相关论文: Substitution tilings with transcendental inflation…
In this paper, we investigate the evolution of the early universe within an emergent fractional cosmological framework. The underlying formulation is conceptually rooted in generalized measure constructions, closely related to fractal…
We study the tilt of the primordial gravitational waves spectrum. A hint of blue tilt is shown from analyzing the BICEP2 and POLARBEAR data. Motivated by this, we explore the possibilities of blue tensor spectra from the very early universe…
We study the spectral properties of ergodic Schr\"{o}dinger operators that are associated to a certain family of non-primitive substitutions on a binary alphabet. The corresponding subshifts provide examples of dynamical systems that go…
We analyze the core dynamics of critically coupled, superheavy gauge vortices in the (2+1) dimensional Einstein-Abelian-Higgs system. By numerically solving the Eistein and field equations for various values of the symmetry breaking scale,…
We introduce subshifts of quasi-finite type as a generalization of the well-known subshifts of finite type. This generalization is much less rigid and therefore contains the symbolic dynamics of many non-uniform systems, e.g., piecewise…
We propose a new scenario for early cosmology, where inflationary de Sitter phase dynamically occurs. The effect emerges as a result of dynamics of the topologically nontrivial sectors in expanding universe. Technically the effect can be…
This paper is concerned with the concept of linear repetitivity in the theory of tilings. We prove a general uniform subadditive ergodic theorem for linearly repetitive tilings. This theorem unifies and extends various known (sub)additive…
This is an analysis of the additivity of the entropy of thermodynamical systems with finite heat baths. It is presented an expression for the physical entropy of weakly interacting ergodic systems, and it is shown that it is valid for both…
It has been proposed that, without invoking supersymmetry, it is possible to solve the hierarchy problem provided the fundamental scale in the higher dimensional theory is at a much lower scale than the Planck scale. In this paper we…
This paper aims to better understand the link better understand the links between aperiodicity in subshifts and pattern complexity. Our main contribution deals with substitutive subshifts, an equivalent to substitutive tilings in the…
We present a suite of algorithmic techniques for handling substitution tilings by treating a tile's hierarchy of supertiles in a purely combinatorial fashion using finite state automata. The resulting techniques are very convenient for…
Extra-natural inflation is (de)constructed. Explicit models are compared with cosmological observations. The models successfully achieve trans-Planckian inflaton field excursions.
Overlap coincidence is an equivalent criterion to pure discrete spectrum of the dynamics of self affine tilings. In the case of one dimension, strong coincidence on m letter irreducible substitution has been introduced in Dekking (1978) and…
It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum fluctuations allow the field to jump uphill,…
Starting with a study of the cosmological solution to the Einstein equations for the internal spacetime of an extreme supermassive cosmic string kink, and by evaluating the probability measure for the formation of such a kink in…
Higher-form flux that extends in all 3+1 dimensions of spacetime is a source of positive vacuum energy that can drive meta-stable eternal inflation. If the flux also threads compact extra dimensions, the spontaneous nucleation of a bubble…
Here we consider the anharmonic oscillator that is a dynamical system given by $y_{xx}+\delta y^{n}=0$. We demonstrate that to this equation corresponds a new example of a superintegrable two-dimensional metric with a linear and a…
I summarize the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by…
A framework of inflation is formulated based on symmetry groups and their associated automorphic functions. In this setting the inflaton multiplet takes values in a curved target space constructed from a continuous group $G$ and a discrete…
We show that every subshift factor of a ($-\beta$)-shift is intrinsically ergodic, when $\beta\geq \frac{1+\sqrt{5}}{2}$ and the ($-\beta$)-expansion of $1$ is not periodic with odd period. Moreover, the unique measure of maximal entropy…