Applications of cosmological perturbation theory
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Cosmological perturbation theory is crucial for our understanding of the universe.
The linear theory has been well understood for some time, however developing and
applying the theory beyond linear order is currently at the forefront of research in
theoretical cosmology.
This thesis studies the applications of perturbation theory to cosmology and,
speci cally, to the early universe. Starting with some background material introducing
the well-tested `standard model' of cosmology, we move on to develop the
formalism for perturbation theory up to second order giving evolution equations for
all types of scalar, vector and tensor perturbations, both in gauge dependent and
gauge invariant form. We then move on to the main result of the thesis, showing
that, at second order in perturbation theory, vorticity is sourced by a coupling term
quadratic in energy density and entropy perturbations. This source term implies a
qualitative di erence to linear order. Thus, while at linear order vorticity decays
with the expansion of the universe, the same is not true at higher orders. This
will have important implications on future measurements of the polarisation of the
Cosmic Microwave Background, and could give rise to the generation of a primordial
seed magnetic eld. Having derived this qualitative result, we then estimate
the scale dependence and magnitude of the vorticity power spectrum, nding, for
simple power law inputs a small, blue spectrum.
The nal part of this thesis concerns higher order perturbation theory, deriving, for
the rst time, the metric tensor, gauge transformation rules and governing equations
for fully general third order perturbations. We close with a discussion of natural
extensions to this work and other possible ideas for o -shooting projects in this
continually growing eld.
Authors
Christopherson, Adam J.Collections
- Theses [3706]