Related papers: Squirals and beyond: Substitution tilings with sin…
We argue that in models of inflation with two scalar fields and non-canonical kinetic terms there is a possibility of obtaining a red tilt of the power spectrum of curvature perturbations from noncanonicality-induced interactions between…
We calculate the power spectrum of curvature perturbations when the inflaton field is rolling over the top of a local maximum of a potential. We show that the evolution of the field can be decomposed into a late-time attractor, which is…
We consider topological dynamical systems over $\ZZ$ and, more generally, locally compact, $\sigma$-compact abelian groups. We relate spectral theory and diffraction theory. We first use a a recently developed general framework of…
We consider the Quillen adjunction between fixed points and inflation in the context of equivariant module spectra over equivariant ring spectra, and give numerous examples including some based on geometric fixed points and some on the…
Stochastic inflation describes the global structure of the inflationary universe by modeling the super-Hubble dynamics as a system of matter fields coupled to gravity where the sub-Hubble field fluctuations induce a stochastic force into…
In inflationary scenarios with more than one scalar field, inflation may proceed even if each of the individual fields has a potential too steep for that field to sustain inflation on its own. We show that scalar fields with exponential…
We study a two-parameter family of exactly solvable inflation models with variable sound speed, and derive a corresponding exact expression for the spectrum of curvature perturbations. We generalize this expression to the slow roll case,…
The evolution of gauge invariant second-order scalar perturbations in a general single field inflationary scenario are presented. Different second order gauge invariant expressions for the curvature are considered. We evaluate…
We propose a new version of the hybrid inflation scenario that produces a significantly tilted n>1 spectrum of curvature perturbations. This may happen in supersymmetric models where the inflaton field acquires a mass proportional to the…
Extendibility of inflationary spacetimes with flat spatial geometry is investigated. We find that the past boundary of an inflationary spacetime becomes a so-called parallely propagated curvature singularity if the ratio $\dot{H}/a^2$…
We study the out of equilibrium dynamics of inflationary phase transitions and compute the resulting spectrum of metric perturbations relevant to observation. We show that simple single field models of inflation may produce an adiabatic…
The well-known plastic number substitution gives rise to a ternary inflation tiling of the real line whose inflation factor is the smallest Pisot-Vijayaraghavan number. The corresponding dynamical system has pure point spectrum, and the…
Recently it was argued that an inflationary potential yielding power spectra characterized by a scale-invariant tensorial spectral index and a weakly scale-dependent scalar spectral index might account for a generic large-scale structure…
We study a class of minimally coupled scalar field theories which leads to analytic solutions for the Hubble rate and the scalar field, where the scalar field obeys a generalized tracking law $\dot{\phi}^2\sim H^{-m}$. The inflationary…
In the present paper, we aim to generalize the constant-roll inflation in the non-canonical set-up, particularly in the context of scalar Dirac-Born-Infeld (DBI) theory which has emerged to be prospective candidate for describing inflation…
We study a lattice model where the coupling stochastically switches between repulsive (subtractive) and attractive (additive) at each site with probability p at every time instance. We observe that such kind of coupling stabilizes the local…
While moving down the potential on its classical slow roll trajectory, the inflaton field is subject to quantum jumps, which take it up or down the potential at random. In "stochastic inflation", the impact of these quantum jumps is modeled…
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…
By generalising Rudin's construction of an aperiodic sequence, we derive new substitution-based structures which have purely absolutely continuous diffraction and mixed dynamical spectrum, with absolutely continuous and pure point parts. We…
The class of Cyclotomic Aperiodic Substitution Tilings (CAST) whose vertices are supported by the $2n$-th cyclotomic field $\mathbb{Q}\left(\zeta_{2n}\right)$ is extended to cases with Dense Tile Orientations (DTO). It is shown that every…