  Ghost-free Infinite Derivative Gravity (IDG) is a modified 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.
