Apparent Horizon and Gravitational Thermodynamics of Universe in the Eddington-Born-Infeld Theory

Abstract

The thermodynamics of the Universe in Eddington-Born-Infeld (EBI) theory is restudied by utilizing the holographic-style gravitational equations that dominate the dynamics of the cosmical apparent horizon Υ A and the evolution of Universe. We started from applying the Bigravity method to rewrite the EBI action of the Palatini approach into the Bigravity-type action with an extra metric q µν . With the help of the holographic-style dynamical equations, we discussed the properties of the cosmical apparent horizon Υ A including timelike, spacelike and null characters, which depend on the value of the parameter of state w m in EBI Universe. We also obtained the unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by Υ A in EBI Universe. Finally, we used the Gibbs equation in the positive-heat-out sign convention to derive the generalized second laws of the nondecreasing entropy S (A) tot enclosed by Υ A in EBI universe.

Hawking-Like Radiation as Tunneling from a Cosmological Black Hole in Modified Gravity: Semiclassical Approximation and Beyond

“…In future work, we aim to write the thermodynamics of the cosmological black hole in the setup of the STVG framework based on the procedure performed in Refs. [35,[68][69][70][71][72][73].…”