## Modelling dark energy

##### Abstract

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 CDM 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.