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This thesis is dedicated to studying cosmological inflation, which is a period of accelerated expansion in the very early Universe that is required to explain the observed anisotropies in the cosmic microwave background. Inflation, when…
A novel stochastic technique combining a dilute source grid of $\mathbb{Z}_3$ noise with iterative momentum-smearing is used to study the proton correlation function at rest and in boosted frames on two lattice volumes. The technique makes…
We set up a formalism that can be used to calculate the power spectrum of the curvature perturbations produced during inflation up to arbitrary order in the slow-roll expansion, and explicitly calculate the power spectrum and spectral index…
We present a computer-assisted approach to coarse-graining the evolutionary dynamics of a system of nonidentical oscillators coupled through a (fixed) network structure. The existence of a spectral gap for the coupling network graph…
We describe models of single-field inflation with small and sharp step features in the potential (and sound speed) of the inflaton field, in the context of the Effective Field Theory of Inflation. This approach allows us to study the…
Stochastic inflation rests on the separate-universe approximation, i.e. the ability to describe long-wavelength fluctuations in an inflating universe as homogeneous perturbations of its background dynamics. Although this approximation is…
We present an equation-free computational approach to the study of the coarse-grained dynamics of {\it finite} assemblies of {\it non-identical} coupled oscillators at and near full synchronization. We use coarse-grained observables which…
We study the primordial bispectrum of curvature perturbation in the uniform- density slicing generated by the interaction between the inflaton and isotropic background gauge fields. We derive the action up to cubic order in perturbation and…
In order to go beyond the mean-field approximation, commonly used in the inflationary computations, an identification of the quantum constituents of the inflationary background is made. In particular, the homogeneous scalar field…
We consider cosmological perturbations caused by modulated inflaton velocity. During inflation, the inflaton motion is damped and the velocity is determined by the parameters such as couplings or masses that may depend on light…
During inflation explicit perturbative computations of quantum field theories which contain massless, non-conformal fields exhibit secular effects that grow as powers of the logarithm of the inflationary scale factor. Starobinski\u{\i}'s…
The slow rolling inflation is dual to the random walk of conformal zero-mode. The 2 dimensional Fokker-Planck theory predicts the slow roll parameters of 4d inflation theory. The O(N) enhancements of the two point functions, N is the…
We investigate the origin of non-Markovianity in stochastic inflation and its implications for nonlinear perturbation theory. In the Schwinger--Keldysh formulation, the noise terms sourcing the infrared (IR) Langevin equations are…
We investigate a single field model in the context of the constant-roll inflation in which inflaton moves down to the minimum point of the potential with a constant rate of rolling. We use a quintessential inflationary model obtained by a…
Stochastic $\delta N$ formalism is a powerful tool to calculate the cosmological correlators non-perturbatively. However, it requires the initial data for the amplitude of the noise on the initial flat hypersurface which for a free theory…
Stochastic Inflation is an important framework for understanding the physics of de Sitter space and the phenomenology of inflation. In the leading approximation, this approach results in a Fokker-Planck equation that calculates the…
We study the problem of initial conditions for slow-roll inflation along a plateau-like scalar potential within the framework of fluctuation-dissipation dynamics. We consider, in particular, that inflation was preceded by a…
The primordial spectrum of fluctuations may present a large peak as a result of enhancing features during inflation. This may include, but is not limited to, bumps in the inflaton's potential, phases of ultra-slow-roll or turns in…
We revisit inflation coupled with vector fields employing kinetic coupling in the comoving gauge. It is known that there is a cumulative effect $IN^2$ on the curvature power spectrum. For a large number of e-foldings $N$, this contribution…
We develop a frame-covariant formulation of inflation in the slow-roll approximation by generalizing the inflationary attractor solution for scalar-curvature theories. Our formulation gives rise to new generalized forms for the potential…