Abstract
A rigorous thermodynamic analysis has been done as regards the apparent horizon of a spatially flat Friedmann–Lemaitre–Robertson–Walker universe for the gravitationally induced particle creation scenario with constant specific entropy and an arbitrary particle creation rate Gamma . Assuming a perfect fluid equation of state p=(gamma -1)rho with frac{2}{3} le gamma le 2, the first law, the generalized second law (GSL), and thermodynamic equilibrium have been studied, and an expression for the total entropy (i.e., horizon entropy plus fluid entropy) has been obtained which does not contain Gamma explicitly. Moreover, a lower bound for the fluid temperature T_f has also been found which is given by T_f ge 8left( frac{frac{3gamma }{2}-1}{frac{2}{gamma }-1}right) H^2. It has been shown that the GSL is satisfied for frac{Gamma }{3H} le 1. Further, when Gamma is constant, thermodynamic equilibrium is always possible for frac{1}{2}<frac{Gamma }{3H} < 1, while for frac{Gamma }{3H} le text {min}left{ frac{1}{2},frac{2gamma -2}{3gamma -2} right} and frac{Gamma }{3H} ge 1, equilibrium can never be attained. Thermodynamic arguments also lead us to believe that during the radiation phase, Gamma le H. When Gamma is not a constant, thermodynamic equilibrium holds if ddot{H} ge frac{27}{4}gamma ^2 H^3 left( 1-frac{Gamma }{3H}right) ^2, however, such a condition is by no means necessary for the attainment of equilibrium.
Highlights
There are severe drawbacks corresponding to a finite but incredibly small value of such as the fine-tuning problem which leads to a discrepancy of 50–120 orders of magnitude with respect to its observed value which is about 3 × 10−11 eV4
2, such a condition is by no means necessary for the attainment of equilibrium
This paper dealt with a rigorous thermodynamic analysis at the apparent horizon of a spatially flat FLRW universe for the gravitationally induced particle creation scenario with constant specific entropy and an arbitrary particle creation rate
Summary
There are severe drawbacks corresponding to a finite but incredibly small value of such as the fine-tuning problem which leads to a discrepancy of 50–120 orders of magnitude with respect to its observed value which is about 3 × 10−11 eV4. But each one of them comes with several problems that are yet to be settled Because of these said difficulties in various cosmological models, another well known proposal has been suggested—the gravitationally induced particle creation mechanism. The process of particle creation is classically described by introducing a backreaction term in the Einstein field equations whose negative pressure may provide a self-sustained mechanism of cosmic acceleration. Despite rigorous investigation of various aspects of particle creation mechanism, its thermodynamic implications have never been explored. Such a study has been undertaken in this paper and the essence of this work is that the particle creation rate has been considered arbitrary, not a phenomenological one.
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