Comment on "A holographic model of dark energy and the thermodynamics of a non-flat accelerated expanding universe", by M.R. Setare and S. Shafei (JCAP 09 (2006) 011, arXiv:gr-qc/0606103)

TL;DR

This paper critiques previous work on holographic dark energy thermodynamics in non-flat universes, clarifying the validity of the generalized second law for different horizons and emphasizing the importance of dark matter contributions.

Contribution

It revises prior calculations for the apparent horizon and challenges earlier conclusions about the event horizon, highlighting the role of dark matter in thermodynamic laws.

Findings

The calculation for the apparent horizon $R_A$ should be revised.

The generalized second law holds for the event horizon $L$ at present time regardless of the deceleration parameter.

Including dark matter contributions can violate the generalized second law for $L$.

Abstract

Authors of ref. [1], M.R. Setare and S. Shafei (JCAP 09 (2006) 011), studied the thermodynamics of a holographic dark energy model in a non-flat universe enclosed by the apparent horizon $R_A$ and the event horizon measured from the sphere of the horizon named $L$. In section 3 in ref. [1], Authors showed that for $R_A$ the generalized second law of thermodynamics is respected, while for $L$ it is satisfied for the special range of the deceleration parameter. Here we present that their calculations for $R_A$ should be revised. Also we show that their conclusion for $L$ is not true and the generalized second law is hold for the present time independently of the deceleration parameter. Also if we take into account the contribution of dark matter in the generalized second law which is absent in ref. [1], then the generalized second law for $L$ is violated for the present time.