卷 25, 编号 3 (2019)

We consider modified f(R) gravity with a kinetic curvature scalar, which can be reduced to a chiral cosmological model of special kind. A detailed derivation is presented for the action of a chiral cosmological model as an equivalent to a gravitational model with higher derivatives with respect to the Ricci scalar using Lagrange multipliers and a transition from the Jordan frame to the Einstein one. The equations of the model are written in the spatially flat Friedmann-Robertson-Walker metric on the basis of the constructed chiral cosmological model. Examples of solutions are found, corresponding to a special choice of the field χ = χ_* = const, and its fixed value \(\chi_0=-\sqrt{3/2}\;\text{ln}2\). For this value of χ₀, in the case of the canonical inclusion of the kinetic component of the Ricci scalar, we have obtained a nonlinear second-order differential equation with respect to H, which is not amenable to analytic solution. Therefore we implement a transition to a noncanonical form of the kinetic term. Using a fixed value of χ₀, an exact solution is obtained for power-law inflation. We have considered a transition from the de Sitter and power-law solutions specified in the Jordan frame to the Einstein frame for comparison with the results obtained in f(R) gravity with higher derivatives. It is proved that there is a Weyl conformal transformation which transforms the de Sitter and power-law solutions in one frame to similar solutions in the other.

A certain approach to solving the Wheeler-DeWitt equation in quantum cosmology, based on a type of super-selection rule by which negative frequency solutions are discarded, is discussed. In a preliminary analysis: we recall well-known results in relativistic quantum field theory, showing that adopting this approach of super-selection by discarding a sector of the frequencies does not lead to acceptable results. In the area of quantum cosmology, a qualitatively similar result is obtained: we show that by discarding solutions with negative frequencies, which is usually done in order to demonstrate “strong” results on the resolution of the singularity, important physical processes are lost, namely, the existence of cyclic solutions, which, under certain reasonable assumptions, can be interpreted as processes of creation-annihilation at the Planck scale that are typical of any relativistic quantum field theory.

We consider numerically the dynamics of a flat anisotropic Universe in Einstein—Gauss—Bonnet gravity with positive Λ in dimensions 5 + 1 and 6 + 1. We identify three possible outcomes of the evolution, one singular and two nonsingular ones. The first nonsingular outcome is oscillatory. The second one is the known exponential solution. Its simplest version is the isotropic de Sitter solution. In Gauss—Bonnet cosmology there also exist anisotropic exponential solutions. When an exponential solution being a result of cosmological evolution has two different Hubble parameters, the evolution leads from an initially totally anisotropic stage to a warped product of two isotropic subspaces. We show that such a type of evolution is rather typical and possible even in the case where the de Sitter solution also exists.

Introducing an additional symmetry (δ symmetry) in the Einstein-Hilbert action, we obtain a gravitational field model (δ gravity) based on two symmetric tensors, g_μv and ̃g_μv where an effective metric, given by g_μv = g_μv + ̃g_μv must be defined to describe the trajectories of massless particles. In previous papers, a truncated versions of δ gravity applied to cosmology was presented, where the δ symmetry was fixed in order to simplify the analysis of the model. The model predicts an accelerated expansion of the Universe without a cosmological constant or additional scalar fields, ending in a Big Rip. We present the full-fledged δ gravity, introducing a new kind of matter fields (δ matter) in order to preserve the δ symmetry. In this approach the prediction of the expansion of the Universe is preserved, but the value of the cosmological parameters improve greatly by the inclusion of δ matter. Additionally, δ matter gives us an excellent candidate for Dark Matter.

The dark energy (DE) model of a complementary gravitational field is used to address the entropy-corrected cosmological model. The dominant DE universe can originate from an indirect coupling between vacuum energy and another complementary gravitational field. This idea is used together with entropy-corrected models to study the evolution of DE in the universe. The zero point energy is calculated from one-loop corrections and used to reconstruct the scale factor and the Hubble parameter. It is then used to evaluate the equation of state (EoS) parameter for both interacting and non-interacting DE and the cosmic pressure. The square of sound speed, used to assess the stability of DE models, and the deceleration parameter are obtained. Further, the geometrical statefinder parameters s and r and a new diagnostic statefinder parameter, om(z), are evaluated and used to distinguish between the energy densities of various DE models. It is found that the studied cosmological functions show strong variation with cosmic time, and numerical results show a good agreement with observations.