Theoretical and Observational Constraints on Brane Inflation and Study
  of Scalar Perturbations through the Effective Field Theory Formalism
  In this thesis, consisting of two main parts, we study observational
signatures of cosmic (super)strings in the context of D-brane inflation and
properties of scalar perturbations on generic homogeneous inflating
backgrounds. In the first part we study the production, nature and decay
processes of cosmic superstrings in two widely used effective models of D-brane
inflation, namely the $D3/D7$ and $D3/\bar{D}3$ models. Specifically, we show
that the strings produced in $D3/D7$ are of local axionic type and we place
constraints on the tension while arguing that the supersymmetry breaking
mechanism of the model needs to be altered according to supergravity
constraints on constant Fayet-Iliopoulos terms. Moreover, we study radiative
processes of cosmic superstrings on warped backgrounds. We argue that placing
the string formation in a natural context such as $D3/\bar{D}3$ inflation,
restricts the forms of possible radiation from these objects. Motivated by
these string models, which inevitably result in the presence of heavy moduli
fields during inflation, in the second part, using the Effective Field Theory
(EFT) of inflation, we construct operators that capture the effects of massive
scalars on the low energy dynamics of inflaton perturbations. We compute the
energy scales that define the validity window of the EFT such as the scale
where ultra violet (UV) degrees of freedom become operational and the scale
where the EFT becomes strongly coupled. We show that the low energy operators
related to heavy fields induce a dispersion relation for the light modes
admitting two regimes: a linear and a non linear/dispersive one. Assuming that
these modes cross the Hubble scale within the dispersive regime, we compute
observables related to two- and three-point correlators and show how they are
directly connected with the scale of UV physics.
