Cosmological perturbations in non-local higher-derivative gravity

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.

arXiv comment28 pages; v2: various clarifications, improved discussion of tensor-to-scalar ratio

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• Non-local gravity in D-dimensions: Propagator, entropy and bouncing Cosmology
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• Generalised Boundary Terms for Higher Derivative Theories of Gravity
• Novel higher-curvature variations of $R^2$ inflation
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• UV completion of the Starobinsky model, tensor-to-scalar ratio, and constraints on non-locality
• Perturbations in higher derivative gravity beyond maximally symmetric spacetimes
• An anisotropic bouncing universe in non-local gravity
• Stable, non-singular bouncing universe with only a scalar mode
• Nonlocal de Sitter gravity and its exact cosmological solutions
• Newtonian Potential and Geodesic Completeness in Infinite Derivative Gravity
• Cosmology in nonlocal gravity
• Revealing Infinite Derivative Gravity's true potential: The weak-field limit around de Sitter backgrounds
• Conditions for defocusing around more general metrics in Infinite Derivative Gravity
• Gravitational radiation in Infinite Derivative Gravity and connections to Effective Quantum Gravity
• Criteria for resolving the cosmological singularity in Infinite Derivative Gravity around expanding backgrounds
• The stability of the de-Sitter universe in nonlocal gravity