相关论文: Stewart-Lyth Inverse Problem

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 study the behaviour of inflationary density perturbations in the vicinity of horizon crossing, using numerical evolution of the relevant mode equations. We explore two specific scenarios. In one, inflation is temporarily ended because a…

We derive general analytic formulae for the power spectrum and spectral index of the curvature perturbation produced during inflation driven by a multi-component inflaton field, up to the second order in the slow-roll approximation. We do…

Inflation is often described through the dynamics of a scalar field, slow-rolling in a suitable potential. Ultimately, this inflaton must be identified as the expectation value of a quantum field, evolving in a quantum effective potential.…

One method to reconstruct the scalar field potential of inflation is a perturbative approach, where the values of the potential and its derivatives are calculated as an expansion in departures from the slow-roll approximation. They can then…

We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…

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 show how observations of the perturbation spectra produced during inflation may be used to constrain the parameters of general scalar-tensor theories of gravity, which include both an inflaton and dilaton field. An interesting feature of…

We use a mathematical approach based on the constraints systems in order to reconstruct the equation of state and the inflationary potential for the inflaton field from the observed spectral indices for the density perturbations $n_{s}$ and…

Brief periods of non-slow-roll evolution during inflation can produce interesting observable consequences, as primordial black holes, or an inflationary gravitational wave spectrum enhanced at small scales. We develop a model independent,…

We analyze the impact of breaking diffeomorphism invariance in the inflaton sector. In particular, we consider inflaton models which are invariant under the subgroup of transverse diffeomorphisms and address the possibility of implementing…

We derive the spectral indices and their runnings of single inflation models by a new approach. We perform a dilatation transformation to the linear cosmological perturbations and derive a current (non-)conservation law. Using it, we…

The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we…

The scalar perturbations in inflationary models, based on a two-component diagonal non-linear sigma model, are considered. For inhomogeneities generated at an inflationary stage, the law of motion of the comoving curvature ${\cal R}$ is…

By using the relations between the slow-roll parameters and the power spectrum for the single field slow-roll inflation, we derive the scalar spectral tilt $n_s$ and the tensor to scalar ratio $r$ for the constant slow-roll inflation and…

We extend a previous analysis concerning cosmological fluids with generalized equations of state in order to study inflationary scenarios. In the framework of the slow-roll approximation we find the expressions for the perturbation…

We consider a one-dimensional one-phase inverse Stefan problem for the heat equation. It consists in recovering a boundary influx condition from the knowledge of the position of the moving front, and the initial state. We derived a…

Inverse problems involve making inference about unknown parameters of a physical process using observational data. This paper investigates an important class of inverse problems -- the estimation of the initial condition of a…

We compare the standard single scalar field inflationary predictions with those of an inflationary phase driven by a tachyon field. A slow-roll formalism is defined for tachyon inflation, and we derive the spectra of scalar and tensor…

A novel numerical method for solving inverse scattering problem with fixed-energy data is proposed. The method contains a new important concept: the stability index of the inversion problem. This is a number, computed from the data, which…