相关论文: Substitution tilings with transcendental inflation…
Given a finite set ${S_1...,S_k}$ of substitution maps acting on a certain finite number (up to translations) of tiles in $\rd$, we consider the multi-substitution tiling space associated to each sequence $\bar a\in {1,...,k}^{\mathbb{N}}$.…
We study implications of expansiveness and pointwise periodicity for certain groups and semigroups of transformations. Among other things we prove that every pointwise periodic finitely generated group of cellular automata is necessarily…
A finite collection $P$ of finite sets tiles the integers iff the integers can be expressed as a disjoint union of translates of members of $P$. We associate with such a tiling a doubly infinite sequence with entries from $P$. The set of…
We introduce a novel correlation, $n_s$ - $\Delta N$, connecting CMB parameters to the required total e-folds for eternal inflation. This correlation provides a robust tool for evaluating eternal (string) inflation models using CMB data and…
Methods and concepts for the study of phase transitions mediated by a time-dependent order-parameter field in curved spacetimes are discussed. A practical example is the derivation of an effective (quasi-)potential for the description of…
Thermal inflation was proposed as a mechanism to dilute the density of cosmological moduli. Thermal inflation is driven by a complex scalar field possessing a large vacuum expectation value and a very flat potential, called a `flaton'. Such…
A particular, two-dimensional, tiling model, composed by the so called Wang tiles has been studied at finite temperature by Monte Carlo numerical simulations. In absence of any thermal bath the Wang tiles give the opportunity of building a…
We propose a class of inflation models in which the coefficient of the inflaton kinetic term rapidly changes with energy scale. This may occur especially if the inflaton moves over a long distance during inflation as in the case of…
The discovery of the string theory landscape has recently brought attention to the eternal nature of inflation. In contrast to the common belief that eternal inflation may be a generic feature of most inflationary models, in this note we…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
It is tempting to inflate along one of the many flat directions that arise in supersymmetric theories. The required flatness of the potential to obtain sufficient inflation and to not overproduce density fluctuations occurs naturally.…
With the help of the tachyonic trapping mechanism one can potentially solve a number of problems affecting quintessential inflation models. In this mechanism we introduce a trapping field with a spontaneous symmetry breaking potential. When…
We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on the classical aperiodic tilings of the plane due to Raphael Robinson. Extending those tilings to the Heisenberg…
We study the thermodynamic formalism for particular types of sub-additive sequences on a class of subshifts over countable alphabets. The subshifts we consider include factors of irreducible countable Markov shifts under certain conditions.…
We develop techniques that lay out a basis for generalizations of the famous Thurston's Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the…
We consider D-term hybrid inflation in the framework of superconformal supergravity. In part of the parameter space, inflation continues for subcritical inflaton field value. Consequently, a new type of inflation emerges, which gives…
Supersolid inflation is a class of inflationary theories that simultaneously breaks time and space reparameterization invariance during inflation, with distinctive features for the dynamics of cosmological fluctuations. We investigate…
This paper is about the tiling dynamical systems approach to the study of aperiodic order. We compare and contrast four related types of systems: ordinary (one-dimensional) symbolic systems, one-dimensional tiling systems, multidimensional…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear…