Dark energy in some integrable and nonintegrable FRW cosmological models

Abstract

One of the greatest challenges in cosmology today is to determine the nature of dark energy, the sourse of the observed present acceleration of the Universe. Besides the vacuum energy, various dark energy models have been suggested. The Friedmann - Robertson - Walker (FRW) spacetime plays an important role in modern cosmology. In particular, the most popular models of dark energy work in the FRW spacetime. In this work, a new class of integrable FRW cosmological models is presented. These models induced by the well-known Painlev$\acute{e}$ equations. Some nonintegrable FRW models are also considered. These last models are constructed with the help of Pinney, Schr$\ddot{o}$dinger and hypergeometric equations. Scalar field description and two-dimensional generalizations of some cosmological models are presented. Finally some integrable and nonintegrable $F(R)$ and $F(G)$ gravity models are constructed.

23 pages, title changed, refs added, main results unchanged, accepted for publication in IJMPD

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• Einstein-Cartan gravity with scalar-fermion interactions
• Study of the nucleon radiative captures 8Li(n,gamma)9Li, 9Be(p,gamma)10B, 10Be(n,gamma)11Be, 10B(p,gamma)11C, and 16O(p,gamma)17F at thermal and astrophysical energies
• Study of the neutron and proton capture reactions 10,11b(n, g), 11b(p, g), 14c(p, g), and 15n(p, g) at thermal and astrophysical energies
• Astrophysical S-factor of the radiative proton capture on 14C at low energies
• Some cosmological aspects of Horava-Lifshitz gravity: integrable and nonintegrable models
• Radiative n11B capture accounting 21 and 430 keV resonances
• FRW cosmological models with integrable and nonintegrable differential equations of state
• Some Models of Cyclic and Knot Universes
• Teleparallelism by inhomogeneous dark fluid
• Emergence of the Gambier equation in cosmology