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

TL;DR

This paper explores the thermodynamic laws in a non-flat universe using a holographic dark energy model, finding conditions under which these laws hold at different cosmic epochs and horizons.

Contribution

It investigates the validity of thermodynamic laws in a non-flat universe with holographic dark energy, considering both apparent and event horizons, and identifies conditions for their validity.

Findings

First law is roughly respected at the apparent horizon.

Second law is respected at the apparent horizon.

At late times, the event horizon equals the apparent horizon, and thermodynamic laws hold.

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.