Cyclic, ekpyrotic and little rip universe in modified gravity

We propose the reconstruction of $F(R)$ gravity in such a way that corresponding theory admits cyclic and ekpyrotic universe solutions. The number of explicit examples of such $F(R)$ model is found. The comparison with the reconstructed scalar-tensor theory is made. We also present $F(R)$ gravity which provides the little rip evolution and gives the realistic gravitational alternative for $\Lambda$CDM cosmology. The time for little rip dissolution of bound structures in such theory is estimated. We demonstrate that transformed little rip $F(R)$ solution becomes qualitatively different cosmological solution with Big Bang type singularity in Einstein frame.Comment: LaTeX 11 pages, no figure, typos correcte

Is exponential gravity a viable description for the whole cosmological history?

Here we analysed a particular type of $F(R)$ gravity, the so-called exponential gravity which includes an exponential function of the Ricci scalar in the action. Such term represents a correction to the usual Hilbert-Einstein action. By using Supernovae Ia, Barionic Acoustic Oscillations, Cosmic Microwave Background and $H(z)$ data, the free parameters of the model are well constrained. The results show that such corrections to General Relativity become important at cosmological scales and at late-times, providing an alternative to the dark energy problem. In addition, the fits do not determine any significant difference statistically with respect to the $\Lambda$CDM model. Finally, such model is extended to include the inflationary epoch in the same gravitational Lagrangian. As shown in the paper, the additional terms can reproduce the inflationary epoch and satisfy the constraints from Planck data.Comment: 20 pages, 6 figures, analysis extended, version published in EPJ