The starting point of the analysis is a decades-old idea with a distinguished pedigree. In 1995, Ted Jacobson demonstrated that Einstein’s field equations could be derived from the Clausius relation of thermodynamics, TdS = dQ, applied to local horizons, suggesting that gravity itself might be an emergent, thermodynamic phenomenon rather than a fundamental force. Later work by Sai Akbar and Rong-Gen Cai extended this program to cosmology, showing that the Friedmann equations, which describe how the universe expands, can be recovered by applying what is known as the unified first law of thermodynamics to the apparent horizon of a flat Friedmann–Lemaître–Robertson–Walker universe. This law, formulated by Sean Hayward, reads TdS = −dE + WdV, where E is the total energy inside the horizon, W is the work density, and V is the enclosed volume. In this picture, the Friedmann equations are not imposed dynamical laws but thermodynamic equations of state.

The new study revisits this derivation with a sharp eye on a detail that is easy to miss. The apparent horizon, whose radius in a flat universe is simply the inverse of the Hubble parameter, is a dynamical boundary that grows and shrinks with cosmic evolution. Crucially, it is not comoving: it does not expand along with the fluid of galaxies the way an ordinary box of gas does. Standard cosmological conservation laws are written for comoving volumes that scale with the cube of the scale factor, but the horizon-thermodynamic framework naturally selects the volume enclosed by the apparent horizon, because that is the region causally accessible to an observer. The authors show that the identification of the total energy as the energy density times this horizon volume is not a convenient assumption but a consequence of the Misner-Sharp mass definition, which fixes the energy inside the horizon to be exactly half its radius.

This non-comoving volume has a striking consequence. Even if no particles are being created anywhere in the cosmos, the total number of particles inside the apparent horizon changes with time, simply because the boundary sweeps through the cosmic fluid. When the universe decelerates, the horizon expands faster than the fluid and swallows additional particles; when it accelerates, the opposite happens and particles effectively stream out across the boundary. The researchers call this effect the horizon flux, and their central claim is that it is not a minor geometric artifact but a physically essential ingredient that any consistent thermodynamic treatment of cosmology must include. Neglecting it, they argue, has led previous analyses to incorrect conclusions about which forms of matter can power cosmic acceleration.

To incorporate gravitationally induced particle creation, the team builds on the framework of irreversible thermodynamics developed by Ilya Prigogine and collaborators in the late 1980s. In this picture, the expanding gravitational field transfers energy into the matter sector, producing new particles and generating an effective negative pressure, the so-called creation pressure, that mimics the behavior of dark energy. The particle number density then obeys a modified balance equation featuring a production rate Γ, and the total pressure of the fluid is decomposed into an equilibrium part plus the creation pressure. When this generalized description is inserted into the unified first law applied at the apparent horizon, the modified acceleration equation emerges naturally, with the creation pressure appearing alongside the ordinary matter terms, confirming that modified Friedmann dynamics follows from the horizon-based thermodynamic description.

The heart of the paper is a clean decomposition of how the particle count and the matter entropy inside the horizon actually evolve. The total rate of change splits into two distinct contributions: a genuine bulk creation term, proportional to the production rate Γ times the number of particles, and a geometric horizon flux term, proportional to three times the Hubble parameter times the deceleration parameter q. During the decelerating epoch, when q is positive, both terms push the matter entropy upward. But once the universe transitions to acceleration, the horizon flux turns negative, draining particles from the horizon volume. For the matter entropy to remain non-decreasing, as the second law demands, the bulk creation rate must then satisfy a strict inequality: Γ must be at least as large as minus three times the horizon flux term, meaning production must roughly keep pace with the expansion itself.

Combining this thermodynamic constraint with the background dynamics for a pressureless fluid yields a remarkable result. The deceleration parameter is bounded below by −1, and for any viable accelerating phase the production rate is confined to the range between the Hubble parameter and three times the Hubble parameter. In other words, Γ > H emerges as a robust lower bound demanded simultaneously by the dynamics and by thermodynamic consistency. The authors then show that whenever this condition holds, the acceleration of the scale factor is positive, meaning that cold, pressureless dark matter with a genuine creation rate exceeding the expansion rate can consistently account for late-time cosmic acceleration without invoking any exotic fluid or cosmological constant. This directly challenges recent observational analyses suggesting that particle creation models only work when the produced component has an equation of state more negative than −1/3, a conclusion the authors attribute to those analyses neglecting the horizon contribution altogether.

