Cosmic Horizon Flux and Matter Creation Reshape the Thermodynamic Story of Dark Energy

What if the accelerating expansion of the universe does not require dark energy at all, but instead emerges from a subtle bookkeeping error that cosmologists have been making for decades? A new theoretical study published in The European Physical Journal C by Víctor H. Cárdenas of the Universidad de Valparaíso, Miguel Cruz of the Universidad Veracruzana, and Samuel Lepe of the Pontificia Universidad Católica de Valparaíso argues that a crucial geometric subtlety has been overlooked in one of the most elegant frameworks in modern theoretical physics: the thermodynamic derivation of the equations governing cosmic expansion. By carefully tracking how particles cross the moving boundary of the observable universe, the authors show that ordinary pressureless cold dark matter can, in principle, drive accelerated expansion on its own.

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