The long freeze: an asymptotically static universe from holographic dark energy

TL;DR

This paper explores holographic dark energy models that can lead to an asymptotically static universe, termed the 'long freeze,' where the universe's expansion halts and densities vanish, with specific conditions and limitations analyzed.

Contribution

It introduces the concept of the 'long freeze' in holographic dark energy models and identifies conditions under which the universe becomes asymptotically static, extending previous cosmological models.

Findings

Certain holographic dark energy models can produce a long freeze state.

Adding matter tends to prevent the long freeze, causing recollapse.

Long freeze is possible in a limited set of models with specific conditions.

Abstract

We show that some holographic dark energy models can lead to a future evolution of the universe in which the scale factor $a$ is asymptotically constant, while $\dot a \rightarrow 0$ and the corresponding energy and pressure densities also vanish. We provide specific examples of such models and general conditions that can lead to an asymptotically static universe, which we have called the ``long freeze." In some cases, such evolution can follow an arbitrarily long exponential expansion essentially identical to the asymptotic evolution of $\Lambda$CDM. When nonrelativistic matter is added to the holographic dark energy, it tends to destroy the long freeze behavior, driving the universe to recollapse. We show that a long freeze evolution is still possible, but only for a more limited set of HDE models.