The Generalized Second Law and the Spatial Curvature Index

TL;DR

This paper examines the compatibility of the generalized second law with different spatial curvature types in homogeneous, isotropic universes, finding flat and closed universes consistent but hyperbolic ones not.

Contribution

It demonstrates the conditions under which the generalized second law constrains the spatial curvature index in cosmological models.

Findings

Flat and closed universes satisfy the generalized second law and energy conditions.

Hyperbolic universes are incompatible with these laws under the given assumptions.

Abstract

By applying the generalized second law to the apparent horizon of a homogeneous and isotropic universe and imposing that the equation of state is no less than $-1$, it is seen that universes with either flat or closed spatial sections are consistent with the joint consideration of the aforesaid law and the dominant energy condition, but not so universes with hyperbolic spatial sections