Screening of cosmological constant in non-local gravity

TL;DR

This paper explores a non-local gravity model that can potentially screen the cosmological constant, offering a new approach to the cosmological constant problem, but faces challenges with ghost instabilities.

Contribution

It introduces a simple quadratic non-local gravity model that admits flat spacetime solutions despite a non-zero cosmological constant, highlighting both potential and issues.

Findings

Flat spacetime solutions exist despite the cosmological constant.

Ghost instabilities are present in the solutions.

Conditions to avoid ghosts are only met temporarily.

Abstract

We discuss a possible mechanism to screen a cosmological constant in non-local gravity. We find that in a simple model of of non-local gravity with the Lagrangian of the form, $R+f(\Box^{-1}R)-2\Lambda$ where $f(X)$ is a quadratic function of $X$, there is a flat spacetime solution despite the presence of the cosmological constant $\Lambda$. Unfortunately, however, we also find that this solution contains a ghost in general. Then we discuss the condition to avoid a ghost and find that one can avoid it only for a finite range of `time'. Nevertheless our result suggests the possibility of solving the cosmological constant problem in the context of non-local gravity.