Cosmology Due to Thermodynamics of Apparent Horizon

This study proposes new entropy of the apparent horizon , where is the Bekenstein–Hawking entropy. As parameter one comes to the Bekenstein–Hawking entropy. This allows to consider the generalized Friedmann–Lemaître–Robertson–Walker (FLRW) equations for the barotropic matter fluid with for arbitrary equation of state parameter . The modified Friedmann's equations are found. The addition term in the second modified Friedmann's equation plays the role of a dynamical cosmological constant. The dark energy density, pressure, and the deceleration parameter are found. It is shown that at some parameters and , two phases can be obtained, acceleration and deceleration or the eternal inflation. The model under consideration by using the holographic principle can describe the universe inflation and late time of the universe acceleration. Thus, the holographic dark energy model with the generalized entropy of the apparent horizon is considered. It is shown that entropic cosmology with the entropy proposed is equivalent to cosmology based on the teleparallel gravity with the function . New cosmology based on the generalized entropy can be of interest for a description of inflation and late time of the universe evolution.