Related papers: On the Stewart-Lyth Inverse Problem
We discuss inverse problems of determining the time-dependent source coefficient for a general class of subelliptic heat equations. We show that a single data at an observation point guarantees the existence of a (smooth) solution pair for…
A method is presented which allows for the renormalization of the self-potential for a scalar point charge at rest in static curved space-time. The method is suitable for the scalar field with arbitrary mass $m$ and coupling to the scalar…
In conventional model independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we,…
This work deals with an inverse problem for the Sturm-Liouville operator with non-separated boundary conditions, one of which linearly depends on a spectral parameter. Uniqueness theorem is proved, solution algorithm is constructed and…
The inverse problem for the Sturm- Liouville operator with complex periodic potential and discontinuous coefficients on the axis is studied. Main characteristics of the fundamental solutions are investigated, the spectrum of the operator is…
An interesting inverse optimization spectral problem, with important applications in structural health monitoring and damage detection, material design, seismic wave analysis, sonar detection, and related fields, involves reconstructing a…
A review is presented of recent work by the authors concerning the use of large scale structure and microwave background anisotropy data to determine the potential of the inflaton field. The importance of a detection of the stochastic…
We develop a frame-covariant formulation of inflation in the slow-roll approximation by generalizing the inflationary attractor solution for scalar-curvature theories. Our formulation gives rise to new generalized forms for the potential…
I consider the problem of deriving couplings of a statistical model from measured correlations, a task which generalizes the well-known inverse Ising problem. After reminding that such problem can be mapped on the one of expressing the…
For the inflaton field we determine a new exact solution by using the Lie symmetry analysis. Specifically, we construct a second-order differential master equation for arbitrary scalar field potential by assuming that the spectral index for…
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…
We present new single field inflationary scenarios that produce the critical abundance of primordial black holes as dark matter reconstructing the inflaton potential from an input power spectrum. The method is exact in the slow roll…
In this work we determine the power spectrum of the gravitational potential of the primordial fluctuations for an inflationary model whose \emph{inflaton} is a non-canonical scalar field of the tachyon-type. The respective background field…
The WMAP results on the scalar spectral index n and its running with scale, though preliminary, open a very interesting window to physics at very high energies. We address the problem of finding simple inflaton potentials well motivated by…
We adopt methods from statistical field theory to stochastic inflation. For the example of a free test field in de Sitter and power-law inflation, the power spectrum of long-wavelength fluctuations is computed. We study its dependence on…
A general scalar-tensor theory can be formulated in different parametrizations that are related by a conformal rescaling of the metric and a scalar field redefinition. We compare formulations of slow-roll regimes in the Einstein and Jordan…
In dimension 1, we show that the Taylor expansion of a potential near a generic non degenerate critical point can be recovered from the knowledge of the semi-classical spectrum of the associated Schr\"odinger operator near the corresponding…
The matrix Sturm-Liouville operator with an integrable potential on the half-line is considered. We study the inverse spectral problem, which consists in recovering of this operator by the Weyl matrix. The main result of the paper is the…
We propose a new class of natural inflation models based on a hidden scale invariance. In a very generic Wilsonian effective field theory with an arbitrary number of scalar fields, which exhibits scale invariance via the dilaton, the…
After a review of a traditional analysis, it is shown a variation of a more recent treatment on the spectrum of relic gravitational waves (GWs). Then, a connection between the two different treatments will be analysed. Such a connection…