arXiv subjects

Alexey V. Toporensky

Publications and source records attributed to Alexey V. Toporensky.

16 recordsLinked to original sources

arXiv2026

Slow-roll approximations for Gauss-Bonnet inflation revisited

In our paper we consider the validity of slow-roll approximations for Gauss-Bonnet inflation introduced in [1]. In contrast to the cited paper where the coupling function before the Gauss-Bonnet term have been chosen as a decaying function of the scalar field, here we consider growing coupling functions. We have found that while in [1] new slow-roll approximations work considerably better, now they do not increase the precision. Moreover, we identify some cases where more involved approximations work worse than the standard one. Corresponding explanations of such a situation are given.

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arXiv2025

More accurate slow-roll approximations for inflation in scalar-tensor theories

We propose new versions of the slow-roll approximation for inflationary models with nonminimally coupled scalar fields. We derive more precise expressions for the standard slow-roll parameters as functions of the scalar field. To verify the accuracy of the proposed approximations, we consider inflationary models with the induced gravity term and the fourth-order monomial potential. For specific values of the model parameters, this model is the well-known Higgs-driven inflationary model. We investigate the inflationary dynamics in the Jordan frame and come to the conclusion that the proposed versions of the slow-roll approximation are not only more accurate at the end of inflation, but also give essentially more precise estimations for the tensor-to-scalar ratio $r$ and the amplitude of scalar perturbations $A_s$.

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arXiv2024

New slow-roll approximations for inflation in Einstein-Gauss-Bonnet gravity

We propose new slow-roll approximations for inflationary models with the Gauss-Bonnet term. We find more accurate expressions of the standard slow-roll parameters as functions of the scalar field. To check the accuracy of approximations considered we construct inflationary models with quadratic and quartic monomial potentials and the Gauss-Bonnet term. Numerical analysis of these models indicates that the proposed inflationary scenarios do not contradict to the observation data. New slow-roll approximations show that the constructed inflationary models are in agreement with the observation data, whereas one does not get allowed observational parameters at the same values of parameters of the constructed models in the standard slow-roll approximation.

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arXiv2021

Spin connection and cosmological perturbations in scalar-torsion gravity

In this paper we generalize our previous results on spin connection for the linear scalar cosmological perturbation in $f(T)$ theory to wider class of theories which includes a scalar field $Φ$ non-minimally coupled to torsion, and allows $Φ$-dependence of the function $f$. The case of $f_{TT}=0$, with a scalar field non-minimally coupled to torsion needs a special treatment. In both considered cases we derive self-consistent equations of motion for cosmological perturbation using a solution for non-trivial spin connection.

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arXiv2021

Anisotropic cosmological dynamics in $f(T)$ gravity in the presence of a perfect fluid

We consider the cosmological evolution of a flat anisotropic Universe in $f(T)$ gravity in the presence of a perfect fluid. It is shown that the matter content of the Universe has a significant impact of the nature of a cosmological singularity in the model studied. Depending on the parameters of the $f(T)$ function and the equation of state of the perfect fluid in question the well-known Kasner regime of general relativity can be replaced by a new anisotropic solution, or by an isotropic regime, or the cosmological singularity changes its nature to a non-standard one with a finite values of Hubble parameters. Six possible scenarios of the cosmological evolution for the model studied have been found numerically.

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arXiv2021

Bouncing solutions in $f(T)$ gravity

We consider certain aspects of cosmological dynamics of a spatially curved Universe in $f(T)$ gravity. Local analysis allows us to find conditions for bounces and for static solutions; these conditions appear to be in general less restrictive than in general relativity. We also provide a global analysis of the corresponding cosmological dynamics in the cases when bounces and static configurations exist, by constructing phase diagrams. These diagrams indicate that the fate of a big contracting Universe is not altered significantly when bounces become possible, since they appear to be inaccessible by a sufficiently big Universe.

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arXiv2020

Inflation with a quartic potential in the framework of Einstein-Gauss-Bonnet gravity

We investigate inflationary dynamics in the framework of the Einstein-Gauss-Bonnet gravity. In the model under consideration, the inflaton field is non-minimally coupled to the Gauss-Bonnet curvature invariant, so that the latter appears to be dynamically important. We consider a quartic potential for the inflaton field, in particular the one asymptotically connected to the Higgs inflation, and a wider class of coupling functions not considered in the earlier work. Keeping in mind the observational bounds on the parameters - the amplitude of scalar perturbations $A_s$, spectral index $n_s$ and tensor-to-scalar ratio $r$, we demonstrate that the model a quartic potential and the proposed coupling function is in agreement with observation.

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arXiv2019

Stability analysis of de Sitter solutions in models with the Gauss-Bonnet term

We investigate the scalar field dynamics of models with nonminimally coupled scalar fields in the presence of the Gauss-Bonnet term and derive the structure of the effective potential and conditions for stable de Sitter solutions in general. Specializing to specific couplings, we explore the possibility of realizing the stable de Sitter configurations which may have implications for both the early Universe and late time evolution.

