arXiv subjects

Sergey Yu. Vernov

Publications and source records attributed to Sergey Yu. Vernov.

At least 19 recordsLinked to original sources

arXiv2026

Integrability of $R^2$ gravity cosmological models with radiation

We consider cosmological $R^2$ gravity models with radiation. We find the general solution to the trace equation $\Box R=0$ in the spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. We analyze possible evolution of the Hubble parameter depending on the sign of the radiation energy density and find conditions for the existence of a bounce solution. A scalar field Lagrangian with the induced gravity term and the fourth-order monomial potential can play a role of radiation. In this case, we also obtain the general solution to the field equation. Therefore, the resulting $R^2$ gravity model with a scalar field is integrable in the spatially flat FLRW metric. Using a conformal metric transformation, we obtain a two-field chiral cosmological model that is also integrable in the spatially flat FLRW metric.

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arXiv2025

Inflation in $F(R)$ gravity models revisited after ACT

The $F(R)$ gravity models of inflation are revisited in light of the recent observations of cosmic microwave background radiation by Atacama Cosmology Telescope (ACT) and DESI Collaboration. A detailed study of the evolution equations in the Jordan frame is given and a new description of the slow-roll approximation in the $F(R)$-gravity-based models of inflation is proposed. It is found that all those models of inflation are significantly constrained by demanding a higher (than the Planck Telescope value) cosmological tilt $n_s$ of scalar perturbations and a positive running index $\alpha_s$ favored by ACT. It is not difficult to meet the ACT constraints on the scalar tilt $n_s$ by modifying the existing models of inflation, but simultaneously demanding a positive running $\alpha_s$ would rule out many of them. Using the proposed slow-roll approximation in the Jordan frame, we provide a new modification of the Starobinsky inflation model in the framework of $F(R)$ gravity, which satisfies all ACT constraints. An extension of our ACT-consistent inflation model to the unified $F(R)$-gravity description of Starobinsky-like inflation and production of primordial black holes on a smaller scale is also proposed.

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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

Superpotential method and the amplification of inflationary perturbations

The superpotential method is a reconstruction technique which has proven useful to build exact cosmological solutions. We here employ the superpotential method in order to reconstruct the features necessary for the inflaton potential to drive inflation and lead to the amplification of the curvature perturbations. Such an amplification, at wavelengths shorter than those observed in the cosmic microwave background, is necessary in order to have a significant formation of primordial black holes after inflation ends. The technique is applied to the cases of a minimally coupled inflaton, to the nonminimal coupling case and to $f(R)$ theories of gravity. For such theories, a model dependent analysis of the features leading to the scalar spectrum enhancement is also presented.

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arXiv2024

New Integrable Chiral Cosmological Models with Two Scalar Fields

We construct integrable chiral cosmological models with two scalar fields and potentials represented in terms of hyperbolic functions. Using the conformal transformation of the metric and the corresponding models with induced gravity terms, we obtain the general solutions in the spatially flat, open and closed Friedmann universes and the corresponding integrals of motion. The obtained general solutions can be written in terms of the Jacobi elliptic functions of the conformal time.

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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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arXiv2024

Construction of Chiral Cosmological Models Unifying Inflation and Primordial Black Hole Formation

We propose the method for construction of $F(R,ξ)$ gravity model, unifying inflation and primordial black hole formation. The proposed models are based on the Starobinsky $R+R^2$ inflationary model, so, the function $F(R,ξ)$ is a quadratic polynomial of the Ricci scalar $R$. We show that the potential of the corresponding two-field chiral cosmological model in the Einstein frame can be always found in terms of the elementary functions. The special choice of the function $F(R,ξ)$ allows us to get such a generalization of the hybrid inflation that can describe both inflation, and the primordial black hole formation.

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arXiv2023

Anisotropic solutions for $R^2$ 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.

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arXiv2023

New one-parametric extension of the Starobinsky inflationary model

We propose a one-parametric extension of the Starobinsky $R+R^2$ model by adding the $(R+m^2β^2)^{3/2}$ term. The parameter $m$ is the inflaton mass, which is determined in the same way as in the Starobinsky model, and $β$ is a dimensionless constant. Using the Einstein frame and the scalar field potential, we get the inflationary parameters of the model proposed. The value of the tensor-to-scalar ratio $r$ can be significantly larger than in the Starobinsky model. The considered inflationary model is in a good agreement with the current observational data. The corresponding scalar field potential is a polynomial of the exponential function.

