Viaggiu entropy and the generalized second law in a flat FLRW Universe

TL;DR

This paper investigates the generalized second law in a flat FLRW universe using Viaggiu entropy, finding it prevents the universe from entering the phantom era, aligning with observations and contrasting with Bekenstein-Hawking results.

Contribution

It introduces the use of Viaggiu entropy in analyzing the generalized second law, showing it forbids the phantom era in a flat FLRW universe.

Findings

Viaggiu entropy prevents the EoS parameter from exceeding the cosmological constant.

The analysis aligns with recent cosmological observations.

Contrasts with results from Bekenstein-Hawking formalism.

Abstract

Our aim, in this paper, is to study the generalized second law by considering the dynamical apparent horizon to be endowed with the Hawking temperature and the Viaggiu entropy introduced in a pioneering work in 2014. We have devoted our attention to a flat FLRW universe filled with a perfect fluid having a constant equation of state $p = w\rho$. It is worthwhile to note that we have considered both forms of the Hawking temperature, the original one as well as the truncated version. The latter one is generally used during calculations, however, several arguments have been put forward against it. Our analysis yields a startling result. The Viaggiu entropy naturally forbids the phantom era. In other words, the Viaggiu entropy will never allow the EoS parameter to go beyond the Cosmological Constant. This result is in strong agreement with recent observations and we have deduced it purely by thermodynamic means. This is in striking contrast with the results obtained with the Bekenstein-Hawking formalism.