Evolution of the Cosmological Horizons in a Concordance Universe

TL;DR

This paper investigates how particle and event horizons evolve in an accelerated universe with both cosmological constant and dust, providing new formulas and showing their velocities stay positive.

Contribution

It introduces closed-form expressions for horizon evolution in a universe with two state equations, extending previous single-equation models.

Findings

Horizons' velocities are always positive in the studied model.

Derived generalized formulas for horizon evolution with two state equations.

Confirmed the monotonic increase of horizons in an accelerated universe.

Abstract

The particle and event horizons are widely known and studied concepts, but the study of their properties, in particular their evolution, have only been done so far considering a single state equation in a decelerating universe. This paper is the first of two where we study this problem from a general point of view. Specifically, this paper is devoted to the study of the evolution of these cosmological horizons in an accelerated universe with two state equations, cosmological constant and dust. We have obtained closed-form expressions for the horizons, which have allowed us to compute their velocities in terms of their respective recession velocities that generalize the previous results for one state equation only. With the equations of state considered, it is proved that both velocities remain always positive.