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arXiv2022

On the superstring-inspired quantum correction to the Starobinsky model of inflation

Superstring/M-theory is the theory of quantum gravity that can provide the UV-completion to viable inflation models. We modify the Starobinsky inflation model by adding the Bel-Robinson tensor $T^{μνλρ}$ squared term proposed as the leading quantum correction inspired by superstring theory. The $(R+\frac{1}{6m^2}R^2 -\fracβ{8m^6}T^2)$ model under consideration has two parameters: the inflaton mass $m$ and the string-inspired positive parameter $β$. We derive the equations of motion in the Friedmann-Lemaitre-Robertson-Walker universe and investigate its solutions. We find the physical bounds on the value of the parameter $β$ by demanding the absence of ghosts and consistency of the derived inflationary observables with the measurements of the cosmic microwave background radiation.

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arXiv2022

Analytic extensions of Starobinsky model of inflation

We study several extensions of the Starobinsky model of inflation, which obey all observational constraints on the inflationary parameters, by demanding that both the inflaton scalar potential in the Einstein frame and the $F(R)$ gravity function in the Jordan frame have the explicit dependence upon fields {\it and} parameters in terms of elementary functions. Our models are continuously connected to the original Starobinsky model via changing the parameters. We modify the Starobinsky $(R+R^2)$ model by adding an $R^3$-term, an $R^4$-term, and an $R^{3/2}$-term, respectively, and calculate the scalar potentials, the inflationary observables and the allowed limits on the deformation parameters by using the latest observational bounds. We find that the tensor-to-scalar ratio in the Starobinsky model modified by the $R^{3/2}$-term significantly increases with raising the parameter in front of that term. On the other side, we deform the scalar potential of the Starobinsky model in the Einstein frame in powers of $y=\exp\left(-\sqrt{\frac{2}{3}}ϕ/M_{Pl}\right)$, where $ϕ$ is the canonical inflaton (scalaron) field, calculate the corresponding $F(R)$ gravity functions in the two new cases, and find the restrictions on the deformation parameters in the lowest orders with respect to the variable $y$ that is physically small during slow-roll inflation.

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arXiv2021

Integrable modified gravity cosmological models with an additional scalar field

We consider modified gravity cosmological models that can be transformed into two-field chiral cosmological models by the conformal metric transformation. For the $R^2$ gravity model with an additional scalar field and the corresponding two-field model with the cosmological constant and nonstandard kinetic part of the action, the general solutions have been obtained in the spatially flat FLRW metric. We analyze the correspondence of the cosmic time solutions obtained and different possible evolutions of the Hubble parameters in the Einstein and Jordan frames.

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arXiv2021

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 $r$.

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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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arXiv2019

Reconstruction Procedure for Nonlocal Gauss-Bonnet Models

We investigate the cosmological dynamics of nonlocally corrected gravity involving a function of the inverse d'Alembertian acting on the Gauss-Bonnet term. Casting the dynamical equations in local form, we derive the reconstruction procedure. We find conditions on the model parameters that are sufficient for the existence of de Sitter solutions and obtain these solutions explicitly.

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arXiv2018

Duality between static spherically or hyperbolically symmetric solutions and cosmological solutions in scalar-tensor gravity

We study static spherically and hyperbolically symmetric solutions of the Einstein equations in the presence of a conformally coupled scalar field and compare them with those in the space filled with a minimally coupled scalar field. We then study the Kantowski-Sachs cosmological solutions, which are connected with the static solutions by the duality relations. The main ingredient of these relations is an exchange of roles between the radial and the temporal coordinates, combined with the exchange between the spherical and hyperbolical two-dimensional geometries. A brief discussion of questions such as the relation between the Jordan and the Einstein frames and the description of the singularity crossing is also presented.

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arXiv2017

Bianchi-I cosmological model and crossing singularities

We consider a rather simple method for the description of the Big Bang - Big Crunch cosmological singularity crossing. For the flat Friedmann universe this method gives the same results as more complicated methods, using Weyl symmetry or the transitions between the Jordan and Einstein frames. It is then easily generalized for the case of a Bianchi-I anisotropic universe. We also present early-time and late-time asymptotic solutions for a Bianchi-I universe, filled with a conformally coupled massless scalar field.

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