Screening of cosmological constant for De Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities

TL;DR

This paper explores de Sitter solutions and future singularities in non-local gravity, examining conditions to avoid ghosts, the crossing of the phantom divide, and the potential unification of inflation with late-time acceleration.

Contribution

It provides new insights into finite-time singularities, ghost avoidance, and unification of cosmic acceleration phases in non-local gravity models.

Findings

Finite-time future singularities can occur in non-local gravity.

Adding an R^2 term can cure singularities and unify inflation with late-time acceleration.

Phantom divide crossing can happen near singularities in these models.

Abstract

We investigate de Sitter solutions in non-local gravity as well as in non-local gravity with Lagrange constraint multiplier. We examine a condition to avoid a ghost and discuss a screening scenario for a cosmological constant in de Sitter solutions. Furthermore, we explicitly demonstrate that three types of the finite-time future singularities can occur in non-local gravity and explore their properties. In addition, we evaluate the effective equation of state for the universe and show that the late-time accelerating universe may be effectively the quintessence, cosmological constant or phantom-like phases. In particular, it is found that there is a case in which a crossing of the phantom divide from the non-phantom (quintessence) phase to the phantom one can be realized when a finite-time future singularity occurs. Moreover, it is demonstrated that the addition of an $R^2$ term can cure the finite-time future singularities in non-local gravity. It is also suggested that in the framework of non-local gravity, adding an $R^2$ term leads to possible unification of the early-time inflation with the late-time cosmic acceleration.