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Various approaches to stochastic processes exist, noting that key properties such as measurability and continuity are not trivially satisfied. We introduce a new theory for Gaussian processes using improper linear functionals. Using a…
Single field inflationary models predict nearly Gaussian initial conditions and hence a detection of non-Gaussianity would be a signature of the more complex inflationary scenarios. In this paper we study the effect on the cosmic microwave…
Cosmological production of scalar, non-minimally coupled dark matter depends on the specifics of the inflationary model under consideration. We analyze both Starobinsky inflation and a quadratic potential, solve the full background…
A formula for the power spectrum of curvature perturbations having any initial conditions in inflation is obtained. Based on the physical conditions before inflation, the possibility exists that the initial state of scalar perturbations is…
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…
In this paper, we study the stochastic heat equation in the spatial domain $\mathbb{R}^d$ subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and…
Recently multi-field inflation models that can produce large scalar fluctuations on small scales have drawn a lot of attention, primarily because they could lead to primordial black hole production and generation of large second-order…
Using a new kind of 5D Ricci-flat canonical metric, we obtain by a static foliation an effective 4D Schwarzschild-de Sitter hypersurface. We examine some particular initial conditions which could be responsible for the inflationary…
It is conjectured that inflation, taking account of quantum gravity, leads to a discrete spectrum of cosmological perturbations, instead of the continuous Gaussian spectrum predicted by standard field theory in an unquantized background.…
Inflation predicts a stochastic background of gravitational waves over a broad range of frequencies, from those accessible with cosmic microwave background (CMB) measurements, to those accessible directly with gravitational-wave detectors,…
Cosmological inflation remains to be a unique mechanism of generation of plausible initial conditions in the early universe. In particular, it generates the primordial quasiclassical perturbations with power spectrum determined by the…
For the first time, we investigate the non-perturbative dynamics of single field inflation with a departure from slow-roll. Using simulations, we find that oscillatory features in the potential can drastically alter the course of inflation,…
Certain models of cosmic inflation produce strong cosmological perturbations at short length scales, which may later collapse into primordial black holes. To find the statistics of these strong perturbations and the ensuing black holes, it…
There have been long debates about the initial condition of inflationary perturbations. In this work we explicitly show the decay of excited states during inflation via interactions. For this purpose, we note that the folded shape…
We propose a novel scenario in which scalar perturbations, that seed the large scale structure of the Universe, are generated without relying on a scalar field (the inflaton). In this framework, inflation is driven by a de Sitter space-time…
Since the advent of inflation, several theorems have been proven suggesting that although inflation can (and generically does) continue eternally into the future, it cannot be extended eternally into the past to create a ``steady-state''…
We analyze the stochastic thermodynamics of systems with continuous space of states. The evolution equation, the rate of entropy production, and other results are obtained by a continuous time limit of a discrete time formulation. We point…
In pattern forming systems such as Rayleigh-Benard convection or directional solidification, a large number of linearly stable, patterned steady states exist when the basic, simple steady state is unstable. Which of these steady states will…
We apply the Effective Field Theory of Inflation to study the case where the continuous shift symmetry of the Goldstone boson \pi is softly broken to a discrete subgroup. This case includes and generalizes recently proposed String Theory…
We analyze the effects of spatiotemporal noise on stationary pulse solutions (bumps) in neural field equations on planar domains. Neural fields are integrodifferential equations whose integral kernel describes the strength and polarity of…