n_s = 0.974 plus or minus 0.003, placed beloved models such as Starobinsky inflation uncomfortably close to the edge of the allowed 95 percent confidence region, triggering a wave of theoretical activity as physicists scrambled to find mechanisms that could reconcile their favorite potentials with the data.

But every crisis is also an opportunity. The upward shift in the preferred value of n_s opened a door for a family of models that earlier observations had largely dismissed: fractional power law potentials, in which the inflaton’s potential energy grows as the field raised to a fractional exponent. Farough Parvizi and Kayoomars Karami of the University of Kurdistan in Sanandaj, Iran, seized on this opening in a paper published in The European Physical Journal C. They examined three specific cases, with exponents n equal to one third, two fifths, and two thirds, and asked whether the framework of loop quantum cosmology could push these models’ predictions firmly into the territory favored by the newest joint datasets.

Loop quantum cosmology, or LQC, is the cosmological offspring of loop quantum gravity, an ambitious attempt to quantize spacetime itself. In this picture, space is not a smooth continuum but a discrete fabric woven from fundamental quanta at the Planck scale. One of the theory’s most celebrated achievements is the replacement of the Big Bang singularity with a Big Bounce, in which a collapsing universe rebounds into expansion. Near the bounce, quantum corrections to the classical equations of motion become dominant, but they do not vanish once the universe enters its slow-roll inflationary phase. Two families of corrections survive: holonomy corrections, which modify how curvature is encoded, and inverse volume corrections, which arise because there is a smallest meaningful volume in nature, making the operator corresponding to inverse volume behave differently from its classical counterpart.

Parvizi and Karami focused on the inverse volume corrections, which turn out to be the more observationally promising of the two. Holonomy corrections in the perturbation equations are astonishingly small, on the order of one part in a trillion, placing them far beyond any foreseeable measurement. Inverse volume corrections, by contrast, modify both the background Friedmann equation and the evolution of scalar and tensor perturbations in ways that directly shape the primordial power spectra, the very quantities cosmologists measure on the cosmic microwave background. The corrections are controlled by two parameters: an exponent sigma, which governs how quickly the quantum effects fade as the universe expands, and an amplitude delta, which sets their overall strength at the CMB pivot scale.

Technically, the corrections enter through two functions, alpha and nu, that multiply the effective Friedmann and Klein-Gordon equations. In the semi-classical regime, where the universe is already large and the quantum parameter is small, these functions can be expanded to first order, yielding alpha approximately equal to one plus alpha-zero times the Planck-scale correction, and similarly for nu. The researchers imposed a consistency condition derived from requiring the quantum constraint algebra to remain anomaly-free, which links alpha-zero and nu-zero for values of sigma other than three. This mathematical requirement is not a mere formality: in the deep quantum regime, inverse volume corrections can break general covariance entirely, so the entire analysis must be confined to the semi-classical regime where the effective spacetime description remains valid.

To extract predictions with sufficient precision, the authors went beyond the leading-order slow-roll approximation used in most earlier LQC studies. They employed the second-order slow-roll formalism developed by Tonghua Zhu and collaborators, combined with the uniform asymptotic approximation method, to derive analytical expressions for the scalar spectral index n_s and the tensor-to-scalar ratio r, the ratio of gravitational wave ripples to density ripples. These expressions contain standard slow-roll contributions plus additional terms proportional to the LQC parameters, evaluated at the moment when each wavelength crosses the Hubble horizon. The resulting formulas reveal something striking: the quantum corrections shift n_s downward, while their effect on r remains comparatively minor.

