arXiv subjects

Branko Dragovich

Publications and source records attributed to Branko Dragovich.

At least 19 recordsLinked to original sources

arXiv2024

The Schwarzschild-de Sitter Metric of Nonlocal $\sqrt{dS}$ Gravity

It is already known that a simple nonlocal de Sitter gravity model, which we denote as $\sqrt{dS}$ gravity, contains an exact vacuum cosmological solution which mimics dark energy and dark matter and is in very good agreement with the standard model of cosmology. This success of $\sqrt{dS}$ gravity motivated us to investigate how it works at lower than cosmic scale -- galactic and the solar system. This paper contains our investigation of the corresponding Schwarzschild-de Sitter metric of the $\sqrt{dS}$ gravity model. To get exact solution, it is necessary to solve the corresponding nonlinear differential equation, what is a very complicated and difficult problem. What we obtained is a solution of linearized equation, which is related to space metric far from the massive body, where gravitational field is weak. The obtained approximate solution is of particular interest for examining the possible role of non-local de Sitter gravity $\sqrt{dS}$ in describing the effects in galactic dynamics that are usually attributed to dark matter. The solution has been tested on the Milky Way and the spiral galaxy M33 and is in good agreement with observational measurements.

physics.gen-ph↗

arXiv2023

On a nonlocal de Sitter gravity

In this paper, we briefly review highlights of nonlocal de Sitter gravity based on the nonlocal term $ \sqrt{R - 2Λ}\ \mathcal{F}(\Box)\ \sqrt{R - 2Λ}$ in the Einstein-Hilbert action without matter sector. This nonlocal de Sitter gravity model has several exact cosmological FLRW solutions and one of these solutions contains some effects that are usually assigned to dark matter and dark energy. There are also some other interesting and promising properties of this kind of gravity nonlocality. We also review some anisotropic cosmological solutions, and mention the corresponding nonlocal Schwarzschild-de Sitter metric.

gr-qc↗

arXiv2022

Nonlocal de Sitter gravity and its exact cosmological solutions

This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with $Λ$ term, we introduce nonlocality by the following way: $R - 2 Λ= \sqrt{R-2Λ}\ \sqrt{R-2Λ} \to \sqrt{R-2Λ}\ F(\Box)\ \sqrt{R-2Λ} ,$ where ${F} (\Box) = 1 + \sum_{n= 1}^{+\infty} \big( f_n \Box^n + f_{-n} \Box^{-n} \big) $ is an analytic function of the d'Alembert-Beltrami operator $\Box$ and its inverse $\Box^{-1}$. By this way, $R$ and $Λ$ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator $F(\Box)$ is dimensionless. The corresponding equations of motion for gravitational field $g_{μν}$ are presented. The first step in finding some exact cosmological solutions is solving the equation $\Box \sqrt{R-2Λ} = q \sqrt{R-2Λ} , $ where $ q =ζΛ\quad (ζ\in \mathbb{R})$ is an eigenvalue and $\sqrt{R-2Λ}$ is an eigenfunction of the operator $\Box .$ We presented and discussed several exact cosmological solutions for homogeneous and isotropic universe. One of these solutions mimics effects that are usually assigned to dark matter and dark energy. Some other solutions are examples of the nonsingular bounce ones in flat, closed and open universe. There are also singular and cyclic solutions. All these cosmological solutions are a result of nonlocality and do not exist in the local de Sitter case.

gr-qc↗

arXiv2022

A $p$-Adic Matter in a Closed Universe

In this paper, we introduce a new type of matter that has origin in $p$-adic strings, i.e., strings with a $p$-adic worldsheet. We investigate some properties of this $p$-adic matter, in particular its cosmological aspects. We start with crossing symmetric scattering amplitudes for $p$-adic open strings and related effective nonlocal and nonlinear Lagrangian which describes tachyon dynamics at the tree level. Then, we make a slight modification of this Lagrangian and obtain a new Lagrangian for non-tachyonic scalar field. {Using this new Lagrangian in the weak field approximation as a matter in Einstein gravity with the cosmological constant, one obtains an exponentially expanding FLRW closed universe.} At the end, we discuss the obtained results, i.e., computed mass of the scalar $p$-adic particle, estimated radius of related closed universe and noted $p$-adic matter as a possible candidate for dark matter.

