Nonlocal de Sitter gravity and its exact cosmological solutions

Abstract

This paper is devoted to a simple nonlocal de Sitter gravity model and its exact vacuum cosmological solutions. In the Einstein-Hilbert action with $\Lambda$ term, we introduce nonlocality by the following way: $R-2\Lambda =\sqrt{R-2\Lambda }\sqrt{R-2\Lambda }\to \sqrt{R-2\Lambda }F(\square )\sqrt{R-2\Lambda },$ where $F(\square )=1+{\sum }_{n=1}^{+\infty }(f_n{\square }^n+f_{-n}{\square }^{-n})$ is an analytic function of the d'Alembert-Beltrami operator $\square$ and its inverse ${\square }^{-1}$. By this way, $R$ and $\Lambda$ enter with the same form into nonlocal version as they are in the local one, and nonlocal operator $F(\square )$ is dimensionless. The corresponding equations of motion for gravitational field $g_{\mu \nu }$ are presented. The first step in finding some exact cosmological solutions is solving the equation $\square \sqrt{R-2\Lambda }=q\sqrt{R-2\Lambda },$ where $q=\zeta \Lambda (\zeta \in \mathbb{R})$ is an eigenvalue and $\sqrt{R-2\Lambda }$ is an eigenfunction of the operator $\square .$ 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.

arXiv comment27 pages, 5 figures. Comments welcome

References in corpus (38)

• f(R) Theories Of Gravity
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Modified Gravity and Cosmology
• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Towards singularity and ghost free theories of gravity
• Super-renormalizable Quantum Gravity
• Bouncing Universes in String-inspired Gravity
• Nonlocal Cosmology
• Super-renormalizable & Finite Gravitational Theories
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Stable bounce and inflation in non-local higher derivative cosmology
• Occurrence of exact $R^2$ inflation in non-local UV-complete gravity
• Nonlocal gravity. Conceptual aspects and cosmological predictions
• Generalized ghost-free quadratic curvature gravity
• Accelerating cosmologies from non-local higher-derivative gravity
• Classical properties of non-local, ghost- and singularity-free gravity
• Nonlocal Models of Cosmic Acceleration
• Bouncing and Accelerating Solutions in Nonlocal Stringy Models
• Generalised Quadratic Curvature, Non-Local Infrared Modifications of Gravity and Newtonian Potentials
• Dark energy and dark matter from nonlocal ghost-free gravity theory
• On bouncing solutions in non-local gravity
• Constraint on the Post-Newtonian Parameter gamma on Galactic Size Scales
• $R^2$ inflation to probe non-perturbative quantum gravity
• Non-Local Gravity Cosmology: an Overview
• Schwarzschild $1/r$-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity
• Non-Gaussianities and tensor-to-scalar ratio in non-local $R^2$-like inflation
• Cosmological Daemon
• Cosmological perturbations in non-local higher-derivative gravity
• Cosmological Solutions of a Nonlocal Square Root Gravity
• Analysis of scalar perturbations in cosmological models with a non-local scalar field
• Conformal symmetry and nonlinear extensions of nonlocal gravity
• Some Cosmological Solutions of a Nonlocal Modified Gravity
• Some Cosmological Solutions of a New Nonlocal Gravity Model
• New non-singular cosmological solution of non-local gravity
• New Cosmological Solutions of a Nonlocal Gravity Model
• A $p$-Adic Matter in a Closed Universe
• Effectively nonlocal metric-affine gravity
• Bouncing Cosmologies

Cited by in corpus (4)

• The energy-momentum complex in non-local gravity
• Cosmology in nonlocal gravity
• The Weinberg no-go theorem for cosmological constant and nonlocal gravity
• Stability of the de-Sitter universe: One-loop nonlocal $f(R)$ gravity