Reconstruction of the equation of state for the cyclic universes in homogeneous and isotropic cosmology

TL;DR

This paper reconstructs cyclic universe models within homogeneous and isotropic cosmology using elliptic functions, exploring conditions for non-phantom phases and crossing the phantom divide.

Contribution

It introduces a novel method of reconstructing cyclic universe models using Weierstrass and Jacobian elliptic functions in FLRW cosmology.

Findings

Universe remains in non-phantom phase in several models.

Some models allow crossing of the phantom divide.

Reconstruction provides new insights into cyclic cosmological evolutions.

Abstract

We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.