The team also derives the Generalized Second Law for this open-system setting, writing the total entropy budget as the sum of the horizon entropy and the matter entropy, with contributions from the horizon sector, bulk creation, boundary fluxes, and possible non-adiabaticity per particle. Under the physically natural assumption of adiabatic creation, in which newly produced particles are born in thermal equilibrium with the cosmic fluid and the entropy per particle stays constant, the total entropy production rate reduces to a simple expression governed by a single kinematic factor, one minus q squared, multiplied by a positive coupling. To test this against reality, the authors employed Gaussian Processes, a non-parametric statistical technique, applied to the Cosmic Chronometers dataset, which provides model-independent measurements of the expansion rate across cosmic history. The reconstruction shows that entropy production peaked precisely at the transition from deceleration to acceleration, around redshift 0.6, and then declined smoothly toward zero as the universe approaches a de Sitter state, exactly as the adiabatic framework predicts, without ever crossing into an unphysical regime of negative entropy production.

There are important caveats. The authors note that in the strictly adiabatic limit, where total entropy production vanishes, their framework becomes observationally indistinguishable from the standard Lambda-CDM model at the level of the background expansion, so any detectable departure from the concordance model requires strictly positive entropy production and additional parametrization of the coupling between horizon flux and matter. The production rate in their formulation depends on both the Hubble parameter and its time derivative, extending the usual matter-creation framework in which the rate depends on H alone, and a full statistical confrontation with supernova, baryon acoustic oscillation, and Hubble tension data is left for future work. Still, the conceptual payoff is considerable: a rigorous accounting of the moving horizon boundary transforms matter creation from a phenomenological curiosity into a thermodynamically consistent mechanism, and suggests that the dark energy driving cosmic acceleration may be nothing more than the irreversible work done by spacetime itself as it creates the matter filling the universe.

Subject of Research: Thermodynamic derivation of modified Friedmann equations with horizon flux and gravitationally induced particle creation in cosmology

Article Title: Beyond comoving volume: horizon flux and matter creation in modified cosmology from the unified first law of thermodynamics

Article References: Cárdenas, V. H., Cruz, M., & Lepe, S. (2026). Beyond comoving volume: horizon flux and matter creation in modified cosmology from the unified first law of thermodynamics. The European Physical Journal C, 86(9), Article 1110. https://doi.org/10.1140/epjc/s10052-026-16334-3

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16334-3

Keywords: cosmology, apparent horizon, thermodynamics, particle creation, dark energy, Friedmann equations, generalized second law, cold dark matter, unified first law, FLRW universe, entropy production, Hubble tension

The significance of the achievement lies in what hydrogen can tell us about the largest questions in physics. Hydrogen is the most common element in the universe and the raw material from which stars form, and its atoms emit a characteristic radio signal at a wavelength of 21 centimetres. As that light travels across billions of light years, the expansion of the universe stretches it to longer wavelengths, carrying within it a record of how fast space was expanding when it was emitted. “Its faint radio emission acts like a cosmic tracer, revealing how matter is distributed across space,” said co-author Dr. Arnab Chakraborty, a postdoctoral fellow at the University of Toronto who first proposed the finding. By mapping where this glow is stronger or weaker across the sky, astronomers can reconstruct the large-scale structure of matter at epochs that are extraordinarily difficult to reach by any other means.

Dark energy sits at the heart of why this matters. In the late 1990s, observations of distant supernovae revealed that the universe is not merely expanding but expanding at an ever-increasing rate, a discovery that earned the Nobel Prize in Physics and upended the expectation that gravity would gradually slow cosmic growth. Whatever is responsible for that acceleration is called dark energy, and it currently accounts for roughly seventy per cent of the total energy content of the cosmos. Yet despite decades of effort, physicists still do not know what it is. Competing theories describe it in fundamentally different ways, from a constant energy density inherent to empty space to dynamical fields whose strength changes over cosmic time. Distinguishing between these possibilities requires measuring how the expansion rate of the universe has evolved across billions of years, which is precisely the kind of measurement CHIME was built to make.

