Related papers: Three variations on a theme by Fibonacci
Given a finite collection of two-dimensional tile types, the field of study concerned with covering the plane with tiles of these types exclusively has a long history, having enjoyed great prominence in the last six to seven decades. Much…
Inflaton coupling to a vector field via the $f^2(\phi)F_{\mu\nu}F^{\mu\nu}$ term is used in several contexts in the literature, such as to generate primordial magnetic fields, to produce statistically anisotropic curvature perturbation, to…
In the ``natural inflation'' model, the inflaton potential is periodic. We show that Planck scale physics may induce corrections to the inflaton potential, which is also periodic with a greater frequency. Such high frequency corrections…
Convolutions for Tribonacci numbers involving binomial coefficients are treated with ordinary generating functions and the diagonalization method of Hautus and Klarner. In this way, the relevant generating function can be established, which…
Liouville gravity can be used to precisely model features of 3+1 dimensional cosmology in a simplified 1+1d setting. We study primordial fluctuations in a generally covariant extension of Liouville theory, in the context of single field…
In this work we completely describe the dynamics of triangle tiling billiards. In the first part of this work, we propose a geometric approach of dynamics by introducing natural foliations associated to it. In the second part, we exploit…
We revisit an extension of the well-known formalism for gauge-invariant scalar metric fluctuations, to study the spectrums for both, the inflaton and gauge invariant (scalar) metric fluctuations in the framework of a single field…
Energy level spacing statistics are discussed for a two dimensional quasiperiodic tiling. The property of self-similarity under inflation is used to write a recursion relation for the level spacing distributions defined on square…
We discuss an inflationary scenario based on Lovelock terms. These higher order curvature terms can lead to inflation when there are more than three spatial dimensions. Inflation will end if the extra dimensions are stabilised, so that at…
The present work examines the possibility of warm inflationary paradigm in the modified gravity theory with fractal geometry. By choosing the normal fluid as radiation fluid and the effective fluid (with the extra term in modified field…
Analytic interpolation problems with rationality and derivative constraints are ubiquitous in systems and control. This paper provides a new method for such problems, both in the scalar and matrix case, based on a non-standard Riccati-type…
The Brattelli diagram associated with a given bicolored Dynkin-Coxeter graph of type $A_n$ determines planar fractal sets obtained by infinite dissections of a given triangle. All triangles appearing in the dissection process have angles…
Brane inflation can provide a promissing framework for solving the fine-tuning problem in standard inflationary models. The aim of this paper is to illustrate the mechanism by which this can be achieved. By considering the supersymmetric…
We introduce a new class of multiplications of distributions in one dimension merging together two different regularizations of distributions. Some of the features of these multiplications are discussed in a certain detail. We use our…
Two extensions of ideas lying in the basis of the inflationary scenario of the early Universe and their effect on the large scale structure of the present-day Universe are discussed. The first of them is the possibility of fast phase…
In this talk we discuss three different issues. First of all, there exist several proposals how to solve cosmological problems by adiabatic expansion of the Universe, without any use of inflation. We explain why these models do not solve…
The Fibonacci sequence is obtained as weighted sum along the rows in the Pascal triangle by choosing a periodic up-and-down pattern of weights from the set $\{-1,-\frac{1}{2},0, \frac{1}{2}, 1\}$. A graphical illustration of this identity…
We construct a natural inflation model with the inflaton as a linear combination of the fifth components of Abelian gauge fields in a five-dimensional theory. A seesaw mechanism is introduced to provide a natural milli-charge for matter…
Recent confocal experiments on colloidal solids motivate a fuller study of the projection of three-dimensional fluctuations onto a two-dimensional confocal slice. We show that the effective theory of a projected crystal displays several…
We develop and apply a multi-dimensional account of explanatory depth towards a comparative analysis of inflationary and bouncing paradigms in primordial cosmology. Our analysis builds on earlier work due to Azhar and Loeb (2021) that…