Exact solutions of nonlocal nonlinear field equations in cosmology

The final publication is available at www.springerlink.comWe consider a method for seeking exact solutions of the equation of a nonlocal scalar field in a nonflat metric. In the Friedmann-Robertson-Walker metric, the proposed method can be used in the case of an arbitrary potential except linear and quadratic potentials, and it allows obtaining solutions in quadratures depending on two arbitrary parameters. We find exact solutions for an arbitrary cubic potential, which consideration is motivated by string field theory, and also for exponential, logarithmic, and power potentials. We show that the k-essence field can be added to the model to obtain exact solutions satisfying all the Einstein equations.Peer reviewe

Anisotropic solutions for R2R^2 gravity model with a scalar field

We study anisotropic solutions for the pure $R^2$ gravity model with a scalar field in the Bianchi I metric. The evolution equations have a singularity at zero value of the Ricci scalar $R$ for anisotropic solutions, whereas these equations are smooth for isotropic solutions. So, there is no anisotropic solution with the Ricci scalar smoothly changing its sign during evolution. We have found anisotropic solutions using the conformal transformation of the metric and the Einstein frame. The general solution in the Einstein frame has been found explicitly. The corresponding solution in the Jordan frame has been constructed in quadratures.Comment: 13 pages, accepted for publication in Phys. Atom. Nucle

F(R)F(R) gravity inflationary model with (R+R0)3/2(R+R_0)^{3/2} term

The proposed inflationary model, which is a one-parametric generalization of the Starobinsky $R+R^2$ model, includes the $(R+3m^2\beta^2)^{3/2}$ term, where the parameter $m$ is the inflaton mass, defined in the same way as in the Starobinsky model, and $\beta$ is a dimensionless constant. Using the conformal transformation and the Einstein frame potential, we obtain the inflationary parameters of the model proposed. The value of the tensor-to-scalar ratio $r$ is bigger than in the Starobinsky model. The considered inflationary model produces a good fit to current observation data.Comment: 11 pages, 2 figure

Construction of inflationary scenarios with the Gauss-Bonnet term and nonminimal coupling

Inflationary models with a scalar field nonminimally coupled both with the Ricci scalar and with the Gauss-Bonnet term are studied. We propose the way of generalization of inflationary scenarios with the Gauss-Bonnet term and a scalar field minimally coupled with the Ricci scalar to the corresponding scenarios with a scalar field nonminimally coupled with the Ricci scalar. Using the effective potential, we construct a set of models with the same values of the scalar spectral index $n_s$ and the amplitude of the scalar perturbations $A_s$ and different values of the tensor-to-scalar ratio $r$.Comment: 11 pages, 5 figures, v2: minor corrections, references are added, to appear in EPJ