Physics – General Physics
Scientific paper
2011-04-19
International Journal of Modern Physics D, Vol.20, No12, 2419-2446 (2011)
Physics
General Physics
23 pages, title changed, refs added, main results unchanged, accepted for publication in IJMPD
Scientific paper
10.1142/S0218271811020445
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.
Chechin Leonid
Esmakhanova Kuralay
Myrzakulov Nurgissa
Myrzakulov Ratbay
Myrzakulov Yerlan
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