Mathematics – Logic
Scientific paper
Aug 2007
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2007phdt........20b&link_type=abstract
Proquest Dissertations And Theses 2007. Section 0024, Part 0606 311 pages; [Ph.D. dissertation].United States -- Rhode Island:
Mathematics
Logic
Cosmological Perturbations, Universe, String Theory, Bouncing Models
Scientific paper
In this thesis we examine several models of the early Universe, many of which are motivated by string theory. We generalize and apply the theory of cosmological fluctuations to higher dimensional setups, such as the cyclic/ ekpyrotic scenario and string gas cosmology (SGC), as well as four dimensional ones, such as certain bouncing models and multi-field inflationary ones, with the goal of extracting observable parameters.
We first discuss some of the challenges faced by the existing bouncing models of the Universe, such as the cyclic one but also four dimensional ones. We will see how hard it is to produce a nearly scale-invariant spectrum of fluctuations in said models and to get a given spectrum through the bounce. As a bonus, we will also straighten out some, technical misconceptions in the literature.
The many problems associated with bouncing models will lead us to construct a new inflationary setup within the framework of string gas cosmology, incorporating a trapping of the internal dimensions at the string scale instead of a bounce. In our study of perturbations in the higher dimensional setup as well as the four dimensional effective theory, we find a viable model of the early universe in agreement with observations. Due to the fact that this model avoids a singular bounce, it can be seen as an improved version of the cyclic/ ekpyrotic scenario.
Last but not least, we compute Non-Gaussianities, which might be observable in the near future, in certain models of multi-field inflation, by extending the delta N-formalism. This class of models includes N-flation, a specific type of assisted inflation motivated by string theory. We find that these models are generically indistinguishable with regard to Non-Gaussianities as long as the slow roll approximation remains valid.
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