scholarly journals Some Cosmological Solutions of a New Nonlocal Gravity Model

Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 917
Author(s):  
Ivan Dimitrijevic ◽  
Branko Dragovich ◽  
Alexey S. Koshelev ◽  
Zoran Rakic ◽  
Jelena Stankovic
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Analytic Function ◽  
Cosmological Constant ◽  
Explicit Form ◽  
Gravity Model ◽  
Necessary Conditions ◽  
Equations Of Motion ◽  
Nonlocal Operator ◽  
Cosmological Solutions

In this paper, we investigate a nonlocal modification of general relativity (GR) with action S = 1 16 π G ∫ [ R − 2 Λ + ( R − 4 Λ ) F ( □ ) ( R − 4 Λ ) ] − g d 4 x , where F ( □ ) = ∑ n = 1 + ∞ f n □ n is an analytic function of the d’Alembertian □. We found a few exact cosmological solutions of the corresponding equations of motion. There are two solutions which are valid only if Λ ≠ 0 , k = 0 , and they have no analogs in Einstein’s gravity with cosmological constant Λ . One of these two solutions is a ( t ) = A t e Λ 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 Λ t 2 . For these two solutions, some cosmological aspects are discussed. We also found explicit form of the nonlocal operator F ( □ ) , which satisfies obtained necessary conditions.

scholarly journals New Cosmological Solutions of a Nonlocal Gravity Model

Symmetry ◽  
2021 ◽  
Vol 14 (1) ◽  
pp. 3
Author(s):  
Ivan Dimitrijevic ◽  
Branko Dragovich ◽  
Zoran Rakic ◽  
Jelena Stankovic
Keyword(s):  
Dark Energy ◽  
Eigenvalue Problem ◽  
Gravity Model ◽  
Radiation Effects ◽  
Equations Of Motion ◽  
Flat Space ◽  
Nonlocal Operator ◽  
Cosmological Solutions

A nonlocal gravity model (2) was introduced and considered recently, 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 the background topology. To solve the corresponding equations of motion, we first look for a solution of the eigenvalue problem □(R−4Λ)=q(R−4Λ). We also discuss possible extension of this model with a nonlocal operator, symmetric under □⟷□−1, and its connection with another interesting nonlocal gravity model.

scholarly journals Dark matter from non-relativistic embedding gravity

2021 ◽  
pp. 2150101
Author(s):  
S. A. Paston
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Explicit Form ◽  
Equations Of Motion ◽  
Additional Contribution ◽  
Relativistic Limit ◽  
The Core ◽  
The Stability ◽  
Dimensional Surface

We study the possibility to explain the mystery of the dark matter (DM) through the transition from General Relativity to embedding gravity. This modification of gravity, which was proposed by Regge and Teitelboim, is based on a simple string-inspired geometrical principle: our spacetime is considered here as a four-dimensional surface in a flat bulk. We show that among the solutions of embedding gravity, there is a class of solutions equivalent to solutions of GR with an additional contribution of non-relativistic embedding matter, which can serve as cold DM. We prove the stability of such type of solutions and obtain an explicit form of the equations of motion of embedding matter in the non-relativistic limit. According to them, embedding matter turns out to have a certain self-interaction, which could be useful in the context of solving the core-cusp problem that appears in the [Formula: see text]CDM model.

scholarly journals Generalized Phenomenological Models of Dark Energy

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Prasenjit Paul ◽  
Rikpratik Sengupta
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Energy Density ◽  
Cosmological Constant ◽  
Phenomenological Models ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Free Parameters ◽  
The Universe ◽  
Matter Energy

It was first observed at the end of the last century that the universe is presently accelerating. Ever since, there have been several attempts to explain this observation theoretically. There are two possible approaches. The more conventional one is to modify the matter part of the Einstein field equations, and the second one is to modify the geometry part. We shall consider two phenomenological models based on the former, more conventional approach within the context of general relativity. The phenomenological models in this paper consider a Λ term firstly a function of a¨/a and secondly a function of ρ, where a and ρ are the scale factor and matter energy density, respectively. Constraining the free parameters of the models with the latest observational data gives satisfactory values of parameters as considered by us initially. Without any field theoretic interpretation, we explain the recent observations with a dynamical cosmological constant.