That downward shift is the heart of the result. In the classical theory, without quantum corrections, the three fractional potentials occupy a hierarchy of observational viability when confronted with the joint P-ACT-LB-BK18 constraints. The steepest case, n equal to two thirds, is essentially ruled out at fifty e-folds of expansion and only marginally enters the 95 percent confidence region at sixty e-folds. The intermediate case, n equal to two fifths, fares better, with both e-fold values inside the 95 percent region and the fifty e-fold prediction just touching the boundary of the tighter 68 percent region. The shallowest case, n equal to one third, is the most favored, with its sixty e-fold prediction inside the 95 percent region and its fifty e-fold prediction marginally within the 68 percent region. When the LQC inverse volume corrections are switched on, the predictions slide almost horizontally to the left across the r versus n_s plane, because the dominant effect is the negative shift in the spectral index rather than any substantial change in the tensor-to-scalar ratio.

The magnitude of this slide is tunable. Increasing either the amplitude delta, at fixed exponent sigma, or the exponent sigma, at fixed delta, translates the model predictions further to the left, and the two parameters exhibit a compensatory relationship: smaller values of sigma require larger values of delta to achieve the same shift, and vice versa. By systematically mapping the allowed regions of this two-dimensional parameter space, the researchers found that the shallower potential with n equal to one third tolerates a broad range of quantum geometric corrections, while the steeper n equal to two thirds case permits only a narrow sliver, and none at all for fifty e-folds. Throughout, the analysis respected the perturbative validity condition that the product of alpha-zero and the Planck-scale correction must remain below unity, and sigma was restricted to the range from zero to three, beyond which the observable effects of quantum gravity become undetectable.

The broader message is tantalizing: even strictly perturbative quantum gravity effects, far too subtle to be seen in laboratory experiments, could leave distinct fingerprints on the primordial spectra imprinted in the cosmic microwave background. If future CMB measurements continue to tighten the constraints on n_s and r, the allowed ranges of the LQC parameters sigma and delta will shrink accordingly, turning cosmological observations into a precision test of the discrete structure of spacetime itself. Conversely, if the current tension with models like Starobinsky inflation deepens, mechanisms of the kind explored by Parvizi and Karami may become essential for keeping simple inflationary scenarios alive. Either way, the study demonstrates that the marriage of quantum geometry and precision cosmology is no longer a purely abstract exercise; it is a quantitative program in which every decimal place in the spectral index carries information about the granular texture of space at scales a trillion trillion times smaller than an atom.

Subject of Research: Observational viability of fractional power law inflationary potentials in loop quantum cosmology with inverse volume corrections in light of ACT data

Article Title: Fractional power law inflationary potentials in loop quantum cosmology with inverse volume corrections in light of ACT observations

Article References: Parvizi, F., & Karami, K. (2026). Fractional power law inflationary potentials in loop quantum cosmology with inverse volume corrections in light of ACT observations. The European Physical Journal C, 86(10), Article 1136. https://doi.org/10.1140/epjc/s10052-026-16380-x

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16380-x

Keywords: cosmic inflation, loop quantum cosmology, inverse volume corrections, scalar spectral index, tensor-to-scalar ratio, ACT DR6, Planck, BICEP/Keck, fractional power law potentials, quantum gravity, cosmic microwave background, Big Bounce

The experiment is, at heart, a modern descendant of Henry Cavendish’s 1798 torsion balance, the apparatus he used to weigh the Earth. A torsion pendulum responds to a horizontal force by twisting a thin suspension fibre, and because the restoring torque of such a fibre can be made extraordinarily small, even minuscule forces produce measurable deflections. Cavendish-type balances remain among the most sensitive instruments for measuring gravity from small source masses, and they have been used to pin down the Newtonian gravitational constant and to test whether gravity behaves as expected at centimetre and sub-centimetre scales. The challenge the Shanghai-led team set out to solve is one of readout: how do you detect the nanometre-scale motion of a pendulum twisted by a gravitational pull of order 10^-16 newtons without adding noise, bulk or complexity?