hep-th↗

arXiv2021

New Cosmological Solutions of a Nonlocal Gravity Model

A nonlocal gravity model (2.1) was introduced and considered recently [49], and two exact cosmological solutions in flat space were presented. The first solution is related to some radiation effects generated by nonlocal dynamics on dark energy background, while the second one is a nonsingular time symmetric bounce. In the present paper we investigate other possible exact cosmological solutions and find some the new ones in nonflat space. Used nonlocal gravity dynamics can change background topology. To solve the corresponding eqations of motion, we first look for a solution of the eigenvalue problem $\Box (R -4Λ) = q\ (R - 4Λ) .$ We also discuss possible extension of this model with nonlocal operator symmetric under $\Box \longleftrightarrow \Box^{-1}$ and its connection with another interesting nonlocal gravity model.

gr-qc↗

arXiv2020

From $p$-Adic to Zeta Strings

This article is related to construction of zeta strings from $p$-adic ones. In addition to investigation of $p$-adic string for a particular prime number $p$, it is also interesting to study collective effects taking into account all primes $p$. An idea behind this approach is that a zeta string is a whole thing with infinitely many faces which we see as $p$-adic strings. The name zeta string has origin in the Riemann zeta function contained in related Lagrangian. The starting point in construction a zeta string is Lagrangian for a $p$-adic open string. There are two types of approaches to get a Lagrangian for zeta string from Lagrangian for $p$-adic strings: additive and multiplicative approaches, that are related to two forms of the definition of the Riemann zeta function. As a result of differences in approaches, one obtains several different Lagrangians for zeta strings. We briefly discuss some properties of these Lagrangians, related potentials, equations of motion, mass spectrum and possible connection with ordinary strings. This is a review of published papers with some new views.

hep-th↗

arXiv2019

Variations of Infinite Derivative Modified Gravity

We consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form $P(R) F(\Box) Q(R)$. For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein-Hilbert modified action and basics of gravity perturbations.

hep-th↗

arXiv2017

Ultrametrics in the genetic code and the genome

Ultrametric approach to the genetic code and the genome is considered and developed. $p$-Adic degeneracy of the genetic code is pointed out. Ultrametric tree of the codon space is presented. It is shown that codons and amino acids can be treated as $p$-adic ultrametric networks. Ultrametric modification of the Hamming distance is defined and noted how it can be useful. Ultrametric approach with $p$-adic distance is an attractive and promising trend towards investigation of bioinformation.

q-bio.OT↗

arXiv2017

On Summation of $p$-Adic Series

Summation of the $p$-adic functional series $\sum \varepsilon^n \, n! \, P_k^\varepsilon (n; x)\, x^n ,$ where $P_k^\varepsilon (n; x)$ is a polynomial in $x$ and $n$ with rational coefficients, and $\varepsilon = \pm 1$, is considered. The series is convergent in the domain $|x|_p \leq 1$ for all primes $p$. It is found the general form of polynomials $P_k^\varepsilon (n; x)$ which provide rational sums when $x \in \mathbb{Z}$. A class of generating polynomials $A_k^\varepsilon (n; x)$ plays a central role in the summation procedure. These generating polynomials are related to many sequences of integers. This is a brief review with some new results.

math.NT↗

arXiv2017

On Nonlocal Modified Gravity and its Cosmological Solutions

During hundred years of General Relativity (GR), many significant gravitational phenomena have been predicted and discovered. General Relativity is still the best theory of gravity. Nevertheless, some (quantum) theoretical and (astrophysical and cosmological) phenomenological difficulties of modern gravity have been motivation to search more general theory of gravity than GR. As a result, many modifications of GR have been considered. One of promising recent investigations is Nonlocal Modified Gravity. In this article we present a brief review of some nonlocal gravity models with their cosmological solutions, in which nonlocality is expressed by an analytic function of the d'Alembert-Beltrami operator $\Box$. Some new results are also presented.

