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 ΥA 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 qμν. With the help of the holographic-style dynamical equations, we discussed the property of the cosmical apparent horizon ΥA including timelike, spacelike, and null characters, which depends on the value of the parameter of state wm in EBI Universe. The unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by ΥA 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.
Highlights
Gravitational thermodynamics is quite an interesting question, which has attracted much attention
The inspired work is the first law of thermodynamics for Universe by Cai and Kim [1], which is a part of the effort to seek the connections between thermodynamics and gravity [2] after discovering the black-hole thermodynamics [3, 4]
We applied the Misner-Sharp energy, the Cai-Kim temperature TA, and the Hawking-Bekenstein entropy SA to obtain the unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by ΥA
Summary
Gravitational thermodynamics is quite an interesting question, which has attracted much attention. In [1, 5], Akbar and Cai reversed the formulation by rewriting the Friedmann equations into the heat balance equation and the unified first law of thermodynamics at the cosmical apparent horizon, for General Relativity (GR), Gauss-Bonnet, and Lovelock gravity. We applied the Misner-Sharp energy, the Cai-Kim temperature TA, and the Hawking-Bekenstein entropy SA to obtain the unified first law for the gravitational thermodynamics and the total energy differential for the open system enveloped by ΥA.
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