Quasi-Homogeneous Thermodynamics and Microscopic Structure of the Quantum-Corrected FLRW Universe

TL;DR

This paper introduces a quasi-homogeneous thermodynamic framework for quantum-corrected FLRW universes, revealing phase transitions and microstructure insights through geometric analysis, independent of traditional pressure-volume interpretations.

Contribution

It proposes a novel quasi-homogeneous thermodynamic approach for quantum-corrected cosmology and demonstrates the universality of phase transition behavior via Geometrothermodynamics.

Findings

Quantum corrections induce phase transitions similar to black holes.

Fluctuations in the GUP parameter can trigger phase transitions.

Critical exponent near 1 indicates universality in thermodynamic behavior.

Abstract

The analysis of phase transitions in cosmological spacetimes shows that their existence requires a time-dependent apparent horizon radius, which in turn implies an equation of state different from that of a dark energy fluid. This condition is not compatible with the simultaneous fulfillment of Hayward's unified gravitational first law and the fundamental thermodynamic equation of the apparent horizon. To solve this problem, we introduce an alternative formulation in which the cosmological horizon is modeled as a quasi-homogeneous thermodynamic system. We apply this approach to the Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe under quantum gravity corrections encoded by the Generalized Uncertainty Principle (GUP), promote the deformation parameter to a thermodynamic variable, and obtain a consistent thermodynamic description without relying on the usual pressure-volume interpretation. Using Geometrothermodynamics (GTD), we show that fluctuations of the GUP parameter can induce phase transitions closely resembling those of black hole configurations. Finally, we perform a numerical analysis of the behavior of the GTD scalar curvature near the phase transition point, where we find a scaling behavior characterized by the critical exponent close to 1, independently of the dimension of the equilibrium space. This reveals that quantum gravity corrections not only modify the thermodynamic consistency of cosmological models but also strengthen the notion of thermodynamic universality across gravitational systems. Our findings confirm GTD as a powerful geometric tool to unveil the emergent thermodynamic microstructure of spacetime.