Modelling Dark Energy

One of the most pressing, modern cosmological mysteries is the cause of the accelerated expansion of the universe. The energy density required to cause this large scale opposition to gravity is known to be both far in excess of the known matter content, and remarkably smooth and unclustered across the universe. While the most commonly accepted answer is that a cosmological constant is responsible, alternatives abound. This thesis is primarily concerned with such alternatives; both their theoretical nature and observational consequences. In this thesis, we will dedicate Chapter 1 to a brief review on the fundamentals of general relativity, leading into the basics of theoretical cosmology. Following this we will recall some of the key observations that has lead to the standard ΛCDM cosmology. The standard model has well known problems, many of which can be answered by the theoretical ideas of inflation. In Chapter 2 we explore these ideas, including a summary of classical field theory in the context of cosmology, upon which inflation is based. This also serves as the groundwork for Chapter 3, where the varied models of dark energy (and their motivations) are discussed many of which are also reliant on field theory (such as quintessence). These notions are combined in a model described in Chapter 4, where we describe our own addition to a scenario that unifies dark energy and inflation. This addition involving a coupling of the inflation field to an additional one alter the way reheating takes place after inflation, removing some of the shortcomings of the original proposal. The analysis is extended in Chapter 5, to include the effect of quantum corrections. There we show that although a cursory analysis indicates a coupling between quintessence and some other field does not necessarily give rise to dangerously large quantum corrections, provided the effects of decoupling are taken into account. We move on in Chapter 6 to examine the basics of cosmological perturbation theory, and derive the general equations of motion for density and velocity perturbations for a system of fluids, allowing for the exchange of energy-momentum. We make use of this in Chapters 7 and 8, were we examine the growth of structure in a universe where energy is exchanged between dark matter and dark energy. In particular, in Chapter 7 we see that a particular form of the interaction can lead to an instability in the early universe, and we derive the condition for this to be the case. In Chapter 8, we discuss how a similar interaction can lead to a mimicry of modified gravity, and relate this directly to cosmological observations. Finally we summarise our conclusions and discuss avenues of future research in Chapter 9.