Thermodynamics of cosmological models with generalized $G$ and $\Lambda $


Abstract: Here we investigate spatially flat Friedmann-Robertson-Walker space-time models of the universe to study the thermodynamic behaviors in light of variables $G$ and $\Lambda $. A particular method to find the solutions of Einstein's field equations and mathematical expressions for temperature and entropy of the perfect fluid cosmological models is introduced by using both the equation of state and the assumption $G=G_{0} \,a^{n}$. It is observed that the phantom field of ($\omega <-1)$ is thermodynamically not viable when the temperature increases with the evolution of the universe. The second law of thermodynamics is also constrained by cosmological models with time-dependent $G$ and $\Lambda $. The mathematical expressions for the look-back time, proper distance, luminosity distance, and angular diameter distances are obtained for an isotropic stiff-fluid model and their significances are investigated. The most interesting part of the investigation is that the dynamical and physical behaviors of the models are less constrained by the second law of thermodynamics.

Keywords: Cosmology, cosmological constant, thermodynamics, singularities

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