Searcharxiv⌕ Search

arXiv subjects

S. V. Chervon

Publications and source records attributed to S. V. Chervon.

At least 19 recordsLinked to original sources
arXiv2026

Corrections to inflationary models induced by non-minimal coupling between scalar field and curvature

In this paper, we consider possible corrections to the characteristics of inflationary models based on a specific parametrization of the non-minimal coupling between the scalar field and curvature. At the inflationary stage, these corrections lead to a deformation of the scalar field potential and a corresponding deviation in the determination of the cosmological perturbation parameters. At the same time, it is shown that the proposed parametrization yields a description of the reheating stage dynamics completely analogous to the case of Einstein gravity with minimal coupling between the scalar field and curvature. For a model-independent analysis of inflationary corrections induced by a non-minimal coupling, a classification of inflationary scenarios based on the expansion in series of the dependence of the tensor-to-scalar ratio on the spectral index of scalar perturbations is considered. It is also shown that this approach allows for the inclusion of well-known inflationary models as special cases.

gr-qc↗
arXiv2025

The scalar-torsion gravity corrections in the first-order inflationary models

The corrections to the cosmological models induced by non-minimal coupling between scalar field and torsion are considered. To determine these corrections in explicit form, the power-law parametrization of these corrections are proposed. The estimates of possible influence of non-minimal coupling between scalar field and torsion on cosmological parameters for inflationary models implying linear relation between tensor-to-scalar ratio and spectral index of scalar perturbations are obtained. A procedure for verifying these inflationary models due to the observational constraints on the values of cosmological perturbation parameters is also considered.

gr-qc↗
arXiv2024

Reconstruction the scalar-torsion gravity version from the frame of exact cosmological solutions

We consider cosmological models based on the scalar-torsion gravity implying non-minimal coupling between torsion and the scalar field with certain relations between model's parameters. Based on observational constraints on the values of the parameters of cosmological perturbations, the type of the coupling was determined. It was noted that any inflationary models constructed on the basis of the proposed approach can be verified by observational constraints.

gr-qc↗
arXiv2024

Dynamical system analysis in modified Galileon cosmology

In this paper, we have investigated the phase space analysis in modified Galileon cosmology, where the Galileon term is considered a coupled scalar field, $F(ϕ)$. We focus on the exponential type function of $F(ϕ)$ and the three well-motivated potential functions $V(ϕ)$. We obtain the critical points of the autonomous system, along with their stability conditions and cosmological properties. The critical points of the autonomous system describe different phases of the Universe. In the results of our analysis, we have found the scaling solution for critical points, which determine different evolutionary eras for the Universe. The dark-energy-dominated critical points show stable behavior and indicate the Universe's late-time cosmic acceleration phase. Further, the results are examined with the cosmological data sets of the Hubble rate $H(z)$ and the Supernovae Ia.

gr-qc↗
arXiv2023

Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions

All non-equivalent solutions of vacuum Maxwell equations are found for the case when space-time manifolds admit simply transitive four-parameter groups of motions $G_4(N)$. The potentials of the admissible electromagnetic fields admit the existence of the algebra of motion integrals of the Hamilton-Jacobi and Klein-Gordon-Fock equations which is isomorphic to the algebra of the group operators for the same group $G_4(N)$

math-ph↗
arXiv2023

Modified inflationary models based on scalar-torsion gravity

In this work, we consider the corrections to the cosmological models based on the teleparralel equivalent of general relativity and the scalar-torsion gravity implying non-minimal coupling between scalar field and torsion. To determine these corrections, we consider a power-law parameterization of the deviations between teleparralel equivalent of general relativity and the scalar-torsion gravity. The impact of these deviations on cosmological dynamics, scalar field potential and parameters of cosmological perturbations is considered for different inflationary models.

gr-qc↗
arXiv2022

New method of exponential potentials reconstruction based on given scale factor in phantonical two-field models

