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.

27 pages, 5 figures. Comments welcome

References in corpus (13)

• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Towards a Resolution of the Cosmological Singularity in Non-local Higher Derivative Theories of Gravity
• Accelerating cosmologies from non-local higher-derivative gravity
• Bouncing and Accelerating Solutions in Nonlocal Stringy Models
• Generalised Quadratic Curvature, Non-Local Infrared Modifications of Gravity and Newtonian Potentials
• Constraint on the Post-Newtonian Parameter gamma on Galactic Size Scales
• Non-Local Gravity Cosmology: an Overview
• Cosmological perturbations in non-local higher-derivative gravity
• Some Cosmological Solutions of a New Nonlocal Gravity Model
• New non-singular cosmological solution of non-local gravity
• A $p$-Adic Matter in a Closed Universe
• New Cosmological Solutions of a Nonlocal Gravity Model
• 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