Related papers: Substitution tilings with transcendental inflation…
We discuss two new results on tilings of the plane. In the first, we give sufficient conditions for the tilings associated with an inflation rule to be uniquely ergodic under translations, the conditions holding for the pinwheel inflation…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
We study a new model of quintessential inflation which is inspired by supergravity and string theory. The model features a kinetic pole, which gives rise to the inflationary plateau, and a runaway quintessential tail. We envisage a coupling…
In this paper we introduce a simple discrete stochastic model of eternal inflation that shares many of the most important features of the continuum theory as it is now understood. The model allows us to construct a multiverse and rigorously…
We argue that there may arise a relatively flat inflaton potential over super-Planckian field values with an approximate shift symmetry, if the coefficients of the kinetic terms for many singlet scalars are subject to a certain random…
We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. We focus on the case where the escape is degenerate in the sense that points from…
The periodic tiling conjecture asserts that any finite subset of a lattice $\mathbb{Z^d}$ which tiles that lattice by translations, in fact tiles periodically. We announce here a disproof of this conjecture for sufficiently large $d$, which…
The basic workings of inflationary models are summarized, along with 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…
Infinite entanglement fluctuations appear when a quantum field theory on a causally complete domain of space-time is a type $III$ factor. In the weak gravity limit $G_N=0$ this factor can be transformed into a crossed product type $II$…
In this article, we review how strong dynamics can be efficiently employed as a viable alternative to study the mechanism of cosmic inflation. We examine single-field inflation in which the inflaton emerges as a bound state stemming from…
Tilting modules over commutative rings were recently classified in [12]: they correspond bijectively to faithful Gabriel topologies of finite type. In this note we extend this classification by dropping faithfulness. The counterpart of an…
We explore a new class of supersymmetric models of inflation where the inflaton is realised as a combination of a Higgs field and (gauge non-singlet) matter fields, using a "tribrid" structure of the superpotential. Inflation is associated…
We perform a precision investigation of smooth quintessential inflation in which a single canonical scalar field unifies the two known phases of cosmic acceleration. Using a CMB-normalized runaway exponential potential, we obtain sharply…
We associate in a canonical way a substitution to any abstract numeration system built on a regular language. In relationship with the growth order of the letters, we define the notion of two independent substitutions. Our main result is…
Choosing the three phenomenological models of the dynamical cosmological term $\Lambda$, viz., $\Lambda \sim (\dot a/a)^2$, $\Lambda \sim {\ddot a/a}$ and $\Lambda \sim \rho$ where $a$ is the cosmic scale factor, it has been shown by the…
We present a new class of exact inflationary solutions for the evolution of a universe with spatial curvature, filled with a perfect fluid, a scalar field with potential $V_{\pm}(\phi)=\lambda(\phi^2\pm\delta^2)^2$ and a cosmological…
I describe a recently derived stochastic approach to inflaton dynamics which can address some serious problems associated with conventional inflationary theory. Using this theory I derive an exact solution to the stochastic dynamics for the…
We investigate the global structure of inflationary universe both by analytical methods and by computer simulations of stochastic processes in the early Universe. We show that the global structure of the universe depends crucially on the…
We study inflationary solution in an extension of mimetic gravity with the higher derivative interactions coupled to gravity. Because of the higher derivative interactions, the setup is free from the ghost and gradient instabilities while…
It is well-known that the functions $f \in L^1(\mathbb{R}^d)$ whose translates along a lattice $\Lambda$ form a tiling, can be completely characterized in terms of the zero set of their Fourier transform. We construct an example of a…