James Edholm

Behavior of the Newtonian potential for ghost-free gravity and singularity-free gravity

In this paper we show that there is a universal prediction for the Newtonian potential for an infinite derivative, ghost-free, quadratic curvature gravity. We show that in order to make such a theory ghost-free at a perturbative level, the Newtonian potential always falls-off as 1/r in the infrared limit, while at short distances the potential becomes non-singular. We provide examples which can potentially test the scale of gravitational non-locality up to 0.004 eV.

Generalised Boundary Terms for Higher Derivative Theories of Gravity

A bstractIn this paper we wish to find the corresponding Gibbons-Hawking-York term for the most general quadratic in curvature gravity by using Coframe slicing within the Arnowitt-Deser-Misner (ADM) decomposition of spacetime in four dimensions. In order to make sure that the higher derivative gravity is ghost and tachyon free at a perturbative level, one requires infinite covariant derivatives, which yields a generalised covariant infinite derivative theory of gravity. We will be exploring the boundary term for such a covariant infinite derivative theory of gravity.

UV completion of the Starobinsky model, tensor-to-scalar ratio, and constraints on nonlocality

In this paper, we build upon the successes of the ultraviolet (UV) completion of the Starobinsky model of inflation. This involves an extension of the Einstein-Hilbert term by an infinite covariant derivative theory of gravity which is quadratic in curvature. It has been shown that such a theory can potentially resolve the cosmological singularity for a flat, homogeneous and isotropic geometry, and now it can also provide a successful cosmological inflation model, which in the infrared regime matches all the predictions of the Starobinsky model of inflation. The aim of this paper is to show that the tensor-to-scalar ratio is modified by the scale of nonlocality, and in general a wider range of tensor-to-scalar ratios can be obtained in this class of model, which can put a lower bound on the scale of nonlocality for the first time as large as the O(10^14) GeV.

Newtonian Potential and Geodesic Completeness in Infinite Derivative Gravity

Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

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

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.

Criteria for resolving the cosmological singularity in Infinite Derivative Gravity around expanding backgrounds

Einsteins General theory of relativity permits space-time singularities, where null congruences \emph{focus} in the presence of matter, which satisfies an appropriate energy condition. In this paper, we argue that such a singularity may be avoided if two important criteria are satisfied: (1) An additional scalar degree of freedom, besides the massless graviton, must be introduced to the spacetime; and (2) An infinite-derivative extension is required in order to avoid tachyons or ghosts from the graviton propagator.

Gravitational radiation in Infinite Derivative Gravity and connections to Effective Quantum Gravity

The Hulse-Taylor binary provides possibly the best test of GR to date. We find the modified quadrupole formula for infinite derivative gravity (IDG). We investigate the backreaction formula for propagation of gravitational waves, found previously for effective quantum gravity (EQG) for a flat background and extend this calculation to a de Sitter background for both EQG and IDG. We put tighter constraints on EQG using new LIGO data. We also find the power emitted by a binary system within the IDG framework for both circular and elliptical orbits and use the example of the Hulse-Taylor binary to show that IDG is consistent with GR.