hep-th↗

arXiv2015

On Nonlocal Modified Gravity and Cosmology

Despite many nice properties and numerous achievements, general relativity is not a complete theory. One of actual approaches towards more complete theory of gravity is its nonlocal modification. We present here a brief review of nonlocal gravity with its cosmological solutions. In particular, we pay special attention to two nonlocal models and their nonsingular bounce solutions for the cosmic scale factor.

gr-qc↗

arXiv2015

Some Cosmological Solutions of a Nonlocal Modified Gravity

We consider nonlocal modification of the Einstein theory of gravity in framework of the pseudo-Riemannian geometry. The nonlocal term has the form $\mathcal{H}(R) \mathcal{F}(\Box)\mathcal {G}(R)$, where $\mathcal{H}$ and $\mathcal{G}$ are differentiable functions of the scalar curvature $R,$ and $ \mathcal{F}(\Box)= \displaystyle \sum_{n =0}^{\infty} f_{n}\Box^{n}$ is an analytic function of the d'Alambert operator $\Box .$ Using calculus of variations of the action functional, we derived the corresponding equations of motion. The variation of action is induced by variation of the gravitational field, which is the metric tensor $g_{μν}$. Cosmological solutions are found for the case when the Ricci scalar $R$ is constant.

hep-th↗

arXiv2015

Summation of p-Adic Functional Series in Integer Points

Summation of a large class of the functional series, which terms contain factorials, is considered. We first investigated finite partial sums for integer arguments. These sums have the same values in real and all p-adic cases. The corresponding infinite functional series are divergent in the real case, but they are convergent and have p-adic invariant sums in p-adic cases. We found polynomials which generate all significant ingredients of these series and make connection between their real and p-adic properties. In particular, we found connection of one of our integer sequences with the Bell numbers.

math.NT↗

arXiv2014

A New Model of Nonlocal Modified Gravity

We consider a new modified gravity model with nonlocal term of the form $R^{-1} \mathcal{F}(\Box) R. $ This kind of nonlocality is motivated by investigation of applicability of a few unusual ansätze to obtain some exact cosmological solutions. In particular, we find attractive and useful quadratic ansatz $\Box R = q R^{2}.$

hep-th↗

arXiv2014

p-Adic Invariant Summation of Some p-Adic Functional Series

We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer argument. In this paper, we present rather large class of such p-adic functional series with integer coefficients which contain factorials. By recurrence relations, we constructed sequence of polynomials A_k(n;x) which are a generator for a few other sequences also relevant to some problems in number theory and combinatorics.

math.NT↗

arXiv2012

On Measurements, Numbers and p-Adic Mathematical Physics

In this short paper I consider relation between measurements, numbers and p-adic mathematical physics. p-Adic numbers are not result of measurements, but nevertheless they play significant role in description of some systems and phenomena. We illustrate their ability for applications referring to some sectors of p-adic mathematical physics and related topics, in particular, to string theory and the genetic code.

physics.gen-ph↗

arXiv2012

Towards p-Adic Matter in the Universe

Starting from p-adic string theory with tachyons, we introduce a new kind of non-tachyonic matter which may play an important role in evolution of the Universe. This matter retains nonlocal and nonlinear p-adic string dynamics, but does not suffer of negative square mass. In space-time dimensions D = 2 + 4k, what includes D = 6, 10, ..., 26, the kinetic energy term also maintains correct sign. In these spaces this p-adic matter provides negative cosmological constant and time-dependent scalar field solution with negative potential. Their possible cosmological role is discussed. We have also connected non-locality with string world-sheet in effective Lagrangian for p-adic string.

hep-th↗

arXiv2012

On Modified Gravity

We consider some aspects of nonlocal modified gravity, where nonlocality is of the type $R \mathcal{F}(\Box) R$. In particular, using ansatz of the form $\Box R = c R^γ,$ we find a few $R(t)$ solutions for the spatially flat FLRW metric. There are singular and nonsingular bounce solutions. For late cosmic time, scalar curvature R(t) is in low regime and scale factor a(t) is decelerated. R (t) = 0 satisfies all equations when k = -1.

hep-th↗