A UNIFIED DARK ENERGY MODEL FROM A VANISHING SPEED OF SOUND WITH EMERGENT COSMOLOGICAL CONSTANT

2014 ◽  
Vol 23 (02) ◽  
pp. 1450012 ◽  
Author(s):  
ORLANDO LUONGO ◽  
HERNANDO QUEVEDO
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Cosmological Model ◽  
Cosmological Constant ◽  
Energy Budget ◽  
Speed Of Sound ◽  
Dark Energy Model ◽  
Vacuum Energy ◽  
Cosmic Acceleration ◽  
Energy Term

The problem of the cosmic acceleration is here revisited by using the fact that the adiabatic speed of sound can be assumed to be negligible small. Within the context of general relativity, the total energy budget is recovered under the hypothesis of a vanishing speed of sound by assuming the existence of one fluid only. We find a cosmological model which reproduces the main results of the ΛCDM paradigm at late-times, showing an emergent cosmological constant, which is not at all related with the vacuum energy term. As a consequence, the model presented here behaves as a unified dark energy (DE) model.

scholarly journals Nonlocal modified gravity and its cosmological solutions

2014 ◽  
Vol 12 (2) ◽  
pp. 139-150
Author(s):  
Branko Dragovich
Keyword(s):  
General Relativity ◽  
Analytic Function ◽  
Modified Gravity ◽  
Scale Factor ◽  
Complete Theory ◽  
Cosmic Scale ◽  
Nonlocal Models ◽  
Cosmological Solutions ◽  
Theory Of Gravity

Besides great achievements and many nice properties, general relativity as theory of gravity is not a complete theory. There are many attempts to its modification. One of promising modern approaches towards more complete theory of gravity is its nonlocal modification. We present here a brief review of nonlocal gravity with some its cosmological solutions. In particular, we pay special attention to two attractive nonlocal models, in which nonlocality is expressed by an analytic function of the d?Alembert operator ? = 1/?-g ???-gg????. In these models, we are mainly interested in nonsingular bounce solutions for the cosmic scale factor.

DELTA GRAVITY AND THE ACCELERATED EXPANSION OF THE UNIVERSE

2011 ◽  
Vol 20 (supp01) ◽  
pp. 65-72
Author(s):  
JORGE ALFARO
Keyword(s):  
General Relativity ◽  
Gravitational Field ◽  
Cosmological Constant ◽  
Equivalence Principle ◽  
Equations Of Motion ◽  
Accelerated Expansion ◽  
Symmetric Tensors ◽  
Test Particles ◽  
Expansion Of The Universe ◽  
The Universe

We study a model of the gravitational field based on two symmetric tensors. The equations of motion of test particles are derived. We explain how the Equivalence principle is recovered. Outside matter, the predictions of the model coincide exactly with General Relativity, so all classical tests are satisfied. In Cosmology, we get accelerated expansion without a cosmological constant.

scholarly journals DARK ENERGY AND DARK MATTER IN GENERAL RELATIVITY WITH LOCAL SCALE INVARIANCE

2009 ◽  
Vol 24 (20) ◽  
pp. 1583-1595 ◽  
Author(s):  
PAVAN KUMAR ALURI ◽  
PANKAJ JAIN ◽  
NAVEEN K. SINGH
Keyword(s):  
General Relativity ◽  
Dark Matter ◽  
Dark Energy ◽  
Scale Invariance ◽  
Equations Of Motion ◽  
Local Scale ◽  
Theory Of Relativity ◽  
General Theory Of Relativity ◽  
Λcdm Model ◽  
Frw Metric