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arXiv2018

Initial conditions for Inflation in an FRW Universe

We examine the class of initial conditions which give rise to inflation. Our analysis is carried out for several popular models including: Higgs inflation, Starobinsky inflation, chaotic inflation, axion monodromy inflation and non-canonical inflation. In each case we determine the set of initial conditions which give rise to sufficient inflation, with at least $60$ e-foldings. A phase-space analysis has been performed for each of these models and the effect of the initial inflationary energy scale on inflation has been studied numerically. This paper discusses two scenarios of Higgs inflation: (i) the Higgs is coupled to the scalar curvature, (ii) the Higgs Lagrangian contains a non-canonical kinetic term. In both cases we find Higgs inflation to be very robust since it can arise for a large class of initial conditions. One of the central results of our analysis is that, for plateau-like potentials associated with the Higgs and Starobinsky models, inflation can be realised even for initial scalar field values which lie close to the minimum of the potential. This dispels a misconception relating to plateau potentials prevailing in the literature. We also find that inflation in all models is more robust for larger values of the initial energy scale.

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arXiv2018

On Kasner solution in Bianchi I $f(T)$ cosmology

Recently cosmological dynamics of anisotropic Universe in $f(T)$ gravity became an area of intense investigations. Some earlier papers devoted to this issue contain contradictory claims about the nature and propertied of vacuum solutions in this theory. The goal of the present paper is to clarify this situation. We compare properties of $f(T)$ and $f(R)$ vacuum solutions and outline differences between them. The Kasner solution appears to be an exact solution for the $T=0$ branch, and an asymptotic solution for $T \ne 0$ branch. It is shown that Kasner solution is the past attractor if $T<0$, being past and future attractor for $T>0$ branch.

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arXiv2016

Possible evolution of a bouncing universe in cosmological models with non-minimally coupled scalar fields

We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble parameter of the bounce solution essentially depends on the sign of the cosmological constant.

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arXiv2014

Global stability analysis for cosmological models with non-minimally coupled scalar fields

We explore dynamics of cosmological models with a nonminimally coupled scalar field evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models including the Hilbert-Einstein curvature term and the $N$ degree monomial of the scalar field nonminimally coupled to gravity. The potential of the scalar field is the $n$ degree monomial or polynomial. We describe several qualitatively different types of dynamics depending on values of power indices $N$ and $n$. We identify that three main possible pictures correspond to $n 2N$ cases. Some special features connected with the important cases of $N=n$ (including the quadratic potential with quadratic coupling) and $n=2N$ (which shares its asymptotics with the potential of the Higgs-driven inflation) are described separately. A global qualitative analysis allows us to cover the most interesting cases of small $N$ and $n$ by a limiting number of phase-space diagrams. The influence of the cosmological constant to the global features of dynamics is also studied.

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arXiv2014

Asymptotic solutions in f(R)-gravity

We study cosmological solutions in $R + βR^{N}$-gravity for an isotropic Universe filled with ordinary matter with the equation of state parameter $γ$. Using the Bogolyubov-Krylov-Mitropol'skii averaging method we find asymptotic oscillatory solutions in terms of new functions, which have been specially introduced by us for this problem and appeared as a natural generalization of the usual sine and cosine. It is shown that the late-time behaviour of the Universe in the model under investigation is determined by the sign of the difference $γ-γ_{crit}$ where $γ_{crit}=2N/(3N-2)$. If $γ< γ_{crit}$, the Universe reaches the regime of small oscillations near values of Hubble parameter and matter density, corresponding to General Relativity solution. Otherwise higher-curvature corrections become important at late times. We also study numerically basins of attraction for the oscillatory and phantom solutions, which are present in the theory for $N>2$. Some important differences between $N=2$ and $N>2$ cases are discussed.

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arXiv2012

Stable super-inflating cosmological solutions in f(R)-gravity

We consider super-inflating solutions in modified gravity for several popular families of $f(R)$ functions. Using scalar field reformulation of $f(R)$-gravity we describe how the form of effective scalar field potential can be used for explaining existence of stable super-inflation solutions in the theory under consideration. Several new solutions of this type have been found analytically and checked numerically.

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arXiv2012

Cosmological dynamics of fourth order gravity with a Gauss-Bonnet term

We consider cosmological dynamics in fourth order gravity with both $f(R)$ and $Φ(\mathcal {G})$ correction to the Einstein gravity ($\mathcal{G}$ is the Gauss-Bonnet term). The particular case for which both terms are equally important on power-law solutions is described. These solutions and their stability are studied using the dynamical system approach. We also discuss condition of existence and stability of de Sitter solution in a more general situation of power-law $f$ and $Φ$.

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arXiv2006

Regular and Chaotic Regimes in Scalar Field Cosmology

A transient chaos in a closed FRW cosmological model with a scalar field is studied. We describe two different chaotic regimes and show that the type of chaos in this model depends on the scalar field potential. We have found also that for sufficiently steep potentials or for potentials with large cosmological constant the chaotic behavior disappears.

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