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Alexey S. Koshelev

Publications and source records attributed to Alexey S. Koshelev.

At least 37 records · Page 2Linked to original sources
arXiv2018

Towards nonsingular rotating compact object in ghost-free infinite derivative gravity

The vacuum solution of Einstein's theory of general relativity provides a rotating metric with a ring singularity, which is covered by the inner and outer horizons, and an ergo region. In this paper, we will discuss how ghost-free, quadratic curvature, Infinite Derivative Gravity (IDG) may resolve the ring singularity. In IDG the non-locality of the gravitational interaction can smear out the delta-Dirac source distribution by making the metric potential finite everywhere including at $r=0$. We show that the same feature also holds for a rotating metric. We can resolve the ring singularity such that no horizons are formed in the linear regime by smearing out a delta-source distribution on a ring. We will also show that the Kerr-metric does not solve the full non-linear equations of motion of ghost-free quadratic curvature IDG.

gr-qc↗
arXiv2018

Schwarzschild $1/r$-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity

In this paper we will study the complete equations of motion for a ghost free quadratic curvature infinite derivative gravity. We will argue that within the scale of non-locality, Schwarzschild-type singular metric solution is not {\it permissible}. Therefore, Schwarzschild-type vacuum solution which is a prediction in Einstein-Hilbert gravity may {\it not} persist within the region of non-locality. We will also show that just quadratic curvature gravity, without infinite derivatives, always allows Schwarzschild-type singular metric solution.

gr-qc↗
arXiv2018

Finite quantum gravity in dS and AdS spacetimes

We hereby study the properties of a large class of weakly nonlocal gravitational theories around the (anti-) de Sitter spacetime background. In particular, we explicitly prove that the kinetic operator for the graviton field has the same structure as the one in Einstein-Hilbert theory around any maximally symmetric spacetime. Therefore, the perturbative spectrum is the same of standard general relativity, while the propagator on any maximally symmetric spacetime is a mere generalization of the one from Einstein's gravity derived and extensively studied in several previous papers. At quantum level the range of theories here presented is superrenormalizable or finite when proper (non affecting the propagator) terms cubic or higher in curvatures are added. Finally, it is proven that for a large class of nonlocal theories, which in their actions do involve neither the Weyl nor the Riemann tensor, the theory is classically equivalent to the Einstein-Hilbert one with cosmological constant by means of a metric field redefinition at any perturbative order.

hep-th↗
arXiv2018

Conformally-flat, non-singular static metric in infinite derivative gravity

In Einstein's theory of general relativity the vacuum solution yields a blackhole with a curvature singularity, where there exists a point-like source with a Dirac delta distribution which is introduced as a boundary condition in the static case. It has been known for a while that ghost-free infinite derivative theory of gravity can ameliorate such a singularity at least at the level of linear perturbation around the Minkowski background. In this paper, we will show that the Schwarzschild metric does not satisfy the boundary condition at the origin within infinite derivative theory of gravity, since a Dirac delta source is smeared out by non-local gravitational interaction. We will also show that the spacetime metric becomes conformally-flat and singularity-free within the non-local region, which can be also made devoid of an event horizon. Furthermore, the scale of non-locality ought to be as large as that of the Schwarzschild radius, in such a way that the gravitational potential in any metric has to be always bounded by one, implying that gravity remains weak from the infrared all the way up to the ultraviolet regime, in concurrence with the results obtained in [arXiv:1707.00273]. The singular Schwarzschild blackhole can now be potentially replaced by a non-singular compact object, whose core is governed by the mass and the effective scale of non-locality.

gr-qc↗
arXiv2018

Classical properties of non-local, ghost- and singularity-free gravity

In this paper we will show all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit. We have found that in the region of non-locality, in the ultraviolet regime (at short distance from the source), the Ricci tensor and the Ricci scalar are not vanishing, meaning that we do not have a vacuum solution anymore due to the smearing of the source induced by the presence of non-local gravitational interactions. It also follows that, unlike in Einstein's gravity, the Riemann tensor is not traceless and it does not coincide with the Weyl tensor. Secondly, these curvatures are regularized at short distances such that they are singularity-free, in particular the same happens for the Kretschmann invariant. Unlike the others, the Weyl tensor vanishes at short distances, implying that the spacetime metric becomes conformally flat in the region of non-locality, in the ultraviolet. As a consequence, the non-local region can be approximated by a conformally flat manifold with non-negative constant curvatures. We briefly discuss the solution in the non-linear regime, and argue that $1/r$ metric potential cannot be the solution where non-locality is important in the ultraviolet regime.

gr-qc↗
arXiv2018

Behavior of the Newtonian potential for ghost-free gravity and singularity-free gravity

In this paper we show that there is a universal prediction for the Newtonian potential for an infinite derivative, ghost-free, quadratic curvature gravity. We show that in order to make such a theory ghost-free at a perturbative level, the Newtonian potential always falls-off as 1/r in the infrared limit, while at short distances the potential becomes non-singular. We provide examples which can potentially test the scale of gravitational non-locality up to 0.004 eV.

