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B. Dragovich

Publications and source records attributed to B. Dragovich.

14 recordsLinked to original sources
arXiv2022

On the Schwarzschild-de Sitter metric of nonlocal de Sitter gravity

Earlier constructed a simple nonlocal de Sitter gravity model has a cosmological solution in a very good agreement with astronomical observations. In this paper, we continue the investigation of the nonlocal de Sitter model of gravity, focusing on finding an appropriate solution for the Schwarzschild-de Sitter metric. We succeeded to solve the equations of motion in a certain approximation. The obtained approximate solution is of particular interest for examining the possible role of non-local de Sitter gravity in describing the effects in galactic dynamics that are usually attributed to dark matter.

gr-qc↗
arXiv2020

Some Cosmological Solutions of a New Nonlocal Gravity Model

In this paper, we investigate a nonlocal modification of general relativity (GR) with action $S = \frac{1}{16πG} \int [ R- 2Λ+ (R-4Λ) \, \mathcal{F}(\Box) \, (R-4Λ) ] \, \sqrt{-g}\; d^4x ,$ where $\mathcal{F} (\Box) = \sum_{n=1}^{+\infty} f_n \Box^n$ is an analytic function of the d'Alembertian $\Box$. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if $Λ\neq 0, \, k = 0,$ and they have not analogs in Einsten's gravity with cosmological constant $Λ$. One of these two solutions is $ a (t) = A \, \sqrt{t} \, e^{\fracΛ{4} t^2} ,$ that mimics properties similar to an interference between the radiation and the dark energy. Another solution is a nonsingular bounce one -- $ a (t) = A \, e^{Λt^2}$. For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator $\mathcal{F}(\Box)$, which satisfies obtained necessary conditions.

gr-qc↗
arXiv2019

Cosmological Solutions of a Nonlocal Square Root Gravity

In this paper we consider modification of general relativity extending $R - 2 Λ$ by nonlocal term of the form $\sqrt{R-2Λ}\, \mathcal{F}(\Box)\, \sqrt{R-2Λ} ,$ where $\mathcal{F}(\Box)$ is an analytic function of the d'Alembert operator $\Box$. We have found some exact cosmological solutions of the corresponding equations of motion without matter and with $Λ\neq 0$. One of these solutions is $ a (t) = A \, t^{\frac{2}{3}} \, e^{\fracΛ{14} t^2} ,$ which imitates properties similar to an interplay of the dark matter and the dark energy. For this solution we calculated some cosmological parameters which are in a good agreement with observations. This nonlocal gravity model has not the Minkowski space solution. We also found several conditions which function $\mathcal{F}(\Box)$ has to satisfy.

gr-qc↗
arXiv2019

Cosmology of non-local f(R) gravity

We consider a modification of GR with a special type of a non-local f(R). The structure of the non-local operators is motivated by the string field theory and p-adic string theory. The spectrum is derived explicitly and the ghost-free condition for the model is formulated. We pay special attention to the classical stability of the de Sitter solution in our model and formulate the conditions on the model parameters to have a stable configuration. Relevance of unstable configurations for the description of the de Sitter phase during inflation is specifically discussed.

hep-th↗
arXiv2017

$p$-Adic Mathematical Physics: The First 30 Years

$p$-Adic mathematical physics is a branch of modern mathematical physics based on the application of $p$-adic mathematical methods in modeling physical and related phenomena. It emerged in 1987 as a result of efforts to find a non-Archimedean approach to the spacetime and string dynamics at the Planck scale, but then was extended to many other areas including biology. This paper contains a brief review of main achievements in some selected topics of $p$-adic mathematical physics and its applications, especially in the last decade. Attention is mainly paid to developments with promising future prospects.

math-ph↗
arXiv2013

New Cosmological Solutions in Nonlocal Modified Gravity

We consider some cosmological aspects of nonlocal modified gravity with $Λ$ term, where nonlocality is of the type $R \mathcal{F}(\Box) R$. Using ansatz of the form $\Box R = r R +s,$ we find a few a(t) nonsingular bounce cosmological solutions for all three values of spatial curvature parameter k. We also discuss this modified gravity model from F(R) theory point of view.

gr-qc↗
arXiv2005

On decoherence in noncommutative plane with perpendicular magnetic field

In the last years noncommutative quantum mechanics has been investigated intensively. We consider the influence of magnetic field on decoherence of a system in the noncommutative quantum plane. Particularly, we point out a model in which the magnetic field allows {\it in situ} dynamical control of decoherence as well as, in principle, observation of noncommutativity.

quant-ph↗
arXiv2002

Adelic Path Integrals for Quadratic Lagrangians

Feynman's path integral in adelic quantum mechanics is considered. The propagator K(x'',t'';x',t') for one-dimensional adelic systems with quadratic Lagrangians is analytically evaluated. Obtained exact general formula has the form which is invariant under interchange of the number fields R and Q_p.

hep-th↗
arXiv2002

p-Adic and Adelic Minisuperspace Quantum Cosmology

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle-Hawking proposal does not work in models with matter fields. p-Adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few minisuperspace cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

gr-qc↗
arXiv2001

Adelic Quantum Mechanics: Nonarchimedean and Noncommutative Aspects

We present a short review of adelic quantum mechanics pointing out its non-Archimedean and noncommutative aspects. In particular, $p$-adic path integral and adelic quantum cosmology are considered. Some similarities between $p$-adic analysis and q-analysis are noted. The $p$-adic Moyal product is introduced.

hep-th↗
arXiv2000

Some p-adic differential equations

We investigate various properties of p-adic differential equations which have as a solution an analytic function of the form $F_k (x) = \sum_{n\geq 0} n! P_k (n) x^n$, where $P_k (n) = n^k + C_{k-1} n^{k-1} + ...+ C_0$ is a polynomial in n with $C_i\in Z$ (in a more general case $C_i\in Q$ or $C_i\in C_p$). For some special classes of $P_k (n)$, as well as for the general case, the existence of the corresponding linear differential equations of the first- and second-order for $F_k (x)$, is shown. In some cases such equations are constructed. For the second-order differential equations there is no other analytic solution of the form $\sum a_n x^n$. Due to the fact that the corresponding inhomogeneous first-order differential equation exists one can construct infinitely many inhomogeneous second-order equations with the same analytic solution. Relation to some rational sums with the Bernoulli numbers and to $F_k (x)$ for some $x\in Z$ is considered. Some of these differential equations can be related to p-adic dynamics and p-adic information theory.

math-ph↗
arXiv2000

p-Adic Path Integrals for Quadratic Actions

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude ${\cal K}_p (x^{\prime\prime},t^{\prime\prime}; x^\prime,t^\prime)$ for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.

math-ph↗
arXiv2000

p-Adic and Adelic Free Relativistic Particle

We consider spectral problem for a free relativistic particle in p-adic and adelic quantum mechanics. In particular, we found p-adic and adelic eigenfunctions. Within adelic approach there exist quantum states that exhibit discrete structure of spacetime at the Planck scale.

hep-th↗