Cosmological Solutions of Some Nonlocal Gravity Models

I. Dimitrijevic ; B. Dragovich ; Z. Rakic ; J. Stankovic

Trudy Matematicheskogo Instituta imeni V.A. Steklova, Mathematical physics and applications, Tome 306 (2019), pp. 75-82

Résumé

Significant phenomenological success and nice theoretical properties of general relativity (GR) are well known. However, GR is not a complete theory of gravity. Hence, there are many attempts to modify GR. One of the current approaches to a more complete theory of gravity is a nonlocal modification of GR. The nonlocal gravity approach, which we consider here without matter, is based on the action $S = (16 \pi G)^{-1}\int \sqrt {-g} (R - 2\Lambda + P(R) \mathcal F(\Box ) Q(R))\,d^4x$, where $R$ is the scalar curvature, $\Lambda $ is the cosmological constant, $P(R)$ and $Q(R)$ are some differentiable functions of $R$, and $\mathcal F(\Box ) = \sum _{n=1}^{+\infty } f_n \Box ^n$ is an analytic function of the corresponding d'Alembert operator $\Box $. We present here a brief review of some general properties and cosmological solutions for some specific functions $P(R)$ and $Q(R)$.