Cosmological perturbations in non-local higher-derivative gravity

TL;DR

This paper investigates cosmological perturbations in a non-local higher-derivative gravity model, revealing a Starobinsky solution, analyzing vector and tensor perturbations, and demonstrating quantization in a ghost-free de Sitter phase, with results akin to local $f(R)$ models.

Contribution

It introduces a Starobinsky solution in non-local gravity, extends perturbation analysis to vectors and tensors, and shows quantization in a ghost-free de Sitter phase.

Findings

Existence of a Starobinsky solution in the non-local model.

Classical vector and tensor perturbations are well-behaved.

Tensor-to-scalar ratio matches the conventional Starobinsky model.

Abstract

We study cosmological perturbations in a non-local higher-derivative model of gravity introduced by Biswas, Mazumdar and Siegel. We extend previous work, which had focused on classical scalar perturbations around a cosine hyperbolic bounce solution, in three ways. First, we point out the existence of a Starobinsky solution in this model, which is more attractive from a phenomenological point of view (even though it has no bounce). Second, we study classical vector and tensor perturbations. Third, we show how to quantize scalar and tensor perturbations in a de Sitter phase (for choices of parameters such that the model is ghost-free). Our results show that the model is well-behaved at this level, and are very similar to corresponding results in local $f(R)$ models. In particular, for the Starobinsky solution of non-local higher-derivative gravity, we find the same tensor-to-scalar ratio as for the conventional Starobinsky model.