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Thermodynamics of Geodetic Brane Gravity

Gilberto Aguilar-Pérez, Giovany Cruz, Miguel Cruz, Efraín Rojas

TL;DR

The paper develops a thermodynamic framework for Geodetic Brane Gravity cosmology, showing that the apparent-horizon entropy acquires a brane-induced correction that departs from the Bekenstein–Hawking area law. The leading correction can be written as $S_H \approx S_{BH} + γ S_{BH}^δ$, and the horizon temperature generally differs from the bulk temperature, implying non-equilibrium horizon thermodynamics except for stiff matter; the effective Friedmann equation includes ξ multiplying ρ with ξ ≈ 1 for small brane energy μ, yielding late-time evolution close to ΛCDM for small β. The work presents a consistent thermodynamic picture of geodetic brane cosmology and outlines extensions to Lovelock-type brane gravity and observational tests as directions for future study.

Abstract

In this work, we explore the effect at cosmological level of the extra contribution arising from the Geodetic Brane Gravity model within a thermodynamical perspective. As already known, the universe seen as an extended object embedded within a higher dimensional space time, modifies the dynamical background equations, which in turn results in correction contributions to the entropy and temperature of the apparent horizon. Additionally, we investigate the possibility that the apparent horizon and the bulk remain in thermal equilibrium across various matter contents, demonstrating that such properties are highly sensitive to the equation-of-state parameter.

Thermodynamics of Geodetic Brane Gravity

TL;DR

The paper develops a thermodynamic framework for Geodetic Brane Gravity cosmology, showing that the apparent-horizon entropy acquires a brane-induced correction that departs from the Bekenstein–Hawking area law. The leading correction can be written as , and the horizon temperature generally differs from the bulk temperature, implying non-equilibrium horizon thermodynamics except for stiff matter; the effective Friedmann equation includes ξ multiplying ρ with ξ ≈ 1 for small brane energy μ, yielding late-time evolution close to ΛCDM for small β. The work presents a consistent thermodynamic picture of geodetic brane cosmology and outlines extensions to Lovelock-type brane gravity and observational tests as directions for future study.

Abstract

In this work, we explore the effect at cosmological level of the extra contribution arising from the Geodetic Brane Gravity model within a thermodynamical perspective. As already known, the universe seen as an extended object embedded within a higher dimensional space time, modifies the dynamical background equations, which in turn results in correction contributions to the entropy and temperature of the apparent horizon. Additionally, we investigate the possibility that the apparent horizon and the bulk remain in thermal equilibrium across various matter contents, demonstrating that such properties are highly sensitive to the equation-of-state parameter.

Paper Structure

This paper contains 6 sections, 47 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Apparent horizon and thermodynamics
  3. GBG model
  4. Thermodynamics of GBG model
  5. Bulk temperature and heat capacities
  6. Final Remarks

Figures (2)

  • Figure 1: Ratio between the apparent horizon temperature and the bulk temperature for different types of matter.
  • Figure 2: Hubble parameter as function of the cosmological redshift. We have considered the Planck 2018 results for the values of the cosmological parameters involved $(\Omega_{m0}, H_{0})$aghanim2020planck.