Related papers: On the Stewart-Lyth Inverse Problem
We explore the types of slow-roll inflationary potentials that result in scalar perturbations with a constant spectral index, i.e., perturbations that may be described by a single power-law spectrum over all observable scales. We devote…
We consider cosmological models based on the scalar-torsion gravity implying non-minimal coupling between torsion and the scalar field with certain relations between model's parameters. Based on observational constraints on the values of…
The stochastic effective theory approach, often called stochastic inflation, is widely used in cosmology to describe scalar field dynamics during inflation. The existing formulations are, however, more qualitative than quantitative because…
We study inflation in a random multifield potential, using techniques developed by Marsh et al. The potential is a function of a large number of fields, and we choose parameters so that inflation only occurs in regions where the potential…
In this paper we propose a new Bayesian estimation method to solve linear inverse problems in signal and image restoration and reconstruction problems which has the property to be scale invariant. In general, Bayesian estimators are {\em…
We propose a test of single-scalar inflation based on using the well-measured scalar power spectrum to reconstruct the tensor power spectrum, up to a single integration constant. Our test is a sort of integrated version of the single-scalar…
By using the rather stringent nonlinear second order slow-roll approximation, we reconsider the nonlinear second order Abel equation of Stewart and Lyth. We determine a new blue eigenvalue spectrum. Some of the discrete values of the…
We analyze an inverse problem associated with the time-harmonic Rayleigh system on a flat elastic half-space concerning the recovery of Lam\'{e} parameters in a slab beneath a traction-free surface. We employ the Markushevich substitution,…
We investigate perturbations in power-law monomial potentials within inflationary models driven by a single scalar field. By introducing a second term to the original potential, we study how this perturbation influences the slow-roll…
We study in detail the power spectra of scalar and tensor perturbations generated during inflation in loop quantum cosmology (LQC). After clarifying in a novel quantitative way how inverse-volume corrections arise in inhomogeneous settings,…
This paper concerns the simultaneous reconstruction of a sound-soft cavity and its excitation sources from the total-field data. Using the single-layer potential representations on two measurement curves, this co-inversion problem can be…
We suggest a new statement of the inverse spectral problem for Sturm--Liouville-type operators with constant delay. This inverse problem consists in recovering the coefficient (often referred to as potential) of the delayed term in the…
In a previous paper I showed that a classical scalar potential with $V''/V \sim 1$ can be sufficiently flattened by quantum corrections to give rise to slow-roll inflation. In this paper I give a hybrid inflation implementation of that idea…
In this paper, we study various cosmological parameters and quantities in scalar-tensor gravity from inflation and swampland conjecture. Therefore, by selecting different models such as power-law, exponential, and logarithmic in the…
The observation of the B-mode in the cosmic microwave background radiation combined with the so-called Lyth bound suggests the trans-Planckian variation of the inflaton field during inflation. Such a large variation generates concerns over…
Using the factorization approach of quantum mechanics, we obtain a family of isospectral scalar potentials for power law inflationary cosmology. The construction is based on a scattering Wheeler-DeWitt solution. These iso-spectrals have new…
We consider Cosmic Microwave Background constraints on inflation models for which the primordial power spectrum is a mixture of perturbations generated by inflaton fluctuations and fluctuations in a curvaton field. If future experiments do…
We derive the power spectrum $\mathcal P(k)$ of the density perturbations produced during inflation up to second-order corrections in the standard slow-roll approximation for an inflaton with more than one degree of freedom. We also present…
In this paper, the Sturm-Liouville operators on a graph with a cycle are considered. We study the inverse spectral problem, which consists in the recovery of the potentials from several spectra and a sequence of signs related to the…
In this paper, we for the first time get constructive solution for the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The uniqueness of…