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

Abstract

Abstract. We analyse the classical stability of the model proposed by Maggiore and Mancarella, where gravity is modified by a term ∼ m 2 R −2 R to produce the late-time acceleration of the expansion of the universe. Our study takes into account all excitations of the metric that can potentially drive an instability. There are some subtleties in identifying these modes, as a non-local field theory contains dynamical fields which yet do not correspond to degrees of freedom. Since some of them are ghost-like, we clarify the impact of such modes on the stability of the solutions of interest that are the flat space-time and cosmological solutions. We then find that flat space-time is unstable under scalar perturbations, but the instability manifests itself only at cosmological scales, i.e. out of the region of validity of this solution. It is therefore the stability of the FLRW solution which is relevant there, in which case the scalar perturbations are known to be well-behaved by numerical studies. By finding the analytic solution for the late-time behaviour of the scale factor, which leads to a big rip singularity, we argue that the linear perturbations are bounded in the future because of the domination of Hubble friction. In particular, this effect damps the scalar ghost perturbations which were responsible for destabilizing Minkowski space-time. Thus, the model remains phenomenologically viable.

Conformal symmetry and nonlinear extensions of nonlocal gravity

“…(6) the "RR" model. Further work on the RR and RT models has been presented in [51][52][53][54][55][56][57][58][59].…”

Infrared Non-local Modifications of General Relativity

“…The corresponding cosmology not being viable, we proceeded with the study of non-local modified gravity models that are still controlled by a fixed mass parameter, but in which the graviton remains massless [70,71]. These theories contain ghost modes, i.e.…”

“…These theories contain ghost modes, i.e. fields with negative kinetic energy, and we have spent some time understanding their effects both at the classical and quantum levels [68,71,72]. Independent of the work in which I have been involved, the group has been very productive on the phenomenological analysis of these models [73][74][75][76][77][78].…”

“…This chapter is based on, and extends, [68,70,71] Manipulating −1 on curved space-time Now −1 is a right-inverse of ≡ ∇ µ ∇ µ and therefore depends on the metric field g µν . For the reader who is interested in the mathematical details of this operator on curved space-time we suggest a first look at the appendix A.…”

“…Therefore, gravity becomes unstable as soon asM 2 eff < 0. The Maggiore and Maggiore -Mancarella models, which correspond to the case ξ = 0, are currently receiving particular attention [71,76,78,104,119] because their phenomenology seems to privilege them among other non-local models that have been confronted with observations [65,68,70,73,74,97,107,109,110,[120][121][122][123][124]. Indeed, they have recently passed the constraints of a full Boltzmann/Monte Carlo Markov Chain analysis [78], of which they come out as statistically indistinguishable from ΛCDM, with respect to the current precision of the data.…”