Related papers: Function Theory on Inflationary Tessellations

The inflationary flow equations are a frequently used method of surveying the space of inflationary models. In these applications the infinite hierarchy of differential equations is truncated in a way which has been shown to be equivalent…

In this paper we consider several families of potential non-isochronous systems and study their associated period functions. Firstly, we prove some properties of these functions, like their local behavior near the critical point or…

We review sandwich theorems from the theory of convex functions.

We review the relation between the inflationary potential and the spectra of density (scalar) perturbations and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton…

The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…

The onset of condensation of hard spheres in a gravitational field is studied using density functional theory. In particular, we find that the local density approximation yields results identical to those obtained previously using the…

Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

We investigate the cosmic inflation within a class of the scalar-tensor model with the scalar-dependent non-minimal kinetic couplings. The inflationary dynamical potential will be applied. Using the slow-roll approximation, we compute…

Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment…

The correlation functions are calculated for the two dimensional Ising model with free boundary conditions and the two dimensional Ising model with periodic boundary conditions.

A disformal coupling between two scalar fields is considered in the context of cosmological inflation. The coupling introduces novel derivative interactions mixing the kinetic terms of the fields but without introducing superluminal or…

We survey old and new conjectures and results on various types of spherical maximal functions, emphasizing problems with a fractal dilation set.

Inflation is a highly favoured theory for the early Universe. It is compatible with current observations of the cosmic microwave background and large scale structure and is a driver in the quest to detect primordial gravitational waves. It…

We explore the correlations between correlation functions of the primordial curvature perturbation produced during inflation. We find that for general single field inflation, other than the source terms which depend on the model details,…

The mechanism of thermal inflation, a relatively short period of accelerated expansion after primordial inflation, is a desirable ingredient for a certain class of particle physics models if they are not to be in contention with the…

This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).

We study the inflationary scenario in the Tsallis entropy-based cosmology. The Friedmann equations in this setup can be derived by using the first law of thermodynamics. To derive the relations of the power spectra of the scalar and tensor…

This note makes a self-contained exposition of the basic facts of big bang cosmology as they relate to inflation. The fundamental problems with that model are then explored. A quartic scalar potential model of inflation is evaluated which…

This is a personal account of the early work that led to what is now known as the ``preheating stage" of inflationary cosmology. The broader applicability of the underlying instability mechanisms in cosmology are indicated.

I investigate multi-field inflationary models with fields that decay during inflation, leading to staggered inflation. This feature is natural in many models motivated by string theory, for instance if inflatons are related to interbrane…