Related papers: On the Stewart-Lyth Inverse Problem

This paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An…

The scenario of constant-roll inflation is studied where the inflaton is a scalar field with modified kinetic term, known as non-canonical scalar field. This modification leads to some changes in the slow-roll parameters, and also by taking…

The inflaton field responsible for inflation may not be a canonical fundamental scalar. It is possible that the inflaton is a composite of fermions or it may have a decay width. In these cases the standard procedure for calculating the…

We analyse the post-inflationary contribution to the stochastic gravitational wave background due to a resonant feature in the scalar power spectrum, which is characterised by an oscillation in $\log(k)$, complementing our previous work…

In this paper, we study the inverse spectral problem for the Sturm-Liouville operators on a star-shaped graph, which consists in the recovery of the potentials from specral data or several spectra. The uniform stability of these inverse…

We investigate the Lyth relationship between the tensor-scalar ratio, r, and the variation of the inflaton field, Delta phi, over the course of inflation. For inflationary models that produce at least 55 e-folds of inflation, there is a…

We consider the inflaton as a scalar field described by a non-minimal derivative coupling model with a power law potential. We study the slow roll inflation, the rapid oscillation phase, the radiation dominated and the recombination eras…

We explore a square-law k-inflation using the Hamilton-Jacobi approach. Focusing on scenarios where the Hubble parameter exhibits a power-law dependence on the k-field, our analysis encompasses the computations of crucial observables, such…

We study the direct and inverse scattering problems for the Zakharov-Shabat system. Representations for the Jost solutions are obtained in the form of the power series in terms of a transformed spectral parameter. In terms of that…

We develop methods to calculate the curvature power spectrum in models where features in the inflaton potential nonlinearly excite modes and generate high frequency features in the spectrum. The first nontrivial effect of excitations…

The inverse spectral problem is investigated for the matrix Sturm-Liouville equation on a finite interval. Properties of spectral characteristics are provided, a constructive procedure for the solution of the inverse problem along with…

This paper addresses the inverse scattering problem of a random potential associated with the polyharmonic wave equation in two and three dimensions. The random potential is represented as a centered complex-valued generalized microlocally…

In the inflationary cosmology it occurs frequently that the inflaton field is trapped in a local, transient minimum with non-zero vacuum energy. The difficulty regarding the curvature perturbation produced during such a stage is that…

The leading quantum correction to the power spectrum of a gravitationally-coupled light scalar field is calculated, assuming that it is generated during a phase of single-field, slow-roll inflation.

We analyze the inverse spectral problem on the half line associated with elastic surface waves. Here, we extend the treatment of Love waves [arXiv: 1908.10529] to Rayleigh waves. Under certain conditions, and assuming that the Poisson ratio…

(Shortened abstract) While a featureless, nearly scale invariant, primordial scalar power spectrum fits the most recent CMB data rather well, certain features in the spectrum are known to lead to a better fit to the data (although, the…

We consider cosmological inflation generated by a scalar field slowly rolling off from a de Sitter maximum of its potential. The models belong to the class of hilltop models and represent the most general model of this kind in which the…

We introduce a new method to construct, within inverse-scattering theory, an energy-independent separable potential capable of reproducing exactly both phase shift and absorption over a predefined energy range. The approach relies on the…

We show that the generalized slow-roll approach for calculating the power spectrum where the inflationary slow roll parameters are neither small nor slowly varying can be readily extended to models with non-canonical kinetic terms in the…

We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to…