CHIME is a radio telescope hosted by the National Research Council of Canada at the Dominion Radio Astrophysical Observatory near Penticton. Its distinctive design, four cylindrical reflectors arranged in a half-pipe configuration, gives it an enormous field of view and allows it to map the entire northern sky every day as Earth rotates beneath it. The project is a pan-Canadian collaboration built and operated by scientists at the University of British Columbia, McGill University, the University of Toronto and the Dominion Radio Astrophysical Observatory, together with North American partners including Arizona State University. From the outset, the instrument was conceived with one overriding scientific goal: to chart the distribution of hydrogen gas across the early universe, allowing astronomers to calculate how the cosmos has expanded and thereby investigate dark energy directly.

What makes the new result a genuine milestone is that CHIME achieved this detection autonomously. Previously, the collaboration had to cross-correlate its observations with galaxy survey data from other telescopes, using those optical catalogues as a reference to confirm that the telescope was genuinely seeing the cosmic hydrogen signal. Galaxy surveys investigate the same underlying questions about cosmic expansion, but they work in visible light and focus in fine detail on individual galaxies. That approach is extraordinarily expensive, costing millions of dollars more, and it carries a fundamental limitation: galaxies only exist in the parts of the universe that are hot and dense enough to have formed stars. By mapping the combined radio glow that hydrogen emits on its own, CHIME can explore the same questions at a greater scale, reach further back in cosmic time, operate at a fraction of the cost, and do so without relying on anyone else’s results.

The technique CHIME employs is known as hydrogen intensity mapping, and it is as elegant as it is technically punishing. Rather than resolving individual galaxies, the telescope measures the aggregate radio emission from all the hydrogen within large volumes of space, treating the gas as a continuous glowing background whose brightness fluctuations trace the clustering of matter. Because hydrogen pervades regions of the universe that never lit up with stars, intensity mapping can in principle survey cosmic epochs that optical surveys simply cannot reach. The trade-off is that the cosmological signal is astonishingly faint, buried beneath foregrounds that can be millions of times brighter, including radio emission from our own galaxy, from distant galaxies, and from human technology, as well as noise generated by the instrument itself. Extracting the signal demands extraordinary care in calibration, data processing and statistical analysis.

In an accompanying paper, the researchers examined what the observed signal actually reveals about the distribution of hydrogen in the universe. “Our data indicate that roughly two per cent of the hydrogen in the universe was in neutral atomic form at this time, broadly consistent with other measurements,” said co-author Dr. Shabbir Shaikh, a postdoctoral fellow at Arizona State University. “By measuring how that hydrogen is distributed and clustered, CHIME gives us a new way to test our understanding of how galaxies form and evolve.” That figure carries real scientific weight, because the fraction of hydrogen remaining in neutral atomic form constrains models of how gas cools, collapses and ignites into stars across cosmic history. The consistency with independent measurements suggests the telescope is measuring something real about the intergalactic medium when the universe was about five billion years old.

The path to the detection was anything but a sudden flash of insight. The team applied new data analysis and processing techniques to tease the faint signal out of the overwhelming noise of the background universe, human technology and even the telescope itself, and then spent more than a year testing the result to prove it was correct. The measurement is based on 94 nights of observation data collected in 2019. “We worked very hard to convince ourselves that this wasn’t a false alarm,” said Dr. Chakraborty. “After all the tests, the signal remained. That gave us confidence we were seeing real hydrogen from the distant universe.” That deliberate, sceptical pace reflects the hard lessons of the field, where earlier claims of hydrogen intensity mapping detections have been contested, and where the difference between a cosmological signal and a stubborn instrumental artefact can be agonizingly subtle.

For the collaboration, the moment carries both scientific and national significance. “This is a completely new technique for probing the cosmos, delivered by an instrument that was conceived, built and funded by Canadians,” said co-author Dr. Mark Halpern, professor in the UBC department of physics and astronomy and CHIME principal investigator. “It’s a bold new step in the global cosmology program and a Canadian success story.” Co-author Dr. Simon Foreman, an assistant professor at Arizona State University, framed the broader implications: “For a long time, astrophysicists have believed there is great potential in this hydrogen mapping technique with this kind of telescope. By actually showing that the technique works in practice, we’ve opened up a whole new window on the universe. We can use it to test our current theories, and learn new things about galaxies and other properties of the universe.”

