Related papers: Stewart-Lyth Inverse Problem
We investigate radiative corrections to the inflaton potential from heavy fields undergoing a fast-roll phase transition. We find that a logarithmic one-loop correction to the inflaton potential involving this field can induce a temporary…
We propose a novel iterative numerical method to solve the three-dimensional inverse obstacle scattering problem of recovering the shape of the obstacle from far-field measurements. To address the inherent ill-posed nature of the inverse…
Nonlocal integrable partial differential equations possessing a spatial or temporal reflection have constituted an active research area for the past decade. Recently, more general classes of these nonlocal equations have been proposed,…
This paper deals with the Sturm-Liouville problem that feature distribution potential, polynomial dependence on the spectral parameter in the first boundary condition, and analytical dependence, in the second one. We study an inverse…
Using the constant-roll approach, DBI inflationary scenario will be studied and it is sought to compare the result with observational data. By considering the cosmological perturbations of the model, it is realized that some extra terms…
Cosmic microwave anisotropy satellites promise extremely accurate measures of the amplitude of perturbations in the universe. We use a numerical code to test the accuracy of existing approximate expressions for the amplitude of…
Inverse problem to recover simultaneously a scalar coefficient, order of a time-fractional derivative, parameters of multiterm fractional Laplacian and a time-dependent source term occurring in a superdiffusion equation from measurements…
We expound ten principles in an attempt to clarify the debate over infrared loop corrections to the primordial scalar and tensor power spectra from inflation. Among other things we note that existing proposals for nonlinear extensions of…
We take a pragmatic, model independent approach to single field slow-roll inflation by imposing conditions to the slow-roll parameter $\epsilon$ and its derivative $\epsilon^{\prime }.$ To accommodate the recent (large) values of $r$…
The inverse scattering problem is studied for the matrix Sturm-Liouville equation on the line. Necessary and sufficient conditions for the scattering data are obtained.
We construct non-linear inflaton potential energy densities that describe not-necessarily very-slowly-rolling closed and open inflation models, and compute tilted primordial spatial inhomogeneity power spectra that follow from quantum…
We propose a new parametrization of the background equations of motion corresponding to (canonical) single-field models of inflation, which allows a better understanding of the general properties of the solutions and of the corresponding…
In models like axion monodromy, temporal features during inflation which are not associated with its ending can produce scalar, and to a lesser extent, tensor power spectra where deviations from scale-free power law spectra can be as large…
We consider second-order functional differential operators with a constant delay. Properties of their spectral characteristics are obtained and a nonlinear inverse problem is studied, which consists in recovering the operators from their…
In this paper the small-amplitude motion of multiple superposed viscous fluids is studied as a linearized initial-value problem. The analysis results in a closed set of equations for the Laplace transformed amplitudes of the interfaces that…
In this paper, we consider several geometric inverse problems for linear elliptic systems. We prove uniqueness and stability results. In particular, we show the way that the observation depends on the perturbations of the domain. In some…
For nonlinear wave equations with a potential term we prove pointwise space-time decay estimates and develop a perturbation theory for small initial data. We show that the perturbation series has a positive convergence radius by a method…
The slow-roll field equations for the case of non-minimally coupled scalar fields are obtained in two ways: first using the direct generalization of slow-roll conditions in the minimal coupling case to non-minimal one; and, second,…
We compute the spectral index for scalar perturbations generated in a primordial inflationary model. In this model, the transition of the inflationary phase to the radiative era is achieved through the decay of the cosmological term leading…
We explore in detail the dynamics of multi-field inflationary models. We first revisit the two-field case and rederive the coordinate independent expression for the attractor solution with either small or large turn rate, emphasizing the…