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Particle production in de Sitter spacetime arises from the exponential expansion of space, rendering the Bunch-Davies vacuum perceived as a particle-containing state by late-time observers. For states defined as eigenstates of both momentum and the Hamiltonian, the Bunch-Davies vacuum exhibits a constant particle density per physical momentum. We explore particle production beyond this baseline, focusing on deviations from exact de Sitter conditions and non-gravitational interactions, such as slow-roll inflation or interactions arising from the coupling of inflation to other fields. Using Bogoliubov transformations, we calculate the number density of energy/momentum eigenstates. In single-field inflation, this density captures the observed spectral index of the primordial power spectrum, while in two-field models, it reflects the non-gravitational coupling driving background trajectory turning. We present analytical results applicable to various scenarios involving particle production from non-adiabatic processes during inflation.

Correlation functions of light scalar fields in de Sitter spacetime, computed via standard perturbation theory, often exhibit secular growth characterized by time-dependent divergent terms in the form of powers of $\ln a(t)$, where $a(t)$ is the scale factor describing cosmic expansion. It is widely believed that loop corrections further enhance this secular growth. However, in this note, we argue that this is not necessarily the case: Loop corrections can be systematically handled using standard perturbative techniques, such as dimensional regularization, without introducing new $\ln a(t)$ terms. We focus on a canonical massless scalar field $\varphi$ with self-interactions described by a potential $\mathcal{V}(\varphi)$, and analyze correlation functions represented by diagrams with a single vertex and an arbitrary number of loops. In this framework, infrared divergences can be systematically eliminated with counterterms at each order in perturbation theory, leading to loop-corrected correlation functions that are indistinguishable from their tree-level forms, with no secular growth from loops. Furthermore, adopting a Wilsonian perspective, we explore the role of cutoffs in computing loop corrections within effective field theory and identify the effective potential $\mathcal{V}_{\rm eff}(\varphi)$, which guarantees cutoff-independent observables. We conclude that when infrared comoving cutoffs are used to regularize loop integrals, time-dependent Wilsonian coefficients are necessary to maintain cutoff-free correlation functions. Neglecting this time dependence results in secular growth from loops.

A long-standing problem within the study of cosmic inflation consists in fully reconciling the stochastic approach with perturbation theory. A complete connection between both formalisms has remained elusive even in the simple case of a single scalar field with self-interactions determined by an arbitrary potential, in a fixed de Sitter background. Using perturbation theory, we compute the one-point probability density function for primordial fluctuations valid to first order in the potential. We examine under which conditions our solution respects the Fokker-Planck equation encountered within the stochastic approach. We identify discrepancies and elucidate their origins, allowing us to shed light on the status of the stochastic formalism.

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.

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 considerably strengthen this scenario by placing it in a global anti-de Sitter background, where the formation of '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.

We show that a scalar excited state with large occupation numbers during inflation leads to an enhancement of tensor modes and a characteristic pattern of order-one oscillations in the associated stochastic gravitational wave background (SGWB) sourced during inflation. An effective excited state, i.e. a departure from the Bunch-Davies vacuum, can emerge dynamically as the result of a transient non-adiabatic evolution, e.g. a sharp feature along the inflationary history. We provide an explicit example in a multifield context where the sharp feature triggering the excited state is identified with a strong turn in the inflationary trajectory. En passant, we derive a universal expression for the tensor power spectrum sourced at second order by an arbitrary number of scalar degrees of freedom during inflation, crucially taking into account the nontrivial structure of the Hilbert space in multifield setups. The SGWB sourced during inflation can overcome the standard scalar-induced SGWB sourced at horizon re-entry of the fluctuations after inflation, while being less constrained by perturbativity and backreaction bounds. In addition, one may entertain the possibility of detecting both since they peak at different frequencies exhibiting oscillations with distinct periods.

We show that initial conditions for small-field inflation can be determined quantum mechanically by introducing a suitable flattened region in the scalar potential. The inflaton is then driven towards the slow-roll attractor solution exponentially fast, desensitising inflation from the initial velocity and partially evading the so-called overshoot problem. We give an explicit example in the context of hilltop inflation by introducing an ultra slow-roll plateau around the maximum of the potential and analyse its effect on the phase-space trajectories.

The inflationary origin of primordial black holes (PBHs) relies on a large enhancement of the power spectrum $\Delta_\zeta$ of the curvature fluctuation $\zeta$ at wavelengths much shorter than those of the cosmic microwave background anisotropies. This is typically achieved in models where $\zeta$ evolves without interacting significantly with additional (isocurvature) scalar degrees of freedom. However, quantum gravity inspired models are characterized by moduli spaces with highly curved geometries and a large number of scalar fields that could vigorously interact with $\zeta$ (as in the cosmological collider picture). Here we show that isocurvature fluctuations can mix with $\zeta$ inducing large enhancements of its amplitude. This occurs whenever the inflationary trajectory experiences rapid turns in the field space of the model leading to amplifications that are exponentially sensitive to the total angle swept by the turn, which induce characteristic observable signatures on $\Delta_\zeta$. We derive accurate analytical predictions and show that the large enhancements required for PBHs demand non-canonical kinetic terms in the action of the multifield system.