Perhaps the most striking aspect of the announcement is how much untapped data remains. The current measurement uses only a small fraction of what CHIME has collected since operations began, and researchers now have nearly seven years of observations available for analysis. The team is working to expand the analysis to earlier periods in cosmic history, targeting epochs when the universe was only three billion years old, when dark energy’s influence on cosmic expansion was far weaker and its underlying nature may be easier to disentangle from ordinary matter and gravity. If the technique continues to perform at scale, hydrogen intensity mapping could become one of the most cost-effective tools in cosmology, complementing billion-dollar galaxy surveys and offering an independent check on the theories that attempt to explain why the universe’s expansion is speeding up. The project is funded by the Canada Foundation for Innovation, the National Research Council of Canada, the Natural Sciences and Engineering Research Council and the provinces of British Columbia, Ontario and Quebec, with support from the Digital Research Alliance of Canada. What began as a Canadian experiment in the hills of British Columbia has now proven it can hear the universe’s oldest storyteller, and the story it tells is only beginning.

Subject of Research: Hydrogen intensity mapping of the early universe with the CHIME radio telescope to probe dark energy

Article Title: Canadian telescope directly maps earliest glow of hydrogen, opening a new window on the universe

Article References: Canadian telescope directly maps earliest glow of hydrogen, opening a new window on the universe. (n.d.). Original publication

Image Credits: AI Generated

DOI: Not provided

Keywords: CHIME, hydrogen intensity mapping, dark energy, cosmology, 21-cm radio emission, cosmic expansion, radio telescope, large-scale structure, galaxy formation, neutral hydrogen, The Astrophysical Journal, University of British Columbia

The obstacle is known in the trade as the circularity problem, and it has plagued gamma-ray burst cosmology for nearly two decades. The most widely used tool for taming these explosions is the Amati relation, an empirical correlation between the rest-frame spectral peak energy of a burst and its isotropic-equivalent radiated energy. The catch is that the isotropic energy cannot be measured directly. It must be derived from the burst’s bolometric fluence and its luminosity distance, and luminosity distance depends on the cosmological model you assume. Historically, researchers calibrated the Amati relation by assuming a standard Lambda-CDM cosmology, then used the calibrated relation to constrain cosmological models. The reasoning goes in a circle: the answer you get out is quietly shaped by the assumption you put in.

Cosmologists have proposed a variety of escape routes over the years. Some teams interpolated distances from low-redshift supernovae without invoking any particular background cosmology, while others fitted the burst relations and cosmological parameters simultaneously in a single statistical framework. A different strategy, adopted by Amati and collaborators, exploited observational Hubble data gathered from cosmic chronometers, galaxies whose stellar populations act as natural clocks that tick out the age of the Universe at different redshifts. Because these Hubble measurements are essentially model-independent, they can anchor burst calibrations without smuggling in a preferred cosmology. The Delhi team builds on this idea but replaces the older reconstruction techniques, such as Bezier polynomials and Gaussian process regression, with something more modern and more flexible: neural networks.

The choice of machine learning is deliberate. Gaussian process regression, long the standard non-parametric tool in cosmology, implicitly assumes Gaussian statistics and is notoriously sensitive to the choice of kernel function, which can quietly shape the reconstructed curve. Artificial neural networks, by contrast, impose far fewer assumptions on the data and learn the underlying function directly from observations. The researchers trained a network on 32 observational Hubble parameter measurements spanning redshifts from 0.07 to 1.965, drawn from an updated compilation by Ratra and colleagues. With so few data points, architecture choices matter enormously, so the team ran a systematic grid search, scoring candidate networks with a RISK function drawn from statistical decision theory, which measures the expected squared prediction error while accounting for observational uncertainties.

The search converged on a strikingly simple answer: a single hidden layer of 4096 neurons, using the exponential linear unit activation function and the Adam optimizer with a decaying learning rate over 5750 epochs. Wider networks offered no meaningful improvement, and deeper architectures with two, three or four hidden layers showed clear signs of overfitting, producing spurious oscillations rather than smooth reconstructions. Smaller networks underfit the data, yielding higher risk values. The chosen configuration sat in a sweet spot balancing flexibility against generalization, and leave-one-out cross-validation confirmed that normalized residuals scattered around zero with no systematic trend in redshift, indicating the reconstruction was unbiased and not driven by any individual data point.

