Related papers: Parameterizing the Power Spectrum: Beyond the Trun…
One of the challenges in testing gravity with cosmology is the vast freedom opened when extending General Relativity. For linear perturbations, one solution consists in using the Effective Field Theory of Dark Energy (EFT of DE). Even then,…
The analysis of parametrised systems is a growing field in verification, but the analysis of parametrised probabilistic systems is still in its infancy. This is partly because it is much harder: while there are beautiful cut-off results for…
In the era of precision cosmology, establishing the correct magnitude of statistical errors in cosmological parameters is of crucial importance. However, widely used approximations in galaxy surveys analyses can lead to parameter…
We compute the universal generic corrections to the inflationary power spectrum due to unknown high-energy physics. We arrive at this result via a careful integrating out of massive fields in the "in-in" formalism yielding a consistent and…
This paper is concerned with recovering the solution of a final value problem associated with a parabolic equation involving a non linear source and a non-local term, which to the best of our knowledge has not been studied earlier. It is…
Likelihood ratio tests are widely used to test statistical hypotheses about parametric families of probability distributions. If interest is restricted to a subfamily of distributions, then it is natural to inquire if the restricted LRT is…
The Shannon sampling theorem for bandlimited wide sense stationary random processes was established in 1957, which and its extensions to various random processes have been widely studied since then. However, truncation of the Shannon series…
Computing the matter power spectrum, $P(k)$, as a function of cosmological parameters can be prohibitively slow in cosmological analyses, hence emulating this calculation is desirable. Previous analytic approximations are insufficiently…
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions.…
This work investigates a single-field inflationary model, a specific class of the K-essence models where a coupling term exists between canonical Lagrangian and the potential. This coupling term has many effects on key inflationary…
Covariances and variances of linear statistics of a point process can be written as integrals over the truncated two-point correlation function. When the point process consists of the eigenvalues of a random matrix ensemble, there are often…
Power-law inflation with $a(t) \propto t^m$ is conceptually simple and predicts a scalar tilt $n_s = 1 - 2/m$ compatible with CMB data, but in four-dimensional Einstein gravity it typically yields a tensor-to-scalar ratio $r = 16/m$ that is…
In light of the non-perturbative resonance effects that may occur during inflation, we introduce a parametrization for the power spectrum of the stochastic gravitational wave background (SGWB) characterized by narrow-band amplification. We…
An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is…
The line spectral estimation problem consists in recovering the frequencies of a complex valued time signal that is assumed to be sparse in the spectral domain from its discrete observations. Unlike the gridding required by the classical…
The values of, and connection between, the cosmological observables of the primordial power spectrum tilt $n_s$ and the inflationary tensor to scalar ratio $r$ are key guideposts to the physics of inflation. Universality classes can be…
We present a general parametrization for energy density of a quintessence field, a minimally coupled canonical scalar field which rolls down slowly during the late time. This parametrization can mimic all classes of quintessence dynamics,…
We use a toy model to illustrate how to build effective theories for singular potentials. We consider a central attractive 1/r^2 potential perturbed by a 1/r^4 correction. The power-counting rule, an important ingredient of effective…
Inferring stellar parameters and chemical abundances by forward modeling stellar spectra usually requires a spectral synthesis code, or an emulator constructed from a curated training set. In these situations continuum normalization is…
In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…