Exact cosmological solutions of a Chaplygin Gas in Anisotropic Petrov Type D Spacetimes in Eddington-inspired-Born-Infeld gravity: Dark Energy Model

Abstract

We consider a Petrov Type D physical metric g, an auxiliary metric q and a Chaplygin Gas of pressure P in Eddington-inspired-Born-Infeld theory. From the Eddington-inspired-Born-Infeld-Chaplygin Gas equations, we first derive a system of second order nonlinear ordinary differential equations. Then, by a suitable change of variables, we arrive at a system of first order linear ordinary differential equations for the non-vanishing components of the pressure P , the physical metric g and the auxiliary metric q. Thanks to the superposition method, we collect an analytical solution for the nonlinear system obtained, which allows to obtain new exact cosmological solutions for the model considered. By studying the Kretschmann invariant, we see a singularity exists at the origin of the cosmic time. By the Kruskal-like coordinates, we conclude that this solution is the counterpart of the Friedman-Lemaître Robertson-Walker spacetime in the Eddington-inspired-Born-Infeld theory. The Hubble and deceleration parameters in both directions of the physical metric g and the auxiliary metric q, as well as their behaviours over time, are also studied. The thermodynamic behaviour of the Chaplygin Gas model is investigated and, as a result, we show that the third-law of thermodynamics is verified. This means that the value of the entropy of the Chaplygin Gas in the perfect crystal state is zero at a temperature of zero Kelvin, which yields a determined value of the entropy and not an additive constant. Finally, we show that the solutions change asymptotically to the isotropic regime of expansion of Dark Energy. With this, we infer that the Chaplygin Gas can show a unified picture of Dark Energy and Dark Matter cooling during the expansion of the universe.