Cosmic inflation may have led to non-Gaussian initial conditions that cannot be fully parametrised by 3- and/or 4-point functions. In this work, we discuss various strategies to search for primordial non-Gaussianity beyond polyspectra with the help of cosmological data. Our starting point is a generalised local ansatz for the primordial curvature perturbation $\zeta$ of the form $\zeta = \zeta_{\rm G} + \mathcal{F}_{\rm NG} (\zeta_{\rm G})$, where $\zeta_{\rm G}$ is a Gaussian random field and $\mathcal{F}_{\rm NG}$ is an arbitrary function parametrising non-Gaussianity that, in principle, could be reconstructed from data. Noteworthily, in the case of multi-field inflation, the function $\mathcal{F}_{\rm NG}$ can be shown to be determined by the shape of tomographic sections of the landscape potential responsible for driving inflation. We discuss how this generalised local ansatz leads to a probability distribution functional that may be used to extract information about inflation from current and future observations. In particular, we derive various classes of probability distribution functions suitable for the statistical analysis of the cosmic microwave background and large-scale structure.

The recent Planck data on the power spectrum of temperature anisotropies of the cosmic microwave background marginally support deviations from the $\Lambda$CDM model at several multipoles. With a view towards current and forthcoming observational surveys, we trace these features to other observables like the scalar bispectrum and the tensor power spectrum. A possible detection of such bumps in these channels would increase their statistical significance shedding light on the ultra violet mechanisms responsible for their appearance in the data.

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 $\ell \sim 800$.

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.

We study features in the bispectrum of the primordial curvature perturbation correlated with the reconstructed primordial power spectrum from the observed cosmic microwave background temperature data. We first show how the bispectrum can be completely specified in terms of the power spectrum and its first two derivatives, valid for any configuration of interest. Then using a model-independent reconstruction of the primordial power spectrum from the Planck angular power spectrum of temperature anisotropies, we compute the bispectrum in different triangular configurations. We find that in the squeezed limit at k ~ 0.06/Mpc and k ~ 0.014/Mpc there are marginal 2sigma deviations from the standard featureless bispectrum, which meanwhile is consistent with the reconstructed bispectrum in the equilateral configuration.

We study next-to-leading corrections to the effective action of the curvature perturbation obtained by integrating out the coupled heavy isocurvature perturbation. These corrections result from including higher order derivative operators, weighted by the mass scale of the heavy physics, in the effective theory expansion. We find that the correction terms are suppressed by the ratio of the Hubble parameter to the heavy mass scale. The corresponding corrections to the power spectrum of the curvature perturbation are presented for a simple illustrative example.

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.

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.

We generalize previous results on N=1, (3+1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, i.e. that the beta and gamma functions vanish in addition to anomaly cancellation, translate to a Diophantine equation in terms of the quiver data. We re-derive results for low block numbers revealing an new intriguing algebraic structure underlying a class of possible superconformal fixed points of such theories. After explicitly computing the five block case Diophantine equation, we use this structure to reorganize the result in a form that can be applied to arbitrary block numbers. We argue that these theories can be thought of as vectors in the root system of the corresponding quiver and superconformality conditions are shown to associate them to certain subsets of imaginary roots. These methods also allow for an interpretation of Seiberg duality as the action of the affine Weyl group on the root lattice.

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.

We analyze theoretical constraints on the consistency of brane inflation leading to cosmic superstring formation and on the subsequent radiation of these cosmic superstrings. We first investigate the implications of recently elucidated supergravity constraints on models of brane inflation. We show that both D3/D7 and D3/anti-D3 brane inflation are subject to non-trivial constraints. Both models can be shown to satisfy those constraints, but for the case of D3/D7 there may be important consequences for the inflationary mechanism. We then analyze the strong theoretical constraints on the types of allowed radiation by cosmic superstrings, should they be formed; such constraints do not apply to their field theoretical analogues. We argue that in a warped background where one might expect axionic radiation to be enhanced relative to gravitational radiation, neithe F-strings nor D-strings can emit axionic radiation, while FD-strings cannot give rise to Neveu-Schwarz--Neveu-Schwarz particle emission, and their Ramond-Ramond particle emission is not well-defined.

We examine the consequences of recent developments on Fayet-Iliopoulos (FI) terms for D-term inflationary models. There is currently no known way to couple constant FI terms to supergravity consistently; only field-dependent FI terms are allowed. These are natural in string theory and we argue that the FI term in D3/D7 inflation turns out to be of this type, corresponding to a pseudo-anomalous U(1). T he anomaly is canceled by the Green-Schwarz mechanism in 4 dimensions. Inflation proceeds as usual, except that the scale is set by the GS parameter. Cosmic strings resulting from a pseudo-anomalous U(1) have potentially interesting characteristics. Originally expected to be global, they turn out to be local in the string theory context and can support currents. We outline the nature of these strings, discuss bounds on their formation, and summarize resulting cosmological consequences.