Related papers: Function Theory on Inflationary Tessellations
We summarize our work on constant roll inflationary models. It was understood recently that constant roll inflation, in a regime beyond the slow roll approximation, can give models that are in agreement with the observational constraints.…
This is a pedagogical review on polarized structure functions .
We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are…
A procedure is developed for the recovery of the inflationary potential over the interval that affects astrophysical scales ($\approx 1\Mpc - 10^4\Mpc$). The amplitudes of the scalar and tensor metric perturbations and their power-spectrum…
With present and future observations becoming of higher and higher quality, it is timely and necessary to investigate the most significant theoretical uncertainties in the predictions of inflation. We show that our ignorance of the entire…
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
This document is a brief overview of two documents which continue to develop the weight function theory of basis function smoothers and interpolants. One document considers the zero order theory and one considers the positive order theory.
We study constant-roll inflation using the $\beta$-function formalism. We show that the constant rate of the inflaton roll is translated into a first order differential equation for the $\beta$-function which can be solved easily. The…
In this paper, we discuss the inflationary magnetogenesis scenario, in which the coupling function is introduced to break the conformal invariance of electromagnetic action. Unlike in conventional models, we deduce the Maxwell's equations…
A brief review of inflation is presented. After having demonstrated the generality of the inflationary mechanism, the emphasize is put on its simplest realization, namely the single field slow-roll inflationary scenario. Then, it is shown…
These lecture notes have been written for a short introductory course on the status of inflation after Planck and BICEP2, given at the Xth Modave School of Mathematical Physics. The first objective is to give an overview of the theory of…
In this paper we show that the dynamics associated with slow-roll models of inflation can be investigated through a method called deformation procedure. Using the latter, we explicitly derive an expression linking two slow-roll inflationary…
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
In this brief note the operatorial methods are applied to the study of the Airy function and its generalizations.
Automorphic inflation is an application of the framework of automorphic scalar field theory, based on the theory of automorphic forms and representations. In this paper the general framework of automorphic and modular inflation is described…
We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the straightforward evaluation of their definite integrals and…
We develop notions of integrable functions within the theory of schemic motivic integration.
In this work we provide the missing link between two approaches aimed at characterizing the effect of long perturbation modes in Inflation. We consider the Inflationary Fossils' approach (arXiv:1203.0302 and related works) that…
We explore inflationary cosmology in a theory where there are two scalar fields which non-minimally couple to the Ricci scalar and an additional $R^2$ term, which breaks the conformal invariance. Particularly, we investigate the slow-roll…
A geometry-based density functional theory is presented for mixtures of hard spheres, hard needles and hard platelets; both the needles and the platelets are taken to be of vanishing thickness. Geometrical weight functions that are…