Nonlinear stability in nonlocal gravity

Abstract

We address the stability issue of Ricci-flat and maximally symmetric spacetimes in nonlocal gravity to all perturbative orders in the gravitational perturbation. Assuming a potential at least cubic in curvature tensors but quadratic in the Ricci tensor, our proof consists on a mapping of the stability analysis in nonlocal gravity to the same problem in Einstein-Hilbert theory. One of the consequences is that only the graviton field can propagate and the theory is ghost-free at all perturbative orders. All the results known in Einstein gravity in vacuum with or without a cosmological constant can be exported to the case of nonlocal gravity: if a spacetime is stable at all perturbative orders in Einstein gravity, it is stable also in nonlocal gravity. Minkowski and de Sitter spacetimes are particular examples. We also study how the theory affects the propagation of gravitational waves in a cosmological background.

Gravitational-wave luminosity distance in quantum gravity

“…We assume that d S 0 at all scales. Cases where d S = 0 at short scales must be treated separately [25]. In the GR limit in D topological dimensions (standard spacetime, no QG corrections), d H = d k H = d S = D and Γ = D/2 − 1, the usual scaling of a scalar field.…”

Nonlinear stability of Minkowski spacetime in nonlocal gravity

“…The results presented in this paper can be extended to more general classes of metrics, including Ricci flat and (A)dS spacetimes as will be proved elsewhere [22]. So that, such spacetimes, e.g., (A)dS, will be stable in NLG provided they are stable in GR; for a review of (A)dS stability in general relativity see [23].…”

Non-perturbative spectrum of non-local gravity

“…Finally, it was recently proved [44] that Minkowski spacetime is stable not only at higher perturbative order, but also to all orders in the graviton perturbation. This result was then extended to any Ricci-flat spacetime (stable in non-local gravity if stable in general relativity) [45]. Therefore, the field φ µν , or the fields χ and Ψ µν , never propagate at any arbitrarily high perturbative order.…”