Entropy bounds for massive scalar field in positive curvature space

TL;DR

This paper analyzes the thermodynamics of a massive scalar field in a positively curved space, extending entropy bounds analysis beyond the conformal case and establishing new mass-dependent entropy ratios that satisfy key bounds.

Contribution

It provides explicit thermodynamic calculations for a massive scalar field in curved space, extending previous conformal case analyses to include mass effects and verifying entropy bounds.

Findings

Mass-dependent entropy ratios satisfy Bekenstein's and Verlinde's bounds at high temperatures.

Explicit thermodynamic functions are calculated for low- and high-temperature regimes.

The analysis extends entropy bounds to non-conformal, massive scalar fields in curved space.

Abstract

We consider a massive scalar field with arbitrary coupling in $\mathbf{S}^{1}\times \mathbf{S}^{3}$ space, which mimics the thermal expanding universe, and calculate explicitly all relevant thermodynamical functions in the low- and high-temperature regimes, extending previous analysis of entropy bounds and entropy/energy ratios performed in the conformal case. For high temperatures, new mass-dependent entropy ratios are established which, differently to the conformal limit, fulfil Bekenstein's and Verlinde's bounds in the physical region.