Analytical approximation for <ϕ2>< \phi^2 > of a quantized scalar field in ultrastatic asymptotically flat spacetimes

Analytical approximations for of a quantized scalar field in ultrastatic asymptotically flat spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero or nonzero temperature vacuum state. The expression for is divided into low- and high-frequency parts. The expansion for the high-frequency contribution to this quantity is obtained. This expansion is analogous to the DeWitt-Schwinger one. As an example, the low-frequency contribution to $$ is calculated on the background of the small perturbed flat spacetime in a quantum state corresponding to the Minkowski vacuum at the asymptotic. The limits of the applicability of these approximations are discussed.Comment: revtex4, 9 page

Quantum-corrected ultraextremal horizons and validity of WKB in massless limit

We consider quantum backreaction of the quantized scalar field with an arbitrary mass and curvature coupling on ultraextremal horizons. The problem is distinguished in that (in contrast to non-extremal or extremal black holes) the WKB approximation remains valid near $r_{+}$ (which is the radius of the horizon) even in the massless limit. We examine the behavior of the stress-energy tensor of the quantized field near $r_{+}$ and show that quantum-corrected objects under discussion do exist. In the limit of the large mass our results agree with previous ones known in literature.Comment: revtex4, 9 page

Inhomogeneous compact extra dimensions and de Sitter cosmology

In the framework of multidimensional $f(R)$ gravity, we study the metrics of compact extra dimensions assuming that our 4D space has the de Sitter metric. Manifolds described by such metrics could be formed at the inflationary and even higher energy scales. It is shown that in the presence of a scalar field, varying in the extra factor space $\mathbb{M}_2$, it is possible to obtain a variety of inhomogeneous metrics in $\mathbb{M}_2$. Each of these metrics leads to a certain value of the 4D cosmological constant $\Lambda_4$, and in particular, it is possible to obtain $\Lambda_4 =0$, as is confirmed by numerically obtained solutions. A nontrivial scalar field distribution in the extra dimensions is an important feature of this family of models.Comment: 15 pages, 9 figure

Sub-Planckian scale and limits for f(R)f(R) models

We study the Universe evolution starting from the sub-Planckian scale to present times. The requirement for an exponential expansion of the space with the observed metric as a final stage leads to significant restrictions on the parameter values of a $f(R)$-function. An initial metric of the Universe is supposed to be maximally symmetric with the positive curvature

Propagation of Gravitational Waves in Chern-Simons Axion Einstein Gravity

In this paper we shall investigate the propagation of gravitational waves in a flat Friedman-Robertson-Walker background, in the context of a string motivated corrected Einstein gravity. Particularly, we shall consider a misalignment axion Einstein gravity in the presence of a string originating Chern-Simons coupling of the axion field to the Chern-Pontryagin density in four dimensions. We shall focus our study on the propagation of the gravitational waves, and we shall investigate whether there exists any difference in the propagation of the polarization states of the gravitational waves. As we demonstrate, the dispersion relations are different in the Right-handed mode and the Left-handed mode. Finally, we compare the propagation of the axion Chern-Simons Einstein theory with that of standard $F(R)$ gravity.Comment: PRD Accepted. arXiv admin note: text overlap with arXiv:1907.0162

Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes

Analytical approximations for ${}$ and ${}$ of a quantized scalar field in static spherically symmetric spacetimes are obtained. The field is assumed to be both massive and massless, with an arbitrary coupling $\xi$ to the scalar curvature, and in a zero temperature vacuum state. The expressions for ${}$ and ${}$ are divided into low- and high-frequency parts. The contributions of the high-frequency modes to these quantities are calculated for an arbitrary quantum state. As an example, the low-frequency contributions to ${}$ and ${}$ are calculated in asymptotically flat spacetimes in a quantum state corresponding to the Minkowski vacuum (Boulware quantum state). The limits of the applicability of these approximations are discussed.Comment: revtex4, 17 pages; v2: three references adde

Self-force of a point charge in the space-time of a massive wormhole

We consider the self-potential and the self-force for an electrically charged particle at rest in the massive wormhole space-time. We develop general approach for the renormalization of electromagnetic field of such particle in the static space-times and apply it to the space-time of the wormhole with parameter of the mass, $m$. The self-force is found in manifest form; it is an attractive force. We discus the peculiarities due to massive parameter of the wormhole.Comment: 10 pages, 1 figure text correcte

Self-force on a scalar point charge in the long throat

An analytic method is presented which allows for the computation of the self-force for a static particle with a scalar charge in the region of an ultrastatic spacetime which one can call the long throat. The method is based on the approximate WKB solution of a radial mode equation for a scalar field. This field is assumed to be massless, with a coupling $\xi$ to the scalar curvature is satisfying the condition $\xi>1/8$.Comment: 11 pages, 1 figur