Their answer is an optical microcavity coupled directly to the pendulum. The sensor uses a whispering-gallery-mode microresonator, a tiny optical resonator in which light circulates around the rim of a microsphere by continuous total internal reflection. Light is coupled into and out of the cavity through a tapered optical fibre whose tip is held roughly 100 nanometres from the microsphere surface. In this evanescent coupling regime, the amount of light that crosses the nanoscale gap depends exquisitely on its exact width. When the torsion pendulum moves, it changes the cavity-fibre separation, which in turn changes the optical transmission. The exponentially decaying evanescent field thus converts nanoscale displacements into optical signals across that roughly 100-nanometre coupling window, acting as an extremely steep mechanical-to-optical transducer.

The real innovation, however, lies in how the team manipulated the light inside the cavity. By exploiting coupled photon-phonon effects, in which the optical field interacts coherently with a mechanical acoustic mode of the resonator, they induced a regime known as Brillouin-scattering-induced transparency, an analogue of electromagnetically induced transparency familiar from atomic physics. Within this narrow spectral window, the optical dispersion becomes extremely steep, and the group velocity of light, the speed at which information-carrying pulses propagate, collapses to just 2,000 metres per second. That is roughly 150,000 times slower than light in vacuum, and it places the device firmly in the ‘stopped light’ regime that the same group has explored previously for light storage near exceptional points.

Why does slowing light help? The steep dispersion that accompanies stopped light means that a tiny change in the cavity resonance frequency, caused by a tiny displacement of the pendulum, produces a disproportionately large change in the phase and transmission of the probe light. In effect, the slow-light resonance amplifies the optical signature of small mechanical motion. This is conceptually similar to how optomechanically induced transparency and other cavity-enhanced readout schemes have boosted force sensitivity in micro- and nanomechanical resonators, but the stopped-light approach pushes the dispersion slope to an extreme, sharpening the transduction without requiring cryogenic temperatures or exotic materials. The whole readout chain operates at room temperature in a table-top apparatus.

The measured performance is impressive. The team reports a displacement sensitivity of 7.85 picometres per root hertz, meaning they can resolve pendulum motions of a few trillionths of a metre in a one-hertz measurement bandwidth. Converted through the mechanical response of the torsion pendulum, that corresponds to an acceleration sensitivity of 3.06 x 10^-16 g, where g is the standard acceleration due to Earth’s gravity. To put that in perspective, the sensor can detect accelerations roughly sixteen orders of magnitude smaller than the pull you feel standing on the ground. By periodically modulating the position of the source mass, a modulation technique that shifts the gravitational signal to a known frequency where technical noise is lower, the researchers resolved a minimum detectable change in gravitational force of 3.02 x 10^-16 newtons.

The source mass in these experiments was millimetre-scale, comparable to the masses used in the landmark 2021 Vienna experiment that first measured gravitational coupling between millimetre-sized gold spheres. That experiment demonstrated that gravity between small objects can be isolated; the new work shows how a photonic readout can be integrated with such a mechanical sensor to push sensitivity further while keeping the instrument compact. Integration has long been the sticking point for Cavendish-type balances: their optical levers and interferometric readouts are delicate, alignment-heavy and difficult to miniaturise. A microcavity readout, with light delivered through a fibre taper and the transduction happening in a micrometre-scale resonator, points toward on-chip gravitational sensing platforms.

The implications extend beyond metrology. Detecting the gravitational fields of microscopic objects is a prerequisite for microscale gravitational imaging, for constraining short-range deviations from Newtonian gravity, and for proposed tests of gravity’s quantum nature. Several theoretical proposals, including the influential 2017 Bose and Marletto-Vedral schemes, suggest that if two masses become entangled purely through their mutual gravitational interaction, gravity must be quantum-mechanical. Realising such experiments demands sensors that can resolve gravitational forces from ever-smaller masses held in ever-more-controlled quantum states. The acceleration sensitivity demonstrated here, combined with proposals for detecting single gravitons with quantum sensing and for gravitationally induced decoherence tests, suggests that stopped-light-enhanced readout could become a key enabling technology on that road.

