Comment on "Interacting holographic dark energy model and generalized second law of thermodynamics in a non-flat universe", by M.R. Setare (JCAP 01, 023, 2007)

TL;DR

This paper critiques a previous study on holographic dark energy, revealing errors and demonstrating that the generalized second law of thermodynamics is violated in the current universe, contrary to earlier claims.

Contribution

It identifies errors in the prior work and provides a corrected analysis showing the law's violation in the present universe.

Findings

Previous conclusions about the law's validity are incorrect.

The generalized second law is violated in the current universe.

Errors in the original calculations are corrected.

Abstract

Author of Ref. [1], M.R. Setare (JCAP 01, 023, 2007, arXiv:hep-th/0701242), by redefining the event horizon measured from the sphere of the horizon as the system's IR cut-off for an interacting holographic dark energy model in a non-flat universe, showed that the generalized second law of thermodynamics is satisfied for the special range of the deceleration parameter. His paper includes an erroneous calculation of the entropy of the cold dark matter. Also there are some missing terms and some misprints in the equations of his paper. Here we present that his conclusion is not true and the generalized second law is violated for the present time independently of the deceleration parameter.