Ghost-free Infinite Derivative Gravity (IDG) is a modifed gravity theory
which can avoid the singularities predicted by General Relativity.
This thesis examines the effect of IDG on four areas of importance
for theoretical cosmologists and experimentalists. First, the gravitational
potential produced by a point source is derived and compared
to experimental evidence, around both Minkowski and (Anti)
de Sitter backgrounds. Second, the conditions necessary for avoidance
of singularities for perturbations around Minkowski and (Anti)
de Sitter spacetimes are found, as well as for background Friedmann-
Robertson-Walker spacetimes. Third, the modification to perturbations
during primordial inflation is derived and shown to give a constraint
on the mass scale of IDG, and to allow further tests of the
theory. Finally, the effect of IDG on the production and propagation
of gravitational waves is derived and it is shown that IDG gives
almost precisely the same predictions as General Relativity for the
power emitted by a binary system.