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

Deng, Jian-Bo  (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; Ding, Jia-Cheng (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; Fan, Qi-Qi (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; Li, Cong (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China) ; Li, Ping  (Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China)

19 November 2018

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 ${\mathrm{Υ}}_{A}$ 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 ${\mathrm{Υ}}_{A}$ 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 ${\mathrm{Υ}}_{A}$ 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.

Published in: Advances in High Energy Physics 2018 (2018) 7801854