To appreciate why this matters, it helps to recall how deeply gravity and thermodynamics have become entangled. In the 1970s, physicists discovered that black holes possess a temperature and an entropy proportional to the area of their horizon, a result that seemed to suggest spacetime itself has a statistical, atomic-like structure. Later work by Ted Jacobson and others inverted the logic: applying the first law of thermodynamics, dE = T dS + W dV, to a patch of horizon reproduces the Einstein field equations. In other words, gravity may emerge from thermodynamics rather than the other way around. Whenever the gravitational field equations are modified, therefore, the relationship between horizon energy, temperature and entropy must also change, and the standard Bekenstein–Hawking entropy typically has to be supplemented by new terms.

Cotton gravity is one of the more radical recent proposals for such a modification. Introduced by Jun Harada, it replaces the Einstein tensor, the geometric object at the heart of General Relativity, with a rank-three quantity built from the Cotton tensor, and rewrites the matter sector in terms of derivatives of the energy-momentum tensor. The theory has several alluring features: the cosmological constant emerges as an integration constant rather than a parameter inserted by hand, energy-momentum conservation follows automatically from the field equations, and the vacuum is defined by the vanishing of the Cotton tensor rather than the Ricci tensor, allowing a broader class of solutions than Einstein’s theory permits.

But the original formulation has pathologies. It struggles to describe non-vacuum, conformally flat spacetimes such as the Friedmann–Robertson–Walker (FRW) universes that cosmologists use to model our expanding cosmos, and its equations are of third order, making them notoriously difficult to handle. The Codazzi formulation rescues the framework. The authors show that the Cotton field equations can be recast exactly as extended Einstein equations supplemented by a Codazzi tensor, a symmetric object whose covariant derivatives obey a specific symmetry condition. When this tensor vanishes, ordinary General Relativity is recovered. When it does not, it acts as an additional, purely geometric source in the field equations, one that is divergence-free by construction but carries no independent equation of state.

With this machinery in place, the team turned to cosmology. For a homogeneous and isotropic FRW universe, the Codazzi tensor necessarily takes the form of a perfect fluid described by two time-dependent functions, constrained by a differential relation that ties the temporal component, called A(t), to the Hubble parameter. Applying the first law of thermodynamics at the cosmological apparent horizon, using the Kodama–Hayward temperature and allowing the horizon radius to evolve dynamically, they derived the total horizon entropy. It splits into the standard Bekenstein–Hawking area term plus a correction that is an integral over the cosmic history, governed entirely by the time variation of the Codazzi sector.

The consequences are subtle and intriguing. If the temporal component of the Codazzi tensor keeps a fixed sign throughout cosmic history, the correction is definite: positive values enhance the horizon entropy beyond its Einsteinian value, while negative values reduce it, a behavior the authors associate with exotic, phantom-like energy that violates the usual energy conditions. Perhaps most remarkably, the correction can be nonzero even when the expansion history of the universe is indistinguishable from that predicted by General Relativity. Horizon thermodynamics, in other words, is sensitive to the underlying geometry in ways that background kinematics alone are not, offering a potential diagnostic to tell Cotton gravity apart from Einstein’s theory even in regimes where Hubble data would look identical.

The second arena was static, spherically symmetric spacetimes, the standard setting for black hole thermodynamics and a class that includes the Schwarzschild, Reissner–Nordström and Schwarzschild–de Sitter solutions. Here the Codazzi tensor acquires an anisotropic structure with three radial functions, A(r), B(r) and C(r), constrained by compatibility conditions. Applying the first law at the event horizon, with the Hawking temperature set by the gradient of the metric function, the authors again found a Bekenstein–Hawking entropy plus a correction, this time controlled by the anisotropic combination of Codazzi components. A purely geometric analysis, imposing regularity at the horizon, forces that combination to cancel, so constant or geometry-driven anisotropies leave no thermodynamic imprint whatsoever: the Codazzi tensor behaves as a thermodynamically inert background.

