The Holographic Model of Dark Energy and Thermodynamics of Non-Flat Accelerated Expanding Universe

Abstract

Motivated by recent results on non-vanishing spatial curvature \cite{curve} we employ the holographic model of dark energy to investigate the validity of first and second laws of thermodynamics in non-flat (closed) universe enclosed by apparent horizon $R_A$ and the event horizon measured from the sphere of horizon named $L$. We show that for the apparent horizon the first law is roughly respected for different epochs while the second laws of thermodynamics is respected while for $L$ as the system's IR cut-off first law is broken down and second law is respected for special range of deceleration parameter. It is also shown that at late-time universe $L$ is equal to $R_A$ and the thermodynamic laws are hold, when the universe has non-vanishing curvature. Defining the fluid temperature to be proportional to horizon temperature the range for coefficient of proportionality is obtained provided that the generalized second law of thermodynamics is hold.