There are, of course, practical hurdles between a table-top demonstration and a quantum-gravity laboratory. Torsion pendulums are inherently susceptible to thermal noise in the suspension fibre, seismic disturbances and Newtonian background forces from nearby objects, and the evanescent coupling gap of 100 nanometres demands nanometre-precision positioning stability. The researchers also note that the coupled photon-phonon physics that produces stopped light is the same physics that can introduce optomechanical backaction, so careful operating-point selection is needed to ensure that the dispersion enhancement is not eroded by the light’s own mechanical influence. Nonetheless, the demonstration that a room-temperature microcavity can transduce gravitational forces at the 10^-16-newton level marks a genuine advance in nanometrology.

What makes the result especially compelling is its elegance: rather than adding complexity, the team exploited a fundamental optical effect to make the sensor simultaneously simpler and more sensitive. Slow and stopped light has been celebrated for applications ranging from optical buffering to nonlinear enhancement, but using it as the readout engine of a gravitational sensor is a genuinely unexpected twist. If the approach can be scaled to smaller source masses, integrated with levitated or cryogenic mechanical systems, or combined with quantum state preparation of the pendulum itself, the humble Cavendish experiment may yet become a window into the deepest open question in physics: whether the force that holds the cosmos together plays by quantum rules at the smallest scales.

Subject of Research: Stopped-light-enhanced torsion-pendulum sensing of gravitational forces from millimetre-scale masses

Article Title: Stopped-light-enhanced gravitational force sensing

Article References: Zhu, Y., Geng, Q., Xue, B., Sun, Y., Zhang, R., Chen, X., Jiang, X., Azeem, F., Tierz, M., & Wan, W. (2026). Stopped-light-enhanced gravitational force sensing. Nature Nanotechnology. https://doi.org/10.1038/s41565-026-02298-8

Image Credits: AI Generated

DOI: 10.1038/s41565-026-02298-8

Keywords: gravity sensing, torsion pendulum, stopped light, optical microcavity, whispering gallery mode, cavity optomechanics, nanometrology, slow light, force sensitivity, quantum gravity, photon-phonon coupling, Nature Nanotechnology

The framework at the heart of the study is an extension of the familiar black hole metric in which the angular sector of the geometry is warped according to a power law, R(r) = (r/r0)^N. The exponent N acts as a continuous control parameter, analogous to pressure or temperature in a laboratory phase transition. When N is adjusted, the thermodynamic behavior of the black hole changes, and at a specific value the system undergoes a second-order phase transition. Such transitions are governed by mean-field critical exponents, the same universal fingerprints that characterize critical phenomena in magnets, fluids, and superconductors, and the amplitudes of these exponents are explicitly modulated by the deformation exponent itself.

What makes a critical point so interesting for radiation physics is the divergence of thermodynamic response functions. Near a second-order phase transition, quantities such as heat capacity become unboundedly sensitive to infinitesimal changes in state, signaling that the black hole is poised between distinct thermodynamic phases. Baghbani’s analysis shows that as the dilaton black hole approaches this criticality, the effective scattering potential that governs the propagation of quantum fields near the horizon develops a structure that can trap and amplify outgoing radiation, rather than simply filtering it away.

To quantify this effect, the study solves the Klein–Gordon equation for a scalar field propagating in the deformed background, deriving the exact effective scattering potential that controls how quantum waves tunnel through the gravitational barrier surrounding the hole. The fraction of Hawking radiation that actually escapes to infinity, known as the greybody factor, is ordinarily suppressed because the curved spacetime acts like a leaky cavity, reflecting part of the radiation back toward the horizon. Near the critical point, however, the potential develops a pronounced resonant feature, and Baghbani proposes a phenomenological Breit–Wigner resonance model to capture the resulting enhancement of the greybody factor. This is the same mathematical form used to describe resonant scattering in nuclear and particle physics, suggesting a deep analogy between black hole radiance and the resonance phenomena familiar from laboratory experiments.

