Apparent horizon and gravitational thermodynamics of Universe in the Eddington-Born-Infeld theory

TL;DR

This paper explores the thermodynamics of the Universe within the Eddington-Born-Infeld theory, analyzing apparent horizon properties and deriving laws of gravitational thermodynamics using holographic equations.

Contribution

It reformulates the EBI action into a Bigravity-type action and investigates the thermodynamic properties of the apparent horizon in this framework.

Findings

Apparent horizon can be timelike, spacelike, or null depending on the state parameter.

Derived the unified first law for gravitational thermodynamics in EBI universe.

Established the generalized second law of thermodynamics for the EBI cosmological model.

Abstract

The thermodynamics of Universe in the Eddington-Born-Infeld (EBI) theory was restudied by utilizing the holographic-style gravitational equations that dominate the dynamics of the cosmical apparent horizon $\Upsilon_{A}$ and the evolution of Universe. We started in rewriting the EBI action of the Palatini approach into the Bigravity-type action with an extra metric $q_{\mu\nu}$. With the help of the holographic-style dynamical equations, we discussed the property of the cosmical apparent horizon $\Upsilon_{A}$ including timelike, spacelike and null characters, which depends on the value of the parameter of state $w_{m}$ in EBI Universe. The unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by $\Upsilon_{A}$ in EBI Universe were obtained. Finally, applying the positive-heat-out sign convention, we derived the generalized second law of gravitational thermodynamics in EBI universe.