Periodic Cosmological Evolutions of Equation of State for Dark Energy

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 ℘(t), σ(t) and ζ(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-Lemaître-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.

Isochronous cosmologies

“…An example of cyclic universe makes use of a scalar field with a specific potential such that the universe starts from a big bang and ends with a big crunch [14]. Other examples are the ekpyrotic scenario [15] based on brane theory, the string theory inspired bouncing cosmologies [16] and the periodic cosmologies based on Chaplygin gas [17]. All these models make use of some string theory inspired scalar or vector field, or of a perfect fluid with a nonlinear equation of state (see [18] for a review), resulting in a FRW universe filled with some exotic fluid.…”

Non-Minimally Conformally Coupling Cosmology with Multiple Vacua Potential with Cubic-Quintic-Septic Duffing Oscillator Properties

“…In Kurek et al study [71], observational constraints on route to Lambda scenario using the SNIa data sets and other astrophysical sets support the FRW model with oscillating dark energy. Therefore, a number of oscillating cosmological scenarios were constructed by either choosing by hand a periodic EoS such that it could clarify the so-called coincidence problem [64,[72][73][74] due to varying periods of acceleration that may be consistent with observations, picking a periodic scale factor [68], a periodic Hubble parameter [75], special Weierstrass elliptic functions [76], periodic functional approach [77], nonstandard Lagrangians approach [78], time-periodic varying deceleration parameter [79] and so on. There exists in fact an interest to obtain an oscillating universe, although the universe is currently accelerating with time.…”

“…For example, a periodic Hubble parameter can unify both inflation and the late-time acceleration under the same mechanism. Besides, a universe filled with matter and coupled to a dark energy with a homogeneous and a constant EoS parameter can display a periodic behaviour ( [76] and references therein). Recently, from Bars et al [80], it was revealed that cyclic Higgs scenarios based on the Weyl invariant formulation of the standard model are geodesically complete to the past in contrast to the inflationary scenario.…”

Axially magnetized dark energy cosmological model

“…Post supernovae observations, plethora of cosmological models based on accelerating expansion of the universe have been proposed either by modifying the matter part of Einstein's Field Equations or by modifying the gravity theory. Bamba et al [21] have explained the dark energy and dark matter by a two periodic generalizations of the Chaplygin gas type models. Brevik et al [22] constructed cosmological models by establishing an interaction between the DE and dark matter with a homogeneous equation of state parameter.…”