The picture changes when matter enters through the field equations. Combining them yields an algebraic identity linking the Codazzi combination directly to the sum of the energy density and radial pressure. For matter with a linear equation of state, written as pressure equal to omega times density, the entropy correction becomes proportional to (1 + omega) times an integral of the density over the horizon. This produces a clean physical taxonomy. Ordinary matter such as dust or radiation, with omega greater than minus one, generates a positive correction that enhances the entropy above the Bekenstein–Hawking value. A cosmological constant, corresponding to omega exactly equal to minus one, leaves the entropy untouched, a nontrivial consistency check that mirrors the behavior of Schwarzschild–de Sitter black holes in General Relativity. Quintessence-like dark energy, occupying the window between minus one and minus one third, gives a positive but strongly suppressed correction, since its negative pressure nearly cancels its energy density. Phantom energy, with omega below minus one, flips the sign, endowing a black hole with less entropy than a vacuum black hole of the same area.

That last result might seem to threaten the second law of thermodynamics, but the authors argue it does not. The second law constrains the total entropy of the system, horizon plus exterior matter, and a shrinking horizon contribution can be compensated by entropy production in the phantom field, interactions between the horizon and its surroundings, or non-equilibrium processes, with the Codazzi tensor itself potentially acting as a further geometric source of entropy. The negative correction is better read as the signature of an inward thermodynamic flux caused by the violation of the null energy condition, a distinctive fingerprint of exotic matter that horizon thermodynamics can detect even when the surrounding geometry looks conventional.

The broader significance of the work lies in its unification of two perspectives that might at first appear to conflict. Geometry alone, through the Codazzi conditions and horizon regularity, cannot generate entropy corrections, because geometry carries no energy-momentum. Matter is the essential ingredient that breaks the cancellation, and the field equations supply the bridge. When both constraints are imposed consistently, the apparent tension dissolves: for vacuum or cosmological-constant configurations the correction vanishes, while for genuine matter it survives with a sign fixed by the equation of state. The result establishes horizon thermodynamics as a sensitive probe of Cotton gravity, complementary to observations of cosmic expansion or galactic dynamics, and suggests that the statistical ledger written on spacetime horizons may hold clues to whether Einstein’s theory is the whole story, or just the first chapter.

Subject of Research: Horizon thermodynamics of Cotton gravity in the Codazzi parametrization and its modified entropy corrections

Article Title: Thermodynamic formulation of Cotton gravity in the Codazzi parametrization

Article References: Thermodynamic formulation of Cotton gravity in the Codazzi parametrization. (n.d.). https://doi.org/10.1140/epjc/s10052-026-16281-z

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16281-z

Keywords: Cotton gravity, Codazzi tensor, horizon thermodynamics, Bekenstein-Hawking entropy, black holes, dark energy, phantom energy, cosmology, modified gravity, apparent horizon, event horizon, first law of thermodynamics

The stakes of this question are enormous. In 1969, Roger Penrose proposed the cosmic censorship conjecture, arguing that singularities arising from gravitational collapse should always be concealed within event horizons, forever shielded from any external observer. If that conjecture holds, the predictive power of general relativity is preserved, because a naked singularity would be a region where the theory’s equations break down in plain sight, spewing causally connected unpredictability into the observable universe. If it fails, physics as we know it could lose its ability to forecast the future in certain extreme scenarios. Despite decades of effort, no general proof or disproof of cosmic censorship has ever been achieved, and the new study adds a crucial piece to this ongoing investigation.

The central insight of the new research is that the fate of a collapsing matter cloud is governed by the dynamics of the apparent horizon, a surface that marks the boundary of a region where even light cannot escape. Unlike the event horizon, which is defined globally and requires knowledge of the entire future evolution of the spacetime, the apparent horizon is a quasi-local construct: it can be located by examining the geometry of the spacetime at a given moment. Within the apparent horizon lie trapped surfaces, two-dimensional surfaces from which both outgoing and ingoing light rays converge. The authors show that whether the final singularity is visible or hidden depends critically on the relative timing of when these trapped surfaces first form and when the central singularity comes into existence.

