arXiv subjects

Ekaterina O. Pozdeeva

Publications and source records attributed to Ekaterina O. Pozdeeva.

At least 19 recordsLinked to original sources

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 $α_s$ 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 $α_s$ 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 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

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

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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arXiv2021

Deviation from Slow-Roll Regime in the EGB Inflationary Models with $r\sim N_e^{-1}$

We consider Einstein-Gauss-Bonnet (EGB) inflationary models using the effective potential approach. We present evolution equations in the slow-roll regime using the effective potential and the tensor-to-scalar ratio. The choice of the effective potential is related to an expression of the spectral index in terms of e-folding number $N_e$. The satisfaction of the slow-roll regime is mostly related to the form of the tensor-to-scalar ratio $r$. The case of $r\sim1/N^2_e$ leads to a generalization of $α$-attractors inflationary parameters to Einstein-Gauss-Bonnet gravity with exponential effective potential. Moreover, the cosmological attractors include models with $r\sim1/N_e$. And we check the satisfaction of the slow-roll regime during inflation for models with $r\sim1/N_e$.

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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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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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arXiv2016

Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.

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arXiv2016

Cosmological attractor inflation from the RG-improved Higgs sector of finite gauge theory

The possibility to construct an inflationary scenario for renormalization-group improved potentials corresponding to the Higgs sector of finite gauge models is investigated. Taking into account quantum corrections to the renormalization-group potential which sums all leading logs of perturbation theory is essential for a successful realization of the inflationary scenario, with very reasonable parameter values. The inflationary models thus obtained are seen to be in good agreement with the most recent and accurate observational data. More specifically, the values of the relevant inflationary parameters, $n_s$ and $r$, are close to the corresponding ones in the $R^2$ and Higgs-driven inflation scenarios. It is shown that the model here constructed and Higgs-driven inflation belong to the same class of cosmological attractors.

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