Periodic Cosmological Evolutions of Equation of State for Dark Energy

TL;DR

This paper introduces periodic generalizations of Chaplygin gas models using Weierstrass functions to explain dark energy and matter, allowing for non-singular, cyclic universe evolution with diverse dark energy behaviors.

Contribution

It presents novel periodic or quasi-periodic models of dark energy based on Weierstrass functions, enabling cyclic universe scenarios and analysis of dark energy phases.

Findings

Existence of models with perpetual non-phantom or phantom phases.

Models allowing crossing of the phantom divide.

Analysis of scalar fields and potentials in these models.

Abstract

We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass $\wp(t)$, $\sigma(t)$ and $\zeta(t)$ functions with two periods being infinite. If the universe can evolve periodically, a non-singular universe can be realized. Furthermore, we examine the cosmological evolution and nature of the equation of state (EoS) of dark energy in the Friedmann-Lema\^{i}tre-Robertson-Walker cosmology. It is explicitly illustrated that there exist three type models in which the universe always stays in the non-phantom (quintessence) phase, whereas it always evolves in the phantom phase, or the crossing of the phantom divide can be realized. The scalar fields and the corresponding potentials are also analyzed for different types of models.