Related papers: Stewart-Lyth Inverse Problem
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…
Generalized slow roll conditions and parameters are obtained for a general form of scalar-tensor theory (with no external sources), having arbitrary functions describing a nonminimal gravitational coupling F(\phi), a Kahler-like kinetic…
Based on the stochastic gravity, we study the loop corrections to the scalar and tensor perturbations during inflation. Since the loop corrections to scalar perturbations suffer infrared (IR) divergence, we consider the IR regularization to…
The corrections to the cosmological models induced by non-minimal coupling between scalar field and torsion are considered. To determine these corrections in explicit form, the power-law parametrization of these corrections are proposed.…
We study polarized Gowdy cosmologies on the three torus coupled to a massive scalar field. The phase space of the model admits a simple splitting between homogeneous and inhomogeneous sectors after a suitable gauge fixing. The presence of…
To first order in the deviation from scale invariance the inflationary potential and its first two derivatives can be expressed in terms of the spectral indices of the scalar and tensor perturbations, $n$ and $n_T$, and their contributions…
Tachyonic preheating is realized when the inflaton repeatedly returns to a convex region of the potential during the post-inflationary oscillating phase. This will induce a strong tachyonic instability and lead to a rapid fragmentation of…
Integrable PDEs on the line can be analyzed by the so-called Inverse Scattering Transform (IST) method. A particularly powerful aspect of the IST is its ability to predict the large $t$ behavior of the solution. Namely, starting with…
An inverse scattering method based on an auxiliary inverse Sturm-Liouville problem recently proposed by Horv\'ath and Apagyi [Mod. Phys. Lett. B 22, 2137 (2008)] is examined in various aspects and developed further to (re)construct…
I review the standard analysis of adiabatic scalar and tensor perturbations produced by slow-roll inflation driven by a single scalar field, before going on to discuss recent work on the role of non-adiabatic modes during and after…
This paper concerns the inverse scattering problem to reconstruct a local perturbation in a periodic structure. Unlike the periodic problems, the periodicity for the scattered field no longer holds, thus classical methods, which reduce…
In this paper, I present an analytic solution to the equation of motion of the inflaton field in a model of rapid roll inflation with a quartic potential by assuming that the Hubble parameter is a constant during inflation. The result is…
The aim of this paper is to provide a more precise description of the paradigm of corpuscular slow-roll inflation, which was previously introduced by Casadio et al. in [1]. Specifically, we start by expanding the Starobinsky theory on a…
We study the possibility that inflation is driven by a scalar field together with a vector field minimally coupled to gravity. By assuming an effective potential that incorporates both fields into the action, we explore two distinct…
The paper deals with two inverse problems for Sturm--Liouville operator $Ly=-y" +q(x)y$ on the finite interval $[0,\pi]$. The first one is the problem of recovering of a potential by two spectra. We associate with this problem the map $F:\,…
The scenario of the slow-roll inflation is studied in the frame of the scalar-tensor theory of gravity where the scalar field has a non-minimal coupling to the geometric part. After deriving the main dynamical and perturbation equations,…
We study the inflation and the cosmological perturbations generated during the inflation in a local scale invariant model. The local scale invariant model introduces a vector field $S_{\mu}$ in this theory. In this paper, for simplicity, we…
The next generation of cosmological observations will be sensitive to small deviations from a pure power law in the primordial power spectrum of the curvature perturbations. In the context of slow-roll inflation, these deviations are…
We investigate models of `intermediate' inflation, where the scale factor $a(t)$ grows as $a(t) = \exp (A t^f)$, $0 < f < 1$, $A$ constant. These solutions arise as exact analytic solutions for a given class of potentials for the inflaton…
We apply the method of inverse iteration to the Laplace eigenvalue problem with Robin and mixed Dirichlet-Neumann boundary conditions, respectively. For each problem, we prove convergence of the iterates to a non-trivial principal…