Instantons and cosmologies in string theory

This thesis deals with problems in two subdomains of string theory that are a priori unrelated, and in the last chapter, links are established between those two. The first topic of research is that of D-instantons. These are mathematical objects that allow one to compute physical effects that are missed by the standard perturbation theory approach to string theory, and quantum field theory in general. In this thesis, three families of D-instantons are studied, and are shown to be mathematically related to electrically charged black holes. The second topic of this thesis is cosmology in string theory. In recent years, new hope has arisen that string theory might be able to explain two important cosmological events in our universe: inflation and present day acceleration. In this thesis, toy models are studied with the goal of determining whether string theory is at all capable of providing viable scenarios for these. The results show that string theory can certainly generate present day acceleration, however, a realistic scenario for inflation is yet to be found. In the final chapter of this thesis, two mathematical correspondences between D-instantons and cosmologies in string theory are shown. Although both correspondences are technical in nature and no physical consequences can be directly attributed to them, there is hope that the second of these two might help resolve the Big Bang singularity. The standard theory of general relativity does not describe what happened at the time of the Big Bang reliably, as it predicts a singularity in spacetime at that moment. The result in this thesis hypothetically might be hinting at a possible resolution of this, by painting a picture where the universe would have gone through a contraction, and then through a re-expansion that we now call Big Bang, as opposed to the current picture of a universe that "starts" at the Big Bang.