Technically, the analysis is carried out for spherically symmetric collapse of what relativists call a type-I matter field, a broad class that includes most physically reasonable forms of matter, such as dust, perfect fluids, and scalar fields, where the energy-momentum tensor has a well-behaved algebraic structure. The authors work with initial data satisfying C-squared regularity, meaning the relevant functions are twice continuously differentiable, and the weak energy condition, which demands that matter has non-negative energy density as measured by any observer. These are the same broad physical assumptions that underpin most rigorous work on collapse in classical general relativity, giving the results considerable generality within the spherical model.

The key diagnostic tool in the study is the behavior of outgoing null geodesics, the trajectories that light rays follow as they emerge from the region near the forming singularity. If families of future-directed outgoing null geodesics can escape from arbitrarily close to the central singularity, then the singularity is locally visible: light signals generated at or near it can reach distant observers, at least for a finite period before the apparent horizon eventually swallows the region. If, on the other hand, the apparent horizon forms early enough in the collapse, before the singularity has a chance to communicate with the outside, then every outgoing light ray is trapped, and the singularity is destined to be hidden within a black hole. The relative timing of these two events, the birth of trapped surfaces and the birth of the singularity, therefore acts as the decisive switch between the two possible end states.

This timing criterion connects the new work to a long lineage of collapse studies stretching back to the foundational models of the 1930s and the numerical analyses of Eardley and Smarr in 1979, which first made explicit how the apparent horizon curve in a collapsing dust cloud determines what external observers can see. Subsequent work by Christodoulou in the 1980s and 1990s demonstrated both violations of cosmic censorship in dust collapse and the instability of certain naked singularities in scalar field collapse, while Joshi and collaborators showed through the 1990s and 2000s that naked singularities arise in inhomogeneous dust, perfect fluid, and scalar field models under wide classes of initial conditions. The new paper synthesizes this tradition by characterizing, in terms of the apparent horizon’s dynamics, precisely when visibility occurs for a general type-I matter field rather than for one specialized equation of state at a time.

Why does the distinction between apparent horizon and event horizon matter so much? The event horizon of a black hole is teleological: its location at any instant depends on the entire future history of the spacetime, including whether collapse will ever end. This makes it useless for real-time diagnostics, both analytically and in numerical simulations. The apparent horizon, by contrast, is determined by the local geometry, specifically by the vanishing of the expansions of both future-directed null congruences emanating from a closed two-surface. Because of this quasi-local character, apparent horizons can be located in numerical relativity codes during dynamical simulations, and they have become the workhorse of modern black hole physics, from modeling binary mergers detected by gravitational-wave observatories to testing general relativity with future detectors such as LISA. Establishing that the apparent horizon’s evolution controls singularity visibility therefore ties an abstract question about censorship to quantities that observers and simulators can actually compute.

The results also carry weight for observational astrophysics. If naked singularities can form in realistic collapse, they would not be mere mathematical curiosities but potential astrophysical objects with distinct observational signatures. Recent theoretical work has explored how accretion flows around naked singularities differ from those around black holes: hydrodynamic and general-relativistic magnetohydrodynamic simulations of accretion onto Reissner-Nordström-type naked singularities and timelike naked singularities reveal outflows and disc properties that differ qualitatively from the black hole case. Earlier studies by Joshi, Malafarina, and Narayan showed that accretion disc profiles can in principle distinguish black holes from naked singularities. A rigorous characterization of when collapse produces visible singularities, grounded in the apparent horizon dynamics, helps identify the parameter regimes in which such exotic objects might plausibly exist and be searched for with X-ray and gravitational-wave facilities.

There are also connections to quantum gravity and to the critical phenomena discovered by Choptuik in 1993, where scalar field collapse exhibits universal scaling behavior near the threshold of black hole formation, with naked singularities appearing exactly at the critical point. The authors’ own recent research program has extended this picture, examining universality and criticality in massless scalar field collapse and the possible formation of primordial naked singularities in the early universe. If tiny naked singularities were produced in the primordial cosmos, their subsequent quantum evaporation, a possibility explored by Goswami, Joshi, and Singh in 2006, could have left observable imprints. The new timing criterion provides a framework for assessing whether such scenarios are dynamically permitted under generic, physically reasonable initial data.