Standard neural networks, however, have a well-known weakness: they produce point predictions without honest error bars, and can even confidently report inaccurate values. For sparse, noisy cosmological datasets this is a serious liability. The team addressed it in two ways. First, they supplemented the network with bootstrap resampling, generating 1000 resampled datasets by drawing the 32 measurements with replacement, training the network independently on each, and averaging the resulting ensemble of reconstructions. The variance across the ensemble provides an estimate of reconstruction uncertainty, though the authors caution this primarily captures sampling variability rather than full model uncertainty. Second, and more ambitiously, they deployed a Bayesian neural network, which treats every weight and bias in the network as a random variable with its own probability distribution.

The Bayesian formulation, originally developed by Bishop and by MacKay in the 1990s, transforms network training into probabilistic inference. Starting from zero-mean Gaussian priors on all parameters, the network updates its beliefs through the likelihood of the observed Hubble data, yielding a full posterior distribution rather than a single best-fit set of weights. Because the posterior is high-dimensional and nonlinear, the researchers sampled it with the no-u-turn sampler, an adaptive variant of Hamiltonian Monte Carlo implemented in the Pyro probabilistic programming library. Model selection was guided by the widely applicable information criterion, which balances predictive accuracy against model complexity and naturally encodes Occam’s razor. Notably, the analysis found that predictive performance was largely insensitive to network width once sufficient capacity was reached, while the prior variance played the dominant role in regulating effective model complexity.

With the Hubble parameter reconstructed by both methods, the team converted the expansion history into luminosity distances by integrating the inverse expansion rate, then calibrated the Amati relation for two independent burst catalogues: the A220 sample of 220 long gamma-ray bursts assembled by Khadka and Ratra, and the J220 sample from Jia and colleagues, drawn from the Swift and Fermi missions. Because the calibration data extend only to redshift 1.965, the researchers restricted the fitting to 115 bursts from A220 and 129 from J220 below that cutoff, using Markov chain Monte Carlo with the emcee sampler to constrain the relation’s slope, intercept and intrinsic scatter simultaneously.

The results are reassuringly consistent across methods and datasets. For the A220 sample, the artificial network yielded a slope of 1.231 with uncertainties of about 0.09, while the Bayesian network gave 1.218, agreeing within one sigma. Both match previous model-independent calibrations based on Gaussian processes and interpolation techniques, which found slopes near 1.29 to 1.30. For the J220 sample, both networks delivered an identical slope of 1.381 with tighter uncertainties, consistent with simultaneous-fitting and redshift-binning analyses. The J220 sample also showed reduced intrinsic scatter, suggesting a more homogeneous burst population or fewer observational systematics, a difference the authors attribute to variations in sample selection, redshift coverage and measurement uncertainties between the catalogues.

The broader message is twofold. First, the close agreement between the two neural network approaches demonstrates that machine-learning calibration of gamma-ray bursts is robust against the choice of algorithm, strengthening confidence that these explosions can eventually serve as genuine cosmological probes rather than model-dependent curiosities. Second, the Bayesian framework emerges as the preferred tool for the future: it propagates uncertainty from the data through the network parameters to the final prediction in a principled way, captures the epistemic uncertainty that deterministic networks miss, and guards against overfitting when data are sparse. As upcoming missions swell the high-redshift burst sample, and as researchers extend the technique to other burst correlations such as the Ghirlanda, Yonetoku and Dainotti relations, Bayesian networks may become the standard machinery for turning the Universe’s most violent explosions into its most far-reaching measuring sticks.

Subject of Research: Model-independent calibration of gamma-ray burst Amati relation using neural network reconstruction of observational Hubble parameter data

Article Title: Reconstructing gamma-ray burst energy relations with observational H(z) data in a neural network framework

Article References: Aurpa, N. B., Habib, A. D., & Rani, N. (2026). Reconstructing gamma-ray burst energy relations with observational H(z) data in a neural network framework. The European Physical Journal C, 86(9), Article 1133. https://doi.org/10.1140/epjc/s10052-026-16318-3

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16318-3

Keywords: gamma-ray bursts, cosmology, Amati relation, neural networks, Bayesian neural networks, Hubble parameter, circularity problem, luminosity distance, machine learning, observational Hubble data, cosmic expansion, Markov chain Monte Carlo