New Cosmological Solutions of a Nonlocal Gravity Model

Dimitrijevic, Ivan; Драгович, Бранко; Rakic, Zoran; Stanković, Jovana

doi:10.3390/sym14010003

Cited by 10 publications

(8 citation statements)

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“…In papers [38][39][40][41][42][43][44][45][46][47][48][49] and some references therein, there were considered several aspects of type (b) models. A special and very interesting case of (1.1) is…”

Section: Jhep12(2022)054mentioning

confidence: 99%

“…Another interesting example of (1.1) gets when P (R) = Q(R) = R − 4Λ, which can be derived from (1.2) under approximation |R| |2Λ| [48,49]. In the paper [48] two cosmological solutions are presented: (i) a(t) = A √ te Λ 4 t 2 , which mimics properties similar to an interference between radiation and the NΛDE, and (ii) nonsingular bounce solution a(t) = Ae Λt 2 .…”

Section: Jhep12(2022)054mentioning

confidence: 99%

“…In the paper [48] two cosmological solutions are presented: (i) a(t) = A √ te Λ 4 t 2 , which mimics properties similar to an interference between radiation and the NΛDE, and (ii) nonsingular bounce solution a(t) = Ae Λt 2 . The paper [49] contains cosmological solutions which demonstrate how this kind of gravitational nonlocality can change background topology.…”

Section: Jhep12(2022)054mentioning

confidence: 99%

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Nonlocal de Sitter gravity and its exact cosmological solutions

Dimitrijevic

Драгович

Rakic

et al. 2022

J. High Energ. Phys.

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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: $$ R-2\Lambda =\sqrt{R-2\Lambda}\kern1em \sqrt{R-2\Lambda}\to \sqrt{R-2\Lambda}\kern1em F\left(\square \right)\kern1em \sqrt{R-2\Lambda} $$ R − 2 Λ = R − 2 Λ R − 2 Λ → R − 2 Λ F □ R − 2 Λ , where $$ F\left(\square \right)=1+{\sum}_{n=1}^{+\infty}\left({f}_n{\square}^n+{f}_{-n}{\square}^{-n}\right) $$ F □ = 1 + ∑ n = 1 + ∞ f n □ n + f − n □ − n is an analytic function of the d’Alembert-Beltrami operator □ and its inverse □−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(□) is dimensionless. The corresponding equations of motion for gravitational field gμν are presented. The first step in finding some exact cosmological solutions is solving the equation $$ \square \sqrt{R-2\Lambda}=q\sqrt{R-2\Lambda} $$ □ R − 2 Λ = q R − 2 Λ , where q = ζΛ (ζ ∈ R) is an eigenvalue and $$ \sqrt{R-2\Lambda} $$ R − 2 Λ is an eigenfunction of the operator □. 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.

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Section: Jhep12(2022)054mentioning

confidence: 99%

Section: Jhep12(2022)054mentioning

confidence: 99%

Section: Jhep12(2022)054mentioning

confidence: 99%

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Nonlocal de Sitter gravity and its exact cosmological solutions

Dimitrijevic

Драгович

Rakic

et al. 2022

J. High Energ. Phys.

Self Cite

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show abstract

“…At infra-red scales, non-local models of gravity can naturally explain late-time acceleration without introducing exotic material components such as dark matter and dark energy [5]. In addition, they can potentially fix some cosmological and astrophysical problems plaguing the ΛCDM model [19][20][21], black hole stability [22], or stability and traversability of wormhole solutions [23].…”

Section: Introductionmentioning

confidence: 99%

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

2022

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An unambiguous definition of gravitational energy remains one of the unresolved issues of physics today. This problem is related to the non-localization of gravitational energy density. In General Relativity, there have been many proposals for defining the gravitational energy density, notably those proposed by Einstein, Tolman, Landau and Lifshitz, Papapetrou, Møller, and Weinberg. In this review, we firstly explored the energy–momentum complex in an nth order gravitational Lagrangian L=Lgμν,gμν,i1,gμν,i1i2,gμν,i1i2i3,⋯,gμν,i1i2i3⋯in and then in a gravitational Lagrangian as Lg=(R¯+a0R2+∑k=1pakR□kR)−g. Its gravitational part was obtained by invariance of gravitational action under infinitesimal rigid translations using Noether’s theorem. We also showed that this tensor, in general, is not a covariant object but only an affine object, that is, a pseudo-tensor. Therefore, the pseudo-tensor ταη becomes the one introduced by Einstein if we limit ourselves to General Relativity and its extended corrections have been explicitly indicated. The same method was used to derive the energy–momentum complex in fR gravity both in Palatini and metric approaches. Moreover, in the weak field approximation the pseudo-tensor ταη to lowest order in the metric perturbation h was calculated. As a practical application, the power per unit solid angle Ω emitted by a localized source carried by a gravitational wave in a direction x^ for a fixed wave number k under a suitable gauge was obtained, through the average value of the pseudo-tensor over a suitable spacetime domain and the local conservation of the pseudo-tensor. As a cosmological application, in a flat Friedmann–Lemaître–Robertson–Walker spacetime, the gravitational and matter energy density in f(R) gravity both in Palatini and metric formalism was proposed. The gravitational energy–momentum pseudo-tensor could be a useful tool to investigate further modes of gravitational radiation beyond two standard modes required by General Relativity and to deal with non-local theories of gravity involving □−k terms.

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“…The eigenvalue equation (3.1) recently realized to give interesting cosmological solutions in a new class of non-local theories involving higher order scalar curvatures[69].…”

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confidence: 99%

Generalized non-local R2-like inflation

Koshelev

Kumar

Starobinsky

2023

J. High Energ. Phys.

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The R2 inflation which is an extension of general relativity (GR) by quadratic scalar curvature introduces a quasi-de Sitter expansion of the early Universe governed by Ricci scalar being an eigenmode of d’Alembertian operator. In this paper, we derive a most general theory of gravity admitting R2 inflationary solution which turned out to be higher curvature non-local extension of GR. We study in detail inflationary perturbations in this theory and analyse the structure of form-factors that leads to a massive scalar (scalaron) and massless tensor degrees of freedom. We argue that the theory contains only finite number of free parameters which can be fixed by cosmological observations. We derive predictions of our generalized non-local R2-like inflation and obtain the scalar spectral index ns ≈ 1 − $$ \frac{2}{N} $$ 2 N and any value of the tensor-to-scalar ratio r < 0.036. In this theory, tensor spectral index can be either positive or negative nt ≶ 0 and the well-known consistency relation r = –8nt is violated in a non-trivial way. We also compute running of the tensor spectral index and discuss observational implications to distinguish this model from several classes of scalar field models of inflation. These predictions allow us to probe the nature of quantum gravity in the scope of future CMB and gravitational wave observations. Finally we comment on how the features of generalized non-local R2-like inflation cannot be captured by established notions of the so-called effective field theory of single field inflation and how we must redefine the way we pursue inflationary cosmology.

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New Cosmological Solutions of a Nonlocal Gravity Model

Cited by 10 publications

References 50 publications

Nonlocal de Sitter gravity and its exact cosmological solutions

Nonlocal de Sitter gravity and its exact cosmological solutions

Energy-Momentum Complex in Higher Order Curvature-Based Local Gravity

Generalized non-local R2-like inflation

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