Of course, important caveats remain. The analysis is restricted to spherical symmetry, and the cosmic censorship question in full generality, with rotation, gravitational radiation, and arbitrary asymmetries, remains open. Numerical studies of nonspherical collapse, from Shapiro and Teukolsky’s rotating spheroids to modern binary black hole simulations, continue to probe whether censorship holds beyond the symmetric idealization. Nevertheless, by reducing the visibility question to the concrete, computable dynamics of the apparent horizon and trapped surfaces, and by establishing the result for general type-I matter under standard energy and regularity assumptions, Koushiki and Joshi have converted a famously intractable conjecture into a sharply posed dynamical problem. The race between trapped surfaces and the singularity, it turns out, is the whole story, and knowing the rules of that race brings physicists one step closer to deciding whether the universe’s most violent endings are always hidden from view.

Subject of Research: Visibility of spacetime singularities and apparent horizon dynamics in spherical gravitational collapse

Article Title: Apparent horizon and causal structure of spacetime singularities

Article References: Koushiki, & Joshi, P. S. (2026). Apparent horizon and causal structure of spacetime singularities. General Relativity and Gravitation, 58(10), Article 114. https://doi.org/10.1007/s10714-026-03618-y

Image Credits: AI Generated

DOI: 10.1007/s10714-026-03618-y

Keywords: general relativity, gravitational collapse, spacetime singularities, apparent horizon, trapped surfaces, naked singularity, cosmic censorship, black holes, null geodesics, event horizon, type-I matter field, weak energy condition

Wormholes have fascinated physicists since Morris and Thorne’s landmark 1988 paper, which described tunnels connecting distant regions of the universe that matter and light could safely traverse. The catch has always been exotic matter: to hold a wormhole throat open against its own tendency to collapse, the spacetime must violate the Null Energy Condition, meaning the sum of energy density and pressure must go negative. Ordinary matter never does this. Most previous approaches therefore began by assuming a mathematically convenient shape function for the throat and then calculated what strange substance would be needed to support it. The new study flips that logic entirely.

Singh and Jaswant start from a four-dimensional, static, spherically symmetric spacetime — the classic setting for a charged black hole embedded in a universe with a cosmological constant, described by the Reissner–Nordström–de Sitter metric. Rather than treating the surrounding matter as an idealized perfect fluid, they model it as an imperfect fluid, complete with radial heat flux and anisotropic shear stress, a more faithful picture of the swirling, friction-laden accretion disks that feed real black holes. Onto this geometry they impose an almost eta-Ricci–Yamabe soliton, a hybrid of the Ricci and Yamabe geometric flows that smooth and deform curved spaces, with all coupling parameters allowed to vary smoothly with the radial coordinate.

The soliton equation balances a deformation term, the Ricci curvature, a Yamabe-type scalar curvature contribution, and a scaling factor omega multiplied by a one-form aligned with the radial direction. Because the spacetime is static and spherically symmetric, these parameters can depend only on radius, allowing the geometric flow to dynamically adapt to the thermodynamic state of the surrounding fluid. Solving the temporal and radial components of the soliton equation yields explicit expressions for the expansion parameter lambda and the scaling factor omega in terms of the metric function, the Ricci tensor, and the coupling functions — the mathematical machinery that drives everything that follows.

The first major result concerns the black hole’s apparent horizon, the surface where the metric function vanishes. For the geometric flow to remain finite there, the authors prove using L’Hôpital’s rule that a precise cancellation must occur: the product of the Ricci coupling and the temporal curvature component at the horizon must equal half the metric’s radial slope. Remarkably, that quantity is exactly the surface gravity, which Hawking’s famous relation ties to the horizon temperature. The result is a striking thermogeometric identity — alpha times the temporal curvature equals two pi times the Hawking temperature — linking the soliton’s regularization of the horizon directly to black hole thermodynamics.

