In 1987, Krasnikov considered an infinite set of higher derivative terms acting on the curvature terms and showed that by choosing the coefficients wisely, the propagator would be ghost-free and exponentially suppressed in the ultraviolet regime.
[3] In 2011, Biswas, Gerwick, Koivisto and Mazumdar demonstrated that the most general infinite derivative action in 4 dimensions, around constant curvature backgrounds, parity invariant and torsion free, can be expressed by:[4] where the
A lower bound was obtained on the mass scale of IDG using experimental data on the strength of gravity at short distances,[6] as well as by using data on inflation[7] and on the bending of light around the Sun.
[8] The GHY boundary terms were found using the ADM 3+1 spacetime decomposition.
[10][11] The effect of IDG on black holes and the propagator was examined by Modesto.
[12][13][14] Modesto further looked at the renormalisability of the theory,[15][16] as well as showing that it could generate "super-accelerated" bouncing solutions instead of a big bang singularity.
[17] Calcagni and Nardelli investigated the effect of IDG on the diffusion equation.
[18] IDG modifies the way gravitational waves are produced and how they propagate through space.
The amount of power radiated away through gravitational waves by binary systems is reduced, although this effect is far smaller than the current observational precision.
[19] This theory is shown to be stable and propagates finite number of degrees of freedom.
[20] This action can produce a bouncing cosmology, by taking a flat FRW metric with a scale factor
[24] This action avoids a curvature singularity for a small perturbation to a flat background near the origin, while recovering the
This is done using the linearised equations of motion which is a valid approximation because if the perturbation is small enough and the mass scale
[25][26] It was shown that in non-local gravity, Schwarzschild singularities are stable to small perturbations.
[27] Further stability analysis of black holes was carried out by Myung and Park.