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arXiv2017

$R^2$ inflation to probe non-perturbative quantum gravity

It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, $R+R^2$, or shortly $R^2$, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local $R^2$ model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ($n_s$), a tensor-to-scalar ratio ($r$) and a tensor tilt ($n_t$). It appears that $n_s$ remains the same as in the local $R^2$ inflation in the leading slow-roll approximation, while $r$ and $n_t$ get modified due to modification of the tensor power spectrum. This class of models allows for any value of $r<0.07$ with a modified consistency relation which can be fixed by future observations of primordial $B$-modes of the CMB polarization. This makes the UV complete $R^2$ gravity a natural target for future CMB probes.

hep-th↗
arXiv2017

Effective models of inflation from a non-local framework

The dilaton is a possible inflaton candidate following recent CMB data allowing a non-minimal coupling to the Ricci curvature scalar in the early Universe. In this paper, we introduce an approach that has seldom been used in the literature, namely dilaton inflation with non-local features. More concretely, employing non-local features expressed in J. High Energy Phys. 04 (2007) 029, we study quadratic variations around a de Sitter geometry of an effective action with a non-local dilaton. The non-locality refers to an infinite derivative kinetic term involving the operator $\mathcal{F}\left(\Box\right)$. Algebraic roots of the characteristic equation $\mathcal{F}(z)=0$ play a crucial role in determining the properties of the theory. We subsequently study the cases when $\mathcal{F}\left(\Box\right)$ has one real root and one complex root, from which we retrieve two concrete effective models of inflation. In the first case we retrieve a class of single field inflations with universal prediction of $n_{s}\sim0.967$ with any value of the tensor to scalar ratio $r<0.1$ intrinsically controlled by the root of the characteristic equation. The second case involves a new class of two field conformally invariant models with a peculiar quadratic cross-product of scalar fields. In this latter case, we obtain Starobinsky like inflation through a spontaneously broken conformal invariance. Furthermore, an uplifted minimum of the potential, which accounts for the vacuum energy after inflation is produced naturally through this mechanism intrinsically within our approach.

hep-th↗
arXiv2017

Do massive compact objects without event horizon exist in infinite derivative gravity?

Einstein's General theory of relativity is plagued by cosmological and blackhole type singularities Recently, it has been shown that infinite derivative, ghost free, gravity can yield non-singular cosmological and mini-blackhole solutions. In particular, the theory possesses a {\it mass-gap} determined by the scale of new physics. We will use this property to argue that it is possible to form a non-singular super-massive compact objects without having any event horizon in this class of theories.

gr-qc↗
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↗
arXiv2016

Defocusing of Null Rays in Infinite Derivative Gravity

Einstein's General theory of relativity permits spacetime singularities, where null geodesic congruences focus in the presence of matter, which satisfies an appropriate energy condition. In this paper, we provide a minimal defocusing condition for null congruences without assuming any Ansatz-dependent background solution. The two important criteria are: (1) an additional scalar degree of freedom, besides the massless graviton must be introduced into the spacetime; and (2) an infinite derivative theory of gravity is required in order to avoid tachyons or ghosts in the graviton propagator. In this regard, our analysis strengthens earlier arguments for constructing non-singular bouncing cosmologies within an infinite derivative theory of gravity, without assuming any Ansatz to solve the full equations of motion.

gr-qc↗
arXiv2016

Occurrence of exact $R^2$ inflation in non-local UV-complete gravity

The $R+R^2$, shortly named "$R^2$" ("Starobinsky") inflationary model, represents a fully consistent example of a one-parameter inflationary scenario. This model has a "graceful exit" from inflation and provides a mechanism for subsequent creation and final thermalization of the standard matter. Moreover, it produces a very good fit of the observed spectrum of primordial perturbations. In the present paper we show explicitly that the $R^2$ inflationary spacetime is an exact solution of a range of weakly non-local (quasi-polynomial) gravitational theories, which provide an ultraviolet completion of the $R^2$ theory. These theories are ghost-free, super-renormalizable or finite at quantum level, and perturbatively unitary. Their spectrum consists of the graviton and the scalaron that is responsible for driving the inflation. Notably, any further extension of the spectrum leads to propagating ghost degrees of freedom. We are aimed at presenting a detailed construction of such theories in the so called Weyl basis. Further, we give a special account to the cosmological implications of this theory by considering perturbations during inflation. The highlight of the non-local model is the prediction of a modified, in comparison to a local $R^2$ model, value for the ratio of tensor and scalar power spectra $r$, depending on the parameters of the theory. The relevant parameters are under control to be successfully confronted with existing observational data. Furthermore, the modified $r$ can surely meet future observational constraints.