The pivotal transition arrives when the accretion fluid enters a dark-energy-like regime. Under a barotropic equation of state relating pressure to density, the fluid’s state parameter gamma classifies cosmic eras: dust, radiation, and dark energy. When gamma reaches minus one, the fluid develops extreme negative radial pressure and violates the Null Energy Condition. The authors show that in this regime the soliton’s scaling factor becomes strictly positive at the horizon, and through an exact mapping onto the Morris–Thorne wormhole metric, this positivity forces the flare-out condition — the requirement that the throat geometry opens outward rather than pinching shut. Simultaneously, the temporal coordinate is regularized so the redshift function stays finite, preventing an event horizon from forming. Both criteria together constitute a rigorous topological transition from black hole to traversable wormhole, generated endogenously by the flow rather than assumed beforehand.

The analysis goes further, establishing that the transition is stable and localized. At the throat, the radial derivative of the soliton’s scaling factor strictly dominates the local curvature gradient, providing the structural repulsion needed to keep the passage open. Far away, the exotic stress decays exponentially, and the soliton’s influence fades smoothly: in an asymptotically flat universe its effect vanishes entirely, while in a de Sitter background it converges to the ordinary cosmological expansion. The wormhole’s exotic geometry is thus confined to the throat, leaving the deep-space universe untouched — a property the authors call cosmological safety.

Stability under gravitational waves is addressed through a tensorial perturbation analysis. Introducing a first-order metric perturbation and working in the transverse-traceless gauge, the authors show that the soliton flow converts the wave equation into a damped wave equation, with a friction term proportional to the flow’s coupling parameter. Provided that parameter remains positive, incoming perturbations decay rather than grow. In a concrete numerical example with mass one, charge 0.60, and cosmological constant 0.05, the apparent horizon sits at roughly 1.93 units, the scaling factor at the throat evaluates to about 0.37, and the perturbation frequency squared is positive — confirming that the throat dampens shocks and remains linearly stable.

The authors are careful to state the framework’s central limitation. Because the model operates within standard general relativity, the topological transition still depends on real matter entering the dark energy era and violating the Null Energy Condition — the long-standing exotic matter problem of classical wormhole physics. Their proposed remedy is to integrate the endogenous geometric flow into modified f(R) gravity, where higher-curvature terms could play the role of effective exotic matter and allow the flare-out condition to be satisfied with ordinary, positive-pressure matter. Extensions to rotating Kerr-like geometries and global stability checks via quasinormal mode analysis are also on the agenda.

For now, the result stands as a compelling piece of mathematical physics: a demonstration that geometric flows of the Ricci–Yamabe family, coupled to realistic imperfect fluids, can de-singularize a black hole horizon and organically sculpt a traversable wormhole throat, with thermodynamic fingerprints of Hawking radiation woven into the mechanism. No one expects a passable spacetime tunnel to appear in the sky tomorrow, but the study reframes wormhole formation as an emergent consequence of geometric evolution — and offers a concrete mathematical pathway that future work in modified gravity may be able to travel without exotic matter at all.

Subject of Research: Geometric soliton flows transforming black hole spacetimes into traversable wormholes in general relativity

Article Title: Traversable wormhole de-singularization: almost (\eta )-Ricci–Yamabe solitons in static spherically symmetric imperfect fluid spacetimes

Article References: Singh, J. P., & Jaswant (2026). Traversable wormhole de-singularization: almost $$\eta $$-Ricci–Yamabe solitons in static spherically symmetric imperfect fluid spacetimes. The European Physical Journal C, 86(10), Article 1141. https://doi.org/10.1140/epjc/s10052-026-16321-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16321-8

Keywords: traversable wormholes, black holes, Ricci–Yamabe solitons, geometric flow, imperfect fluid, Null Energy Condition, Hawking temperature, Morris–Thorne metric, general relativity, dark energy, apparent horizon, stability analysis

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