Evolution of the Cosmological Horizons in a Universe with Countably Infinitely Many State Equations

TL;DR

This paper analyzes the evolution of cosmological horizons in an accelerated universe with infinitely many constant state equations, deriving generalized formulas and studying their behavior at key cosmic epochs.

Contribution

It introduces a framework for understanding horizons in universes with countably infinite state equations, extending previous models with new generalized expressions.

Findings

Horizon values depend on a single dominant state equation.

Derived simple formulas for horizons in complex cosmological models.

Compared particle and event horizons to determine dominance conditions.

Abstract

This paper is the second of two papers devoted to the study of the evolution of the cosmological horizons (particle and event horizons). Specifically, in this paper we consider the extremely general case of an accelerated universe with countably infinitely many constant state equations, and we obtain simple expressions in terms of their respective recession velocities that generalize the previous results for one and two state equations. We also provide a qualitative study of the values of the horizons and their velocities at the origin of the universe and at the far future, and we prove that these values only depend on one dominant state equation. Finally, we compare both horizons and determine when one is larger that the other.