Cosmological evolution of generalized non-local gravity

TL;DR

This paper introduces a generalized non-local gravity model modifying general relativity with a specific non-local term, analyzes its stability, and explores its cosmological implications, including phantom-like behavior and stable configurations for even exponents.

Contribution

The paper develops a new class of non-local gravity models with a parameter n, analyzing their stability and cosmological evolution, extending previous models as special cases.

Findings

Half of the scalar fields are ghost-like.

Stable models require even values of n.

The universe exhibits three dominant evolutionary phases.

Abstract

We construct a class of generalized non-local gravity (GNLG) model which is the modified theory of general relativity (GR) obtained by adding a term $m^{2n-2} R\Box^{-n}R$ to the Einstein-Hilbert action. Concretely, we not only study the gravitational equation for the GNLG model by introducing auxiliary scalar fields, but also analyse the classical stability and examine the cosmological consequences of the model for different exponent $n$. We find that the half of the scalar fields are always ghost-like and the exponent $n$ must be taken even number for a stable GNLG model. Meanwhile, the model spontaneously generates three dominant phases of the evolution of the universe, and the equation of state parameters turn out to be phantom-like. Furthermore, we clarify in another way that exponent $n$ should be even numbers by discuss the spherically symmetric static solutions in Newtonian gauge. It is worth stressing that the results given by us can include ones in refs. [28, 34] as the special case of $n=2$.