We consider a generalization of Einstein's general theory of relativity such that it respects local scale invariance. This requires the introduction of a scalar and a vector field in the action. We show that the theory naturally displays both dark energy and dark matter. We solve the resulting equations of motion assuming an FRW metric. The solutions are found to be almost identical to those corresponding to the standard ΛCDM model.

scholarly journals The shape of bouncing universes

2017 ◽  
Vol 26 (12) ◽  
pp. 1743016 ◽  
Author(s):  
John D. Barrow ◽  
Chandrima Ganguly
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Cosmological Constant ◽  
Inflexion Point ◽  
De Sitter ◽  
Positive Cosmological Constant ◽  
Entropy Increase

What happens to the most general closed oscillating universes in general relativity? We sketch the development of interest in cyclic universes from the early work of Friedmann and Tolman to modern variations introduced by the presence of a cosmological constant. Then we show what happens in the cyclic evolution of the most general closed anisotropic universes provided by the Mixmaster universe. We show that in the presence of entropy increase its cycles grow in size and age, increasingly approaching flatness. But these cycles also grow increasingly anisotropic at their expansion maxima. If there is a positive cosmological constant, or dark energy, present then these oscillations always end and the last cycle evolves from an anisotropic inflexion point towards a de Sitter future of everlasting expansion.

scholarly journals A null test to probe the scale dependence of the growth of structure as a test of general relativity

2019 ◽  
Vol 492 (1) ◽  
pp. L34-L39 ◽  
Author(s):  
Felipe Oliveira Franco ◽  
Camille Bonvin ◽  
Chris Clarkson
Keyword(s):  
General Relativity ◽  
Dark Energy ◽  
Cosmological Constant ◽  
Cosmological Parameters ◽  
Scale Dependence ◽  
Scale Invariant ◽  
Square Kilometre Array ◽  
Massive Neutrinos ◽  
Dipole Pattern

ABSTRACT The main science driver for the coming generation of cosmological surveys is understanding dark energy that relies on testing general relativity on the largest scales. Once we move beyond the simplest explanation for dark energy of a cosmological constant, the space of possible theories becomes both vast and extremely hard to compute realistic observables. A key discriminator of a cosmological constant, however, is that the growth of structure is scale invariant on large scales. By carefully weighting observables derived from distributions of galaxies and a dipole pattern in their apparent sizes, we construct a null test that vanishes for any model of gravity or dark energy where the growth of structure is scale independent. It relies only on very few assumptions about cosmology, and does not require any modelling of the growth of structure. We show that with a survey like the Dark Energy Spectroscopic Instrument (DESI) a scale dependence of the order of 10–20 per cent can be detected at 3σ with the null test, which will drop by a factor of 2 for a survey like the Square Kilometre Array. We also show that the null test is very insensitive to typical uncertainties in other cosmological parameters including massive neutrinos and scale-dependent bias, making this a key null test for dark energy.

scholarly journals The effect of the cosmological constant on a quadrupole signal in the linearized approximation

2018 ◽  
Vol 27 (02) ◽  
pp. 1850004 ◽  
Author(s):  
László Ábel Somlai ◽  
Mátyás Vasúth
Keyword(s):  
General Relativity ◽  
Cosmological Constant ◽  
Gravitational Wave ◽  
Equations Of Motion ◽  
Luminosity Distance ◽  
Background Term ◽  
Self Consistent ◽  
Linearized Theory

In this study the effects of a nonzero cosmological constant [Formula: see text] on a quadrupole gravitational wave (GW) signal are analyzed. The linearized approximation of general relativity was used, so the perturbed metric can be written as the sum of [Formula: see text] GWs and [Formula: see text] background term, originated from [Formula: see text]. The [Formula: see text] term was also included in this study. To derive physically relevant consequences of [Formula: see text] comoving coordinates are used. In these coordinates, the equations of motion (EoMs) are not self-consistent so the result of the linearized theory has to be transformed to the FRW frame. The luminosity distance and the same order of the magnitude of frequency in accordance with the detected GWs were used to demonstrate the effects of the cosmological constant.

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