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Entropy 2012, 14(11), 2351-2374; doi:10.3390/e14112351

Periodic Cosmological Evolutions of Equation of State for Dark Energy 

1,2,* , 3, 2, 2, 2 and 2
1 Kobayashi-Maskawa Institute for the Origin of Particles and the Universe, Nagoya University, Nagoya 464-8602, Japan 2 Eurasian International Center for Theoretical Physics, Eurasian National University, Astana 010008, Kazakhstan 3 Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, India
* Author to whom correspondence should be addressed.
Received: 27 August 2012 / Revised: 27 September 2012 / Accepted: 23 October 2012 / Published: 20 November 2012
(This article belongs to the Special Issue Modified Gravity: From Black Holes Entropy to Current Cosmology)
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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 ξ(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.
Keywords: dark energy; cosmology; particle-theory and field-theory models of the early universe dark energy; cosmology; particle-theory and field-theory models of the early universe
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Bamba, K.; Debnath, U.; Yesmakhanova, K.; Tsyba, P.; Nugmanova, G.; Myrzakulov, R. Periodic Cosmological Evolutions of Equation of State for Dark Energy . Entropy 2012, 14, 2351-2374.

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