相关论文: Squirals and beyond: Substitution tilings with sin…

In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the…

We study an inflationary scenario where thermal inflation is followed by fast-roll inflation. This is a rather generic possibility based on the effective potentials of spontaneous symmetry breaking in the context of particle physics models.…

We show how observations of the density perturbation (scalar) spectrum and the gravitational wave (tensor) spectrum allow a reconstruction of the potential responsible for cosmological inflation. A complete functional reconstruction or a…

We present a general scheme how to construct a substitution rule for generating $d$-dimensional analogues of the paperfolding structures. This substitution is proven to be primitive, so that the translation action on the hull forms a…

Recently there have been differing viewpoints on how to evaluate the curvature power spectrum generated during inflation. In a series of papers by some authors it has been argued that the renormalization scheme adopted for the inflaton…

Recently Taylor and Socolar introduced an aperiodic mono-tile. The associated tiling can be viewed as a substitution tiling. We use the substitution rule for this tiling and apply the algorithm of \cite{AL} to check overlap coincidence. It…

We study the amplitude and spectral tilt of density perturbations in the simplest hybrid inflation models. We give an exact expression for the amplitude of quantum fluctuations on all scales in the limit where we can neglect the…

The background evolution in two-field inflation can feature two distinct stages, corresponding to the evolution along two successive field directions. When the second stage occurs at a significantly lower energy scale, the inflationary…

Multi-field inflation with a curved scalar geometry has been found to support background trajectories that violate the slow-roll, slow-turn conditions and thus have the potential to evade the swampland constraints. In order to understand…

In this work we investigate characteristic modifications of the spectrum of cosmological perturbations and the spectral index due to chain inflation. We find two types of effects. First, modifications of the spectral index depending on…

Combining the Kaplan surface mode approach for chiral fermions with added terms motivated by Eichten and Preskill suggests the possibility for a lattice regularization of the standard model which is finite, exactly gauge invariant, and only…

We develop an integral form for the bispectrum in general single-field inflation whose domain of validity includes models of inflation where the background evolution is not constrained to be slowly varying everywhere. Our integral form…

We study linear scalar perturbations in single-field models of inflation featuring a non-attractor phase. These models lead to a peak in the curvature power spectrum that may result in the formation of primordial black holes. We develop a…

We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…

The paper establishes an equivalence between pure point diffraction and certain types of model sets, called inter model sets, in the context of substitution point sets and substitution tilings. The key ingredients are a new type of…

We consider the spectrum of primordial fluctuations produced by inflationary models where the inflaton potential is the sum of two exponential terms. A wide range of spectra result, with the only constraint being that the scalar spectrum…

Suppose a set of prototiles allows $N$ different substitution rules. In this paper we study tilings of $\mathbb{R}^d$ constructed from random application of the substitution rules. The space of all possible tilings obtained from all…

We show that a string-inspired Planck scale modification of general relativity can have observable cosmological effects. Specifically, we present a complete analysis of the inflationary perturbation spectrum produced by a phenomenological…

The scenario of constant-roll inflation is studied where the inflaton is a scalar field with modified kinetic term, known as non-canonical scalar field. This modification leads to some changes in the slow-roll parameters, and also by taking…

The pinwheel tiling is the paradigm for a substitution tiling with circular symmetry, in the sense that the corresponding autocorrelation is circularly symmetric. As a consequence, its diffraction measure is also circularly symmetric, so…