### Abstract

Cosmology motivated by string theory has been studied extensively in the recent literature. String theory is promising because it has interesting features such as unifying gravity, electromagnetic, weak and strong nuclear forces. However, even the energy scale of the experiments at the Large Hadron Collider (~TeV) is too low to detect any strong evidence for string theory. The energy scale of inflation can be above ~ 109 TeV. Therefore, it is expected to find some signature of string theory in cosmology.String theory predicts ten space-time dimensions. In the brane world scenario, our four dimensional Universe is confined onto the higher dimensional object called the Brane in the ten dimensional space time. The Dirac-Born-Infeld (DBI) inflation is based on this idea. DBI inflation predicts a characteristic statistical feature in the Cosmic Microwave Background (CMB) temperature anisotropies. In this thesis, we study the predictions of the DBI inflation models on the CMB temperature anisotropies.

In chapter 1, the idea of inflation in the early stage of the Universe is introduced after explaining why we need inflation in addition to the standard Big Bang scenario. At the end of this chapter, we introduce the CMB observables that quantify the statistical properties of the CMB anisotropies.

In chapter 2, we introduce the cosmological perturbation theory for general multi-field inflation including DBI inflation. After studying the linear perturbation theory, we introduce the higher order perturbations that produce the non- Gaussianities. The analytic formulae for the CMB observables that are valid in cases with the effective single field dynamics around horizon crossing are summarised at the end of this chapter.

In chapter 3, the idea of DBI inflation is introduced. Some analytic predictions for the CMB observables are given in a simple single field DBI inflation model. After introducing the microphysical constraint that excludes the single field DBI inflation, we show that this constraint can be significantly relaxed if the trajectory in the field space is bent in multi-field DBI inflation models.

In chapter 4, we study the specific two-field DBI inflation model with a potential that is derived in string theory. The potential contains only the leading order term ignoring all other possible corrections in string theory. After studying how curves in the trajectories in the field space affect the CMB observable, we show that this model is excluded by observation in the regime where the analytic formulae introduced in chapter 2 are valid. At the end of this chapter, we discuss the cases where we cannot use the analytic formulae and discuss possible implications

In chapter 5, we study the two-field DBI inflation model with a potential that has the essential feature of the potential obtained with other corrections in addition to the leading term in string theory. In this model, inflation is driven by the motion of a D3 brane along the radial direction and at later times instabilities develop in the angular directions. It is shown that it is actually possible to satisfy the microphysical constraint with a turn in the trajectory in the field space. However, this particular choice of potential is excluded with the constraint on the local type non-Gaussianity by the latest CMB observations of the PLANCK satellite.

We discuss the future perspective of DBI inflation models in the last chapter.

Date of Award | Feb 2014 |
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Original language | English |

Supervisor | Kazuya Koyama (Supervisor) & David Bacon (Supervisor) |