hep-th↗
arXiv2016

Consistent Higher Derivative Gravitational theories with stable de Sitter and Anti-de Sitter Backgrounds

In this paper we provide the criteria for any generally covariant, parity preserving, and torsion free theory of gravity to possess a stable de Sitter (dS) or anti-de Sitter (AdS) background. By stability we mean the absence of tachyonic or ghost-like states in the perturbative spectrum that can lead to classical instabilities and violation of quantum unitarity. While we find that the usual suspects, the F(R) and F(G) theories, can indeed possess consistent (A)dS backgrounds, G being the Gauss-Bonnet term, another interesting class of theories, string-inspired infinite derivative gravity, can also be consistent around such curved vacuum solutions. Our study should not only be relevant for quantum gravity and early universe cosmology involving ultraviolet physics, but also for modifications of gravity in the infra-red sector vying to replace dark energy .

gr-qc↗
arXiv2016

Gravitational theories with stable (anti-)de Sitter backgrounds

In this article we will construct the most general torsion-free parity-invariant covariant theory of gravity that is free from ghost-like and tachyonic nstabilities around constant curvature space-times in four dimensions. Specifically, this includes the Minkowski, de Sitter and anti-de Sitter backgrounds. We will first argue in details how starting from a general covariant action for the metric one arrives at an "equivalent" action that at most contains terms that are quadratic in curvatures but nevertheless is sufficient for the purpose of studying stability of the original action. We will then briefly discuss how such a "quadratic curvature action" can be decomposed in a covariant formalism into separate sectors involving the tensor, vector and scalar modes of the metric tensor; most of the details of the analysis however, will be presented in an accompanying paper. We will find that only the transverse and trace-less spin-2 graviton with its two helicity states and possibly a spin-0 Brans-Dicke type scalar degree of freedom are left to propagate in 4 dimensions. This will also enable us to arrive at the consistency conditions required to make the theory perturbatively stable around constant curvature backgrounds. This will be included as a chapter in the book entitled "At the Frontier of Spacetime - Scalar-Tensor Theory, Bells Inequality, Machs Principle, Exotic Smoothness" (Springer 2016)

hep-th↗
arXiv2014

Cosmological perturbations in non-local higher-derivative gravity

We study cosmological perturbations in a non-local higher-derivative model of gravity introduced by Biswas, Mazumdar and Siegel. We extend previous work, which had focused on classical scalar perturbations around a cosine hyperbolic bounce solution, in three ways. First, we point out the existence of a Starobinsky solution in this model, which is more attractive from a phenomenological point of view (even though it has no bounce). Second, we study classical vector and tensor perturbations. Third, we show how to quantize scalar and tensor perturbations in a de Sitter phase (for choices of parameters such that the model is ghost-free). Our results show that the model is well-behaved at this level, and are very similar to corresponding results in local $f(R)$ models. In particular, for the Starobinsky solution of non-local higher-derivative gravity, we find the same tensor-to-scalar ratio as for the conventional Starobinsky model.

hep-th↗
arXiv2014

Geodesic completeness and homogeneity condition for cosmic inflation

There are two disjointed problems in cosmology within General Relativity (GR), which can be addressed simultaneously by studying the nature of geodesics around $t\rightarrow 0$, where $t$ is the physical time. One is related to the past geodesic completeness of the inflationary trajectory due to the presence of a cosmological singularity, and the other one is related to the homogeneity condition required to inflate a local space-time patch of the universe. We will show that both the problems have a common origin, arising from how the causal structure of null and timelike geodesics are structured within GR. In particular, we will show how a non-local extension of GR can address both problems, while satisfying the null energy condition for the matter sources.

gr-qc↗
arXiv2014

Cosmological Solutions in Nonlocal Models

A non-local modified gravity model with an analytic function of the d'Alembert operator that has been proposed as a possible way of resolving the singularities problems in cosmology is considered. We show that the anzats that is usually used to obtain exact solutions in this model provides a connection with $f(R)$ gravity models.

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