Cosmology, new entropy and thermodynamics of apparent horizon

Abstract

We propose a new nonadditive entropy of the apparent horizon $S_K=S_{BH}/(1+\gamma S_{BH}^2)$, where $S_{BH}$ is the Bekenstein–Hawking (BH) entropy and consider the description of a new cosmology. When parameter $\gamma$ vanishes ($\gamma \to 0$) our entropy $S_K$ is converted into BH entropy $S_{BH}$. By using the holographic principle a new model of holographic dark energy is studied. We obtain the generalised Friedmann equations for Friedmann–Lemaître–Robertson–Walker (FLRW) space-time for the barotropic matter fluid with the equation of state (EoS) $p=w\rho$. From the second modified Friedmann equation we find a dynamical cosmological constant. The density of the dark energy ${\rho }_D$, pressure $p_D$, and the deceleration parameter $q$ corresponding to our model are computed. It is shown that at some EoS parameter $w$ and the entropy parameter $\gamma$ there are phases of universe acceleration, deceleration and eternal inflation. Our model, with the help of the holographic principle, can describe the universe inflation and late time of the universe acceleration. We show that the current deceleration parameter $q_0\approx -0.535$ is realized at some model parameters. Entropic cosmology with our entropy proposed is equivalent to cosmology based on the teleparallel gravity with the function $F\left(T\right)$. The generalised entropy of the apparent horizon with the holographic dark energy model can be of interest for new cosmology.