We investigate two-field cosmological model with phantom and canonical fields (phantonical model as a generalisation of the quintom model for global universe evolution, including early inflationary stage). The model is represented as the chiral cosmological model with the target space conformal to 2D pseudo-Euclidean space. We found three sorts of exact solutions for a constant potential by direct integration of dynamic equations and proposed new method of exact solution construction also extended for e-folds N-formalism for the case of non-constant exponential potential. We show that the exact solutions of cosmological dynamic equations can be obtained in explicit form for any type of scale factor evolution $a(t)$ which implies the explicit inverse dependence $t=t(a)$, considering the quasi de Sitter expansion of the universe with non-negligible kinetic energies of scalar fields and showing that the appeared effective cosmological constant can be considered as the source of second accelerated expansion of the universe. Further we analyze cosmological perturbations in the two-field model under consideration reducing it to the single field one. Such transition give us the way of cosmological parameters calculation and comparison them to observational data. We find that in proposed two-field cosmological model the isocurvature perturbations are negligible, and observable curvature perturbations are induced by adiabatic modes only. The series of phantonical models based on exact inflationary solutions are represented, and it is shown the correspondence to observational data for these models.

gr-qc↗
arXiv2020

Exact and slow-roll solutions for exponential power-law inflation connected with f(R) gravity and observational constraints

We investigate an ability of the exponential power-law inflation to be phenomenologically correct model of the early universe. GR scalar cosmology equations we study in Ivanov-Salopek-Bond (or Hamilton-Jacobi like) representation where the Hubble parameter $H$ is the function of a scalar field $ϕ$. Such approach admits calculation of the potential for given $H(ϕ)$ and consequently reconstruction of $f(R)$ gravity in parametric form. By this manner the Starobinsky potential and non-minimal Higgs potential (and consequently the corresponding $f(R)$ gravity) were reconstructed using constraints on model's parameters. Also comparison to observation (PLANCK 2018) data shows that both models give correct values for scalar spectral index and tensor-to-scalar ratio under wide range of exponential-power-law model's parameters.

gr-qc↗
arXiv2020

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

We describe how to reconstruct generalized scalar-tensor gravity (GSTG) theory, which admits exact solutions for physical type of the 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 a priori specified relation between the Hubble parameter $H$ and a function of non-minimal coupling $F=1+δF$ as $H\propto\sqrt{F}$. Deviations from Einstein gravity $δF$ induce a corresponding deviations of the potential $δV$ from a constant value and modify the dynamics from 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 consideration allows us to substitute the physical potential into obtained equations and then to calculate the non-minimal coupling function and kinetic term that are define GSTG parameters. With this method, we reconstruct GSTG for polynomial, exponential, Higgs, Higgs-Starobinsky and Coleman-Weinberg potentials. Special attention we pay to parameters of cosmological perturbations and prove correspondence obtained solutions to observational data from Planck.

gr-qc↗
arXiv2019

Superpotential method for chiral cosmological models connected with modified gravity

We consider the Chiral Cosmological Models (CCMs) and modified gravity theories associated with them. Generalization of the superpotential method for a general CCM with several scalar fields is performed, and the method of construction CCMs admitting exact solutions is developed. New classes of exact solutions in the two-component CCM connected with an $f(R)$ gravity model with an additional scalar field have been constructed. We construct new cosmological solutions for a diagonal metric of the target space, including modified power-law solutions. In particular, we propose the reconstruction procedure based on the superpotential method and present examples of kinetic part reconstruction for periodic and hyperbolic Hubble parameters. We also focus on a cyclic type of Universe dubbed the Quasi-Steady State (QSS) model, with the aim of constructing single- and double-field potentials for one and the same behaviour of the Hubble parameter using the developed superpotential method for the CCM. The realization of this task includes a new set of solutions for a CCM with a scale factor characterized by the QSS theory. We also propose a method for reducing the two-field CCM to the single scalar field model.

gr-qc↗
arXiv2018

Kinetic Scalar Curvature Extended $f(R)$ Gravity

In this work we study a modified version of vacuum $f(R)$ gravity with a kinetic term which consists of the first derivatives of the Ricci scalar. We develop the general formalism of this kinetic Ricci modified $f(R)$ gravity and we emphasize on cosmological applications for a spatially flat cosmological background. By using the formalism of this theory, we investigate how it is possible to realize various cosmological scenarios. Also we demonstrate that this theoretical framework can be treated as a reconstruction method, in the context of which it is possible to realize various exotic cosmologies for ordinary Einstein-Hilbert action. Finally, we derive the scalar-tensor counterpart theory of this kinetic Ricci modified $f(R)$ gravity, and we show the mathematical equivalence of the two theories.

