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

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.

Stability analysis and future singularity of them2R□-2Rmodel of non-local gravity

“…25 For a study of the type of future singularities caused by phantom dark energy see [34] and for the case where this occurs with the Deser-Woodard type of non-locality see [30]. case here, but we can still find the explicit solution for a(t) in the far future by proceeding perturbatively.…”

“…This fact has actually been one of the main theoretical justifications for studying non-local actions [6,13,44]. The problem with this interpretation however is that the nonlocal corrections one would expect from gravitational/matter loops look nothing like (1.1) 30 . Recently, in [33] the authors have actually shown that a large class of phenomenological models, including (1.1), fails indeed to capture even qualitatively the non-local effects that are expected from quantum corrections on cosmological backgrounds.…”

Inflationary Cosmology in Modified Gravity Theories

“…Such a theory can be regarded as modified gravity because the R 2 term or its higher derivative term of the trace-anomaly term R, which leads to the long enough inflation and graceful exit from it [21], is the effective action of gravity, where is the covariant d'Alembertian for a scalar quantity. (In References [23][24][25], the features of inflation in non-local gravity including such a non-local term as R has been analyzed in detail.) In this paper, we review the main results in References [26][27][28].…”

Nonlocal theory of massive gravity

“…Its theoretical structure and cosmological consequences for different choices of the function f (✷ −1 R) have been discussed in a number of papers, see e.g. [77][78][79][80][81][82][83][84][85][86][87]. In this approach there is no basic principle that fixes the function f (✷ −1 R), which is therefore chosen on purely phenomenological grounds, and can be reconstructed so to fit any given expansion history [88,89].…”