Cosmological Solutions of a Nonlocal Square Root Gravity

Abstract

In this paper we consider modification of general relativity extending $R-2\Lambda$ by nonlocal term of the form $\sqrt{R-2\Lambda }\mathcal{F}(\square )\sqrt{R-2\Lambda },$ where $\mathcal{F}(\square )$ is an analytic function of the d'Alembert operator $\square$. We have found some exact cosmological solutions of the corresponding equations of motion without matter and with $\Lambda \ne 0$. One of these solutions is $a(t)=A{t}^{\frac{2}{3}}{e}^{\frac{\Lambda }{14}{t}^2},$ which imitates properties similar to an interplay of the dark matter and the dark energy. For this solution we calculated some cosmological parameters which are in a good agreement with observations. This nonlocal gravity model has not the Minkowski space solution. We also found several conditions which function $\mathcal{F}(\square )$ has to satisfy.

version published in Phys. Lett. B

References in corpus (25)

• 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
• Nonlocal Cosmology
• Super-renormalizable & Finite Gravitational Theories
• Occurrence of exact $R^2$ inflation in non-local UV-complete gravity
• Nonlocal gravity. Conceptual aspects and cosmological predictions
• Classical properties of non-local, ghost- and singularity-free gravity
• Nonlocal Models of Cosmic Acceleration
• $p$-Adic Mathematical Physics: The First 30 Years
• Bouncing and Accelerating Solutions in Nonlocal Stringy Models
• Generalised Quadratic Curvature, Non-Local Infrared Modifications of Gravity and Newtonian Potentials
• On bouncing solutions in non-local gravity
• Schwarzschild $1/r$-singularity is not permissible in ghost free quadratic curvature infinite derivative gravity
• Some Cosmological Solutions of a Nonlocal Modified Gravity
• On Modified Gravity
• On Nonlocal Modified Gravity and its Cosmological Solutions
• Cosmological solutions in modified gravity with monomial nonlocality
• On Nonlocal Modified Gravity and Cosmology
• Variations of Infinite Derivative Modified Gravity
• Cosmology of non-local f(R) gravity
• Bouncing Cosmologies

Cited by in corpus (15)

• New rotating black holes in non-linear Maxwell $f(\mathcal{R})$ gravity
• Introduction to modified gravity
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Some Cosmological Solutions of a New Nonlocal Gravity Model
• Quintessential Inflation with Dynamical Higgs Generation as an Affine Gravity
• Nonlocal de Sitter gravity and its exact cosmological solutions
• Dynamically Generated Inflationary Lambda-CDM
• A $p$-Adic Matter in a Closed Universe
• On the causality properties in non-local gravity theories
• New Cosmological Solutions of a Nonlocal Gravity Model
• Cosmology in nonlocal gravity
• Anisotropic Cosmology in the Local Limit of Nonlocal Gravity
• Probing Dark Energy Properties in $fQ,C)$ Gravity with FLRW Cosmological Models
• Non-Riemannian Volume Elements Dynamically Generate Inflation
• A novel nonlocal spin-1/2 theory: classical and quantum aspects