Modified cosmology from the thermodynamics of apparent horizon

In the realm of the Bekenstein-Hawking entropy, the thermodynamics of apparent horizon bridges with the usual FLRW (Friedmann-Lematre-Robertson-Walker) equation only for a special case where the matter field is given by a perfect fluid having equation of state (EoS) parameter = -1, i.e. p = - with and p representing the energy density and the pressure of the fluid, respectively. To include the case p = -, we consider the modification of the Bekenstein-Hawking entropy in the present work.