gr-qc↗
arXiv2017

Exact solutions for scalar field cosmology in f(R) gravity

We look for exact solutions in scalar field cosmology. To achieve this we use $f(R)$ modified gravity with a scalar field and do not specify the the form of the $f(R)$ function. In particular, we study Friedmann universe assuming that acceleration of the scalar curvature is negligible. We first present solutions for special cases and then the general solution. Using initial conditions which represent the universe at the present epoch, we evaluated the constants of integration. This allows for the comparison of the scale factor in the new solutions with that of the $ΛCDM$ solution, thereby affecting the age of the universe in $f(R)$ gravity.

gr-qc↗
arXiv2014

Chiral Cosmological Models: Dark Sector Fields Description

The present review is devoted to a Chiral Cosmological Model as the self-gravitating nonlinear sigma model with the potential of (self)interactions employed in cosmology. The chiral cosmological model has successive applications in descriptions of the inflationary epoch of the Universe evolution; the present accelerated expansion of the Universe also can be described by the chiral fields multiplet as the dark energy in wide sense. To be more illustrative we are often addressed to the two-component chiral cosmological model. Namely, the two-component chiral cosmological model describing the phantom field with interaction to a canonical scalar field is analyzed in details. New generalized model of quintom character is proposed and exact solutions are founded out. In the review we represented the perturbation theory for chiral cosmological model with the aim to describe the structure formation using the progress achieved in the inflation theory. It was shown that cosmological perturbations from chiral fields can be decomposed for inflaton and the dark sector perturbations. The two-component model is investigated in details, the general solution for shortwave approximation is obtained and analyzed for power law Universe expansion. New issue for understanding the features of Universe evolution is proposed by consideration of the dark sector fields on the inflaton background. The results are illustrated for the solutions in the long-wave approximation.

gr-qc↗
arXiv2013

An Emergent Universe with Dark Sector Fields in a Chiral Cosmological Model

We consider the emergent universe scenario supported by a chiral cosmological model with two interacting dark sector fields: phantom and canonical. We investigate the general properties of the evolution of the kinetic and potential energies as well as the development of the equation of state with time. We present three models based on asymptotic solutions and investigate the phantom part of the potential and chiral metric components. The exact solution corresponding to a global emergent universe scenario, starting from the infinite past and evolving to the infinite future, has been obtained for the first time for a chiral cosmological model. The behavior of the chiral metric components responsible for the kinetic interaction between the phantom and canonical scalar fields has been analyzed as well.

gr-qc↗
arXiv2013

Exact Global Phantonical Solutions in the Emergent Universe

We present new classes of exact solutions for an Emergent Universe supported by phantom and canonical scalar fields in the framework of a two-component chiral cosmological model. We outline in detail the method of deriving exact solutions, discuss the potential and kinetic interaction for the model and calculate key cosmological parameters. We suggest that this this model be called a {\it phantonical Emergent Universe} because of the necessity to have phantom and canonical chiral fields. The solutions obtained are valid for all time.

gr-qc↗
arXiv2011

Mathematical Physics : Problems and Solutions of The Students Training Contest Olympiad in Mathematical and Theoretical Physics (May 21st - 24th, 2010)

The present issue of the series < > represents the Proceedings of the Students Training Contest Olympiad in Mathematical and Theoretical Physics and includes the statements and the solutions of the problems offered to the participants. The contest Olympiad was held on May 21st-24th, 2010 by Scientific Research Laboratory of Mathematical Physics of Samara State University, Steklov Mathematical Institute of Russia's Academy of Sciences, and Moscow Institute of Physics and Technology (State University) in cooperation. The present Proceedings is intended to be used by the students of physical and mechanical-mathematical departments of the universities, who are interested in acquiring a deeper knowledge of the methods of mathematical and theoretical physics, and could be also useful for the persons involved in teaching mathematical and theoretical physics.

math-ph↗
arXiv2009

Wormholes supported by chiral fields

We consider static, spherically symmetric solutions of general relativity with a nonlinear sigma model (NSM) as a source, i.e., a set of scalar fields $Φ= (Φ^1,...,Φ^n)$ (so-called chiral fields) parametrizing a target space with a metric $h_{ab}(Φ)$. 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 $h_{ab}$. If the matrix $h_{ab}$ 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.

gr-qc↗