The dynamical side of the story is told by quasinormal modes, the characteristic ringing frequencies at which a perturbed black hole settles back to equilibrium. Working in the eikonal limit, where the perturbations have short wavelengths, the study establishes a correspondence between these modes and the unstable photon orbit, the precarious circular light trajectory that hovers just outside the horizon. Third-order WKB computations of the quasinormal mode spectra reveal that the deformation exponent N modulates both the oscillation frequency of the ringdown and the Lyapunov damping rate that controls how quickly the ringing decays. In other words, the same geometric parameter that drives the thermodynamic phase transition also reshapes the black hole’s gravitational-wave signature, offering a potential observational handle on the underlying physics.

A crucial consistency check comes from the limits of the model. When the deformation exponent N approaches zero from below and the dilaton parameter α goes to zero, all thermodynamic, dynamical, and radiative quantities reduce smoothly to the Reissner–Nordström–AdS limit, the well-understood solution describing a charged black hole in anti-de Sitter space. This means the exotic behavior near criticality is not an artifact of the deformation but a genuine feature that interpolates between known black hole physics and a new regime of critical behavior. The recovery of established results in appropriate limits is an important sanity test for any proposal in gravitational theory.

The broader significance of the work lies in its suggestion that quantum gravitational effects, normally hopelessly beyond experimental reach, might be amplified by manipulating the geometry of spacetime itself. Hawking radiation is far too weak to detect for astrophysical black holes, but in analog systems and in highly controlled theoretical backgrounds, the interplay between geometry and quantum fields becomes tractable. If geometric deformation provides a tunable knob for the greybody factor and the radiation spectrum, it opens a pathway for probing how quantum mechanics and general relativity conspire at horizons, a question at the very frontier of theoretical physics.

The study also connects to an active body of research on black hole phase transitions and thermodynamic geometry. Critical phenomena in black hole thermodynamics have been explored extensively in charged and rotating solutions, in extended thermodynamics where the cosmological constant is treated as pressure, and in Ruppeiner-style geometric formulations of statistical mechanics. What distinguishes the present analysis is the treatment of a pure geometric deformation exponent as an active control parameter, rather than varying charge, rotation, or background curvature. This reframing suggests that the landscape of black hole phases is richer than previously appreciated and that some of its most dramatic features occur where response functions diverge.

Caveats remain. The resonant enhancement of the greybody factor is currently a phenomenological model rather than a direct numerical computation, and the author is explicit that direct numerical evaluation of the greybody factor is required to confirm the predicted enhancement. Moreover, the four-dimensional dilaton black hole with a deformed angular sector is a theoretical construction, and whether configurations of this type exist in nature or can be realized in analogue systems is an open question. Quasinormal mode calculations at third WKB order likewise carry controlled but finite uncertainties that full numerical evolution would help pin down.

Even so, the picture that emerges is striking. A single geometric parameter governs a second-order phase transition, reshapes the scattering potential for quantum fields, breathes resonant structure into the escaping radiation, and rewrites the ringdown spectrum, all while recovering known black hole physics in the appropriate limits. As gravitational-wave detectors grow more sensitive and analogue gravity experiments grow more sophisticated, the idea that black hole radiation can be critically enhanced by warping geometry may evolve from an elegant calculation into a guiding principle for the hunt for quantum gravity. The study, published as Volume 58, article 102 of General Relativity and Gravitation, was received in April 2026, accepted in late August 2026, and published on 1 September 2026.

Subject of Research: Critical enhancement of Hawking radiation in geometrically deformed dilaton black holes

Article Title: Critical enhancement of Hawking radiation in geometrically deformed dilaton black holes

Article References: Baghbani, R. (2026). Critical enhancement of Hawking radiation in geometrically deformed dilaton black holes. General Relativity and Gravitation, 58(9), Article 102. https://doi.org/10.1007/s10714-026-03607-1

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03607-1

Keywords: Hawking radiation, dilaton black holes, geometric deformation, black hole thermodynamics, phase transition, critical phenomena, greybody factor, quasinormal modes, Breit-Wigner resonance, photon orbit, eikonal limit, quantum gravity