Flrw Universe Analysis Achieves Consistent Cosmology Without Relying on a Time-Dependent Radius

The nature of phase transitions within the expanding universe presents a significant challenge to current cosmological models, often requiring unconventional equations of state and conflicting with established gravitational laws. Carlos E. Romero-Figueroa of the Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, and Hernando Quevedo from the Dipartimento di Fisica, Universitá di Roma “La Sapienza”, alongside their colleagues, address this issue by proposing a novel framework based on quasi-homogeneous thermodynamics. Their research introduces a new way to model the cosmological horizon, moving away from traditional pressure-volume interpretations and incorporating corrections arising from the Generalized Uncertainty Principle. By applying Geometrothermodynamics to the Friedmann-Lemaître-Robertson-Walker universe, the team demonstrates that fluctuations in these quantum corrections can indeed trigger phase transitions mirroring those observed in black holes. Importantly, their numerical analysis reveals a universal scaling behaviour near these transition points, suggesting a deeper connection between gravitational systems and reinforcing the potential of Geometrothermodynamics to illuminate the fundamental microstructure of spacetime.

Geometrothermodynamics of Black Holes and Cosmology

The central focus is the application of geometrothermodynamics, a framework using Riemannian geometry to describe thermodynamic systems, to understand the properties of black holes and cosmological models. This approach seeks a deeper understanding of the connection between gravity, thermodynamics, and potentially, quantum gravity. Studying systems that are quasi-homogeneous, a generalization of homogeneous systems, allows for more realistic modeling of complex systems like black holes and the expanding universe, providing a more accurate thermodynamic description. The core idea is to represent thermodynamic properties as geometric quantities on a Riemannian manifold, where the curvature reveals information about the stability and phase transitions of the system.

A major goal is to identify phase transitions in black holes and cosmological models by analyzing the geometric properties of the thermodynamic manifold, utilizing Langer’s theory of metastable states. The research aims to probe the microstructure of black holes and the universe, what is happening at the smallest scales. The geometric approach, combined with GUP, is seen as a way to reveal information about this microstructure, specifically applied to the FRW universe, focusing on the apparent horizon. Treating the apparent horizon as a thermodynamic entity allows for the application of geometrothermodynamics. Exploration of quasi-homogeneous systems and higher-order GUPs could lead to the discovery of new thermodynamic phenomena not captured by traditional approaches.

Apparent Horizon Radius and Equation of State

Scientists have demonstrated a novel approach to understanding phase transitions within cosmological spacetimes, revealing a critical link between a time-dependent apparent horizon radius and an equation of state differing from that of dark energy. The research addresses an inconsistency arising from simultaneously applying Hayward’s unified gravitational first law and the fundamental equation of the apparent horizon, proposing a quasi-homogeneous system model for the cosmological horizon. Experiments revealed that fluctuations in the GUP parameter can induce phase transitions mirroring those observed in black hole configurations.

Utilizing Geometrothermodynamics, the team measured the scalar curvature near the phase transition point, discovering a scaling behavior characterized by a critical exponent consistently close to 1, irrespective of the equilibrium space’s dimensionality. This finding confirms that gravity corrections not only refine the consistency of cosmological models but also reinforce the concept of universality across diverse gravitational systems, solidifying GTD as a powerful geometric tool for probing spacetime’s emergent microstructure. Measurements confirm a fixed and unified minimal length scale of ∆xmin = 4p|β|, independent of the deformation parameter’s sign, distinguishing this GUP formulation from others. The study establishes a modified equation of state, given by P = TAπ6V1/3 + 8πβ3V + 1V4/33 × 61/3V2/3 −4 × (6π)2/3β36π1/3, where P represents work density, V is the volume enclosed by the cosmological horizon, and TA is the geometric temperature of the horizon.

The work introduces a fluctuating thermodynamic variable interpretation of the deformation parameter β, viewing the cosmological horizon as a quasi-homogeneous thermodynamic system. This approach allows for the induction of phase transitions while maintaining compatibility with established thermodynamic scaling relations. Analysis of the GUP-corrected FLRW horizon and thermodynamics, using a 4-dimensional spherically symmetric spacetime, yielded a horizon temperature resembling that of a black hole, TA = 12πRA, and a modified MS energy, Eeff, incorporating both matter and gravitational contributions. The team precisely determined the apparent horizon radius, RA = 1qH2 + ka2, and demonstrated that the geometric entropy is a function of the area, S = A4 + 4πβ ln Aσ, where β is the GUP parameter and σ is a positive integration constant.

Cosmological Horizons and Modified Dark Energy Equations of

This work presents a novel approach to understanding phase transitions within cosmological spacetimes, demonstrating that their existence necessitates a time-dependent apparent horizon radius and, consequently, an equation of state distinct from standard dark energy models. This formulation avoids reliance on conventional pressure-volume interpretations, offering a consistent description of the universe’s thermodynamic behaviour. This finding suggests a fundamental universality linking gravitational systems and reinforces the effectiveness of Geometrothermodynamics as a tool for probing the underlying microstructure of spacetime. The authors acknowledge limitations inherent in the approximations used within the GUP framework, but propose that future research could explore the implications of these findings for more complex cosmological models and potentially refine our understanding of quantum gravity.