New exact solutions in standard inflationary models

The exact solutions in the standard inflationary model based on the self-interacting scalar field minimally coupled to gravity are considered. The shape's freedom of the self-interacting potential $V(\phi)$ is postulated to obtain a new set of the exact solutions in the framework of Friedmann-Robertson-Walker Universes. The general solution was found in the case of power law inflation. We obtained new solutions and compared them with obtained ones earlir for the exponential type inflation.Comment: 12 pages, Latex, to appear in: Phys.Lett.

Phenomenology of Λ\Lambda-CDM model: a possibility of accelerating Universe with positive pressure

Among various phenomenological $\Lambda$ models, a time-dependent model $\dot \Lambda\sim H^3$ is selected here to investigate the $\Lambda$-CDM cosmology. Using this model the expressions for the time-dependent equation of state parameter $\omega$ and other physical parameters are derived. It is shown that in $H^3$ model accelerated expansion of the Universe takes place at negative energy density, but with a positive pressure. It has also been possible to obtain the change of sign of the deceleration parameter $q$ during cosmic evolution.Comment: 16 Latex pages, 11 figures, Considerable modifications in the text; Accepted in IJT

The exact solutions in verified cosmological models based on generalized scalar-tensor gravity

© Published under licence by IOP Publishing Ltd. We consider the cosmological models built on the basis of scalar-tensor gravity, in which the non-minimal coupling of a scalar field and the Ricci scalar leads to the evolution of the field, the deviation of its potential from the flat shape and the difference in the dynamics of the early universe from pure exponential expansion. It is shown that such models are in a good agreement with modern observational data. As an example of the application of the proposed approach, the exact solutions for the different models of cosmological inflation were obtained

Relic gravitational waves in cosmological models based on the modified gravity theories

We consider cosmological models based on the generalized scalar-tensor gravity, which correspond to the observational constraints on the parameters of cosmological perturbations for any model’s parameters. The estimates of the energy density of relic gravitational waves for such a cosmological models were made. The possibility of direct detection of such a gravitational waves using modern and prospective methods was discussed as well

Cosmological Solutions in the Tensor-Multi-Scalar Theory of Gravity with the Higgs Potential

© 2020, Pleiades Publishing, Ltd. Abstract: We consider a generalization of Higgs inflation, based on cosmology of general relativity (GR), to the case of a two-field model of the tensor-multiscalar theory of gravity (TMS TG). Cosmological solutions are found in the case where a scalar field with the Higgs potential, as a source of TMS TG is in the slow-rolling mode. Solutions with power and exponential-power-law evolution of the scale factor are obtained for various limiting forms of the Higgs potential

Wormholes supported by chiral fields

We consider static, spherically symmetric solutions of general relativity with a non-linear sigma model (NSM) as a source, i.e., a set of scalar fields Φ = (Φ1,...,Φn) (so-called chiral fields) parametrizing a target space with a metric hab(Φ). For NSM with zero potential V (Φ), it is shown that the space-time geometry is the same as with a single scalar field but depends on hab. If the matrix hab is positive-definite, we obtain the Fisher metric, originally found for a canonical scalar field with positive kinetic energy; otherwise we obtain metrics corresponding to a phantom scalar field, including singular and nonsingular horizons (of infinite area) and wormholes. In particular, the Schwarzschild metric can correspond to a nontrivial chiral field configuration, which in this case has zero stress-energy. Some explicit examples of chiral field configurations are considered. Some qualitative properties of NSM configurations with nonzero potentials are pointed out. © Pleiades Publishing, Ltd., 2009

Method of multiple scales in scalar field cosmology

In this work, the method of multiple scales is applied to analysis of cosmological dynamics. The method is used to construct solutions to the dynamic equations of the Universe filled with a scalar field in the Friedman-Robertson-Walker metric. A general scheme is described for choosing small dimensionless parameters of the expansion of model functions and applying the method itself to the equations of cosmological dynamics. Solutions are given that are constructed for two different types of a small parameter - a small field value and a small slow roll parameter

Generalized scalar–tensor theory of gravity reconstruction from physical potentials of a scalar field

© 2020, The Author(s). We describe how to reconstruct generalized scalar–tensor gravity (GSTG) theory, which admits exact solutions for a physical type of potentials. Our consideration deals with cosmological inflationary models based on GSTG with non-minimal coupling of a (non-canonical) scalar field to the Ricci scalar. The basis of proposed approach to the analysis of these models is an a priori specified relation between the Hubble parameter H and a function of a non-minimal coupling F= 1 + δF, H∝F. Deviations from Einstein gravity δF induce corresponding deviations of the potential δV from a constant value and modify the dynamics from a pure de Sitter exponential expansion. We analyze the models with exponential power-law evolution of the scale factor and we find the equations of influence of non-minimal coupling, choosing it in the special form, on the potential and kinetic energies. Such a consideration allows us to substitute the physical potential into the obtained equations and then to calculate the non-minimal coupling function and kinetic term that define the GSTG parameters. With this method, we reconstruct GSTG for the polynomial, exponential, Higgs, Higgs–Starobinsky and Coleman–Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove the correspondence of the obtained solutions to observational data from Planck

Black holes and wormholes in f(R) gravity with a kinetic curvature scalar

We study the chiral self-gravitating model (CSGM) of a special type in the spherically symmetric static spacetime in Einstein frame. Such CSGM is derived, by virtue of Weyl conformal transformation, from a gravity model in the Jordan frame corresponding to a modified f(R) gravity with a kinetic scalar curvature. We investigate the model using harmonic coordinates and consider a special case of the scaling transformation from the Jordan frame. We find classes of solutions corresponding to a zero potential and we investigate horizons, centers and the asymptotic behavior of the obtained solutions. Other classes of solutions (for the potential not equal to zero) are found using a special relation (ansatz) between the metric components. Investigations of horizons, centers and asymptotic behavior of obtained solutions for this new case are performed as well. Comparative analysis with similar solutions obtained earlier in literature is made

Cosmological parameters of f(R) gravity with kinetic scalar curvature

© Published under licence by IOP Publishing Ltd. We study modified f(R) gravity theory with kinetic scalar curvature reducible to chiral cosmological model of a special type. New method of cosmological parameters calculation based on reduction of two-fields model to standard one with single scalar field is proposed. Parametric correspondence to observational data is shown for massive scalar field, power-law and intermediate inflation