A long freeze is hard to achieve in the presence of matter

TL;DR

This paper investigates how adding matter affects the long-term evolution of holographic dark energy models, showing that matter generally prevents the universe from reaching a long freeze state, except in specific cases.

Contribution

It extends previous holographic dark energy models by including matter, analyzing its impact on the universe's long-term behavior and identifying conditions for long freeze scenarios.

Findings

Matter addition tends to prevent long freeze behavior.

Long freeze is possible only in limited HDE models.

Universe may recollapse due to matter influence.

Abstract

Certain holographic dark energy (HDE) models allow for the possibility of a ``long freeze,'' in which the scale factor evolves to a constant in the long-time limit. Here we extend previous calculations by adding a nonrelativistic matter component. The addition of a matter component tends to destroy the long freeze behavior, driving the universe to recollapse. Long freeze evolution is still possible, but only for a limited set of HDE models.