Revealing infinite derivative gravity’s true potential: The weak-field limit around de Sitter backgrounds

Abstract

General Relativity is known to produce singularities in the potential generated by a point source. Our universe can be modelled as a de Sitter (dS) metric and we show that ghost-free Infinite Derivative Gravity (IDG) produces a non-singular potential around a dS background, while returning to the GR prediction at large distances. We also show that although there are an apparently infinite number of coefficients in the theory, only a finite number actually affect the predictions. By writing the linearised equations of motion in a simplified form, we find that at distances below the Hubble length scale, the difference between the IDG potential around a flat background and around a de Sitter background is negligible.

Initial conditions and degrees of freedom of non-local gravity

“…This is a striking resemblance with the scalar-field case, where we had to specify the same number of initial conditions once the auxiliary field was removed. It is well known that the perturbative degrees of freedom are finite, as one can see from the poles of the graviton propagator [21,22,33]. Here we can go beyond that result and make a fully non-perturbative counting.…”

Gravitational radiation in infinite derivative gravity and connections to effective quantum gravity

“…Any entire function can be written as a polynomial γ(k 2 ) = c 0 + c 1 k 2 + c 2 k 4 + • • • , so a priori we have an infinite number of coefficients to choose. However, it was shown that only the first few orders will appreciably affect the predictions of the theory, as terms higher than order ∼ 10 can be described by a rectangle function with a single unknown parameter [33].…”

Conditions for defocusing around more general metrics in infinite derivative gravity

“…Infinite derivative actions, which are used in string theory [7], were first applied to gravity by Biswas, Gerwick, Kovisto and Mazumdar [8]. IDG has been investigated around flat Minkowksi backgrounds [9], (Anti) de Sitter backgrounds [10][11][12][13], a rotating metric [14] and the Schwarzschild black hole solution [15].…”