Thermodynamics of the Variable Modified Chaplygin gas

TL;DR

This paper investigates a new thermodynamically stable variant of the Chaplygin gas model, called Variable Modified Chaplygin Gas (VMCG), which can describe the universe's accelerated expansion and transition from big bang to big rip.

Contribution

It introduces a novel VMCG model with a parameter n that influences stability, showing it aligns with observations and obeys thermodynamic laws, unlike previous models.

Findings

VMCG can describe current accelerated expansion.

Parameter n must be negative for stability.

Model supports a smooth transition from big bang to big rip.

Abstract

A cosmological model with a new variant of Chaplygin gas obeying an equation of state(EoS), $P = A\rho - \frac{B}{\rho^{\alpha}}$ where $B= B_{0}a^{n}$ is investigated in the context of its thermodynamical behaviour. Here $B_{0}$ and $n$ are constants and $a$ is the scale factor. We show that the equation of state of this `Variable Modified Chaplygin gas' (VMCG) can describe the current accelerated expansion of the universe. Following standard thermodynamical criteria we mainly discuss the classical thermodynamical stability of the model and find that the new parameter, $n$ introduced in VMCG plays a crucial role in determining the stability considerations and should always be \emph{negative.} We further observe that although the earlier model of Lu explains many of the current observational findings of different probes it fails the desirable tests of thermodynamical stability. We also note that for $n < 0$ our model points to a phantom type of expansion which, however, is found to be compatible with current SNe Ia observations and CMB anisotropy measurements. Further the third law of thermodynamics is obeyed in our case. Our model is very general in the sense that many of earlier works in this field may be obtained as a special case of our solution. An interesting point to note is that the model also apparently suggests a smooth transition from the big bang to the big rip in its whole evaluation process.