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.Comment: PhD thesis, 145 p. Defended OCT 201

Constraints on inflation with LSS surveys: features in the primordial power spectrum

We analyse the efficiency of future large scale structure surveys to unveil the presence of scale dependent features in the primordial spectrum --resulting from cosmic inflation-- imprinted in the distribution of galaxies. Features may appear as a consequence of non-trivial dynamics during cosmic inflation, in which one or more background quantities experienced small but rapid deviations from their characteristic slow-roll evolution. We consider two families of features: localized features and oscillatory extended features. To characterise them we employ various possible templates parametrising their scale dependence and provide forecasts on the constraints on these parametrisations for LSST like surveys. We perform a Fisher matrix analysis for three observables: cosmic microwave background (CMB), galaxy clustering and weak lensing. We find that the combined data set of these observables will be able to limit the presence of features down to levels that are more restrictive than current constraints coming from CMB observations only. In particular, we address the possibility of gaining information on currently known deviations from scale invariance inferred from CMB data, such as the feature appearing at the $\ell \sim 20$ multipole (which is the main contribution to the low-$\ell$ deficit) and a potential feature appearing at $\ell \sim 800$.Comment: 37 pp., 5 Tabs., 10 Figs, v3: changed discussion around templates II, III, added clarifications, comments and references. Matches JCAP versio

Non-Gaussian statistics of de Sitter spectators: A perturbative derivation of stochastic dynamics

Scalar fields interacting with the primordial curvature perturbation during inflation may communicate their statistics to the latter. This situation motivates the study of how the probability density function (PDF) of a light spectator field $\varphi$ in a pure de Sitter space-time, becomes non-Gaussian under the influence of a scalar potential ${\mathcal V(\varphi)}$. One approach to this problem is offered by the stochastic formalism introduced by Starobinsky and Yokoyama. It results in a Fokker-Planck equation for the time-dependent PDF $\rho (\varphi , t)$ describing the statistics of $\varphi$ which, in the limit of equilibrium gives one back the solution $\rho (\varphi) \propto \exp \big[ - \frac{8 \pi^2}{3 H^4} {\mathcal V(\varphi)} \big]$. We study the derivation of $\rho (\varphi , t)$ using quantum field theory tools. Our approach yields an almost Gaussian distribution function, distorted by minor corrections comprised of terms proportional to powers of $\Delta N \times \mathcal O(\partial_\varphi) {\mathcal V(\varphi)}$, where $\Delta N$ is the number of $e$-folds succeeding the Hubble-horizon crossing of $\varphi$'s wavelengths, and $\mathcal O(\partial_\varphi)$ stands for a derivative operator acting on ${\mathcal V(\varphi)}$. This general form is obtained perturbatively and remains valid even with loop corrections. Our solution satisfies a Fokker-Planck equation that receives corrections with respect to the one found within the stochastic approach, allowing us to comment on the validity of the standard equilibrium solution for generic potentials. We posit that higher order corrections to the Fokker-Planck equation may become important towards the equilibrium.Comment: 53 pp. plus reference

Shapes and features of the primordial bispectrum

If time-dependent disruptions from slow-roll occur during inflation, the correlation functions of the primordial curvature perturbation should have scale-dependent features, a case which is marginally supported from the cosmic microwave background (CMB) data. We offer a new approach to analyze the appearance of such features in the primordial bispectrum that yields new consistency relations and justifies the search of oscillating patterns modulated by orthogonal and local templates. Under the assumption of sharp features, we find that the cubic couplings of the curvature perturbation can be expressed in terms of the bispectrum in two specific momentum configurations, for example local and equilateral. This allows us to derive consistency relations among different bispectrum shapes, which in principle could be tested in future CMB surveys. Furthermore, based on the form of the consistency relations, we construct new two-parameter templates for features that include all the known shapes.Comment: (v1) 16 pages, 3 figures, 1 table; (v2) minor clarifications including updated abstract, to appear in Journal of Cosmology and Astroparticle Physic

On degenerate models of cosmic inflation

In this article we discuss the role of current and future CMB measurements in pinning down the model of inflation responsible for the generation of primordial curvature perturbations. By considering a parameterization of the effective field theory of inflation with a modified dispersion relation arising from heavy fields, we derive the dependence of cosmological observables on the scale of heavy physics $\Lambda_{\rm UV}$. Specifically, we show how the $f_{\rm NL}$ non-linearity parameters are related to the phase velocity of curvature perturbations at horizon exit, which is parameterized by $\Lambda_{\rm UV}$. Bicep2 and Planck findings are shown to be consistent with a value $\Lambda_{\rm UV} \sim \Lambda_{\rm GUT}$. However, we find a degeneracy in the parameter space of inflationary models that can only be resolved with a detailed knowledge of the shape of the non-Gaussian bispectrum.Comment: 22pp., 1 fig; v2: added some clarifications and references, corrected typos, matches published versio

Scale invariance of the primordial tensor power spectrum

Future cosmic microwave background polarization experiments will search for evidence of primordial tensor modes at large angular scales, in the multipole range $4 \leq \ell \leq 50.$ Because in that range there is some mild evidence of departures from scale invariance in the power spectrum of primordial curvature perturbations, one may wonder about the possibility of similar deviations appearing in the primordial power spectrum of tensor modes. Here we address this issue and analyze the possible presence of features in the tensor spectrum resulting from the dynamics of primordial fluctuations during inflation. We derive a general, model independent, relation linking features in the spectra of curvature and tensor perturbations. We conclude that even with large deviations from scale invariance in the curvature power spectrum, the tensor spectrum remains scale invariant for all observational purposes.Comment: 22 pages, 4 figures; v2: added references and clarifying comments; v3: added reference and few more comments. Matches published versio

Effective field theory of weakly coupled inflationary models

The application of Effective Field Theory (EFT) methods to inflation has taken a central role in our current understanding of the very early universe. The EFT perspective has been particularly useful in analyzing the self-interactions determining the evolution of co-moving curvature perturbations (Goldstone boson modes) and their influence on low-energy observables. However, the standard EFT formalism, to lowest order in spacetime differential operators, does not provide the most general parametrization of a theory that remains weakly coupled throughout the entire low-energy regime. Here we study the EFT formulation by including spacetime differential operators implying a scale dependence of the Goldstone boson self-interactions and its dispersion relation. These operators are shown to arise naturally from the low-energy interaction of the Goldstone boson with heavy fields that have been integrated out. We find that the EFT then stays weakly coupled all the way up to the cutoff scale at which ultraviolet degrees of freedom become operative. This opens up a regime of new physics where the dispersion relation is dominated by a quadratic dependence on the momentum \omega ~ p^2. In addition, provided that modes crossed the horizon within this energy range, the prediction of inflationary observables - including non-Gaussian signatures - are significantly affected by the new scales characterizing it.Comment: 36 pages, v2: references added, minor changes to match published versio

De Sitter bubbles from anti-de Sitter fluctuations

Cosmological acceleration is difficult to accommodate in theories of fundamental interactions involving supergravity and superstrings. An alternative is that the acceleration is not universal but happens in a large localized region, which is possible in theories admitting regular black holes with de Sitter-like interiors. We point out that, given a global anti-de Sitter background, the formation of such 'de Sitter bubbles' will be enhanced by mechanisms analogous to the Bizon-Rostworowski instability in general relativity. This opens an arena for discussing the production of multiple accelerating universes from anti-de Sitter fluctuations. We demonstrate such collapse enhancement by explicit numerical work in the context of a simple two-dimensional dilaton-gravity model that mimics the spherically symmetric sector of higher-dimensional gravities.Comment: v2: small change