Related papers: Parameterizing the Power Spectrum: Beyond the Trun…
The Planck satellite is expected to improve the measurement of most cosmological parameters by several factors with respect to current WMAP results. The actual performance may depend upon various aspects of the data analysis. In this paper…
As is well known, the non-Gaussianity parameter $f_{_{\rm NL}}$, which is often used to characterize the amplitude of the scalar bi-spectrum, can be expressed completely in terms of the scalar spectral index $n_{\rm s}$ in the squeezed…
In light of the most recent cosmological observations, we provide new updated constraints on the slow-roll inflation in different extended scenarios beyond the $\Lambda\rm{CDM}$ cosmological model. Along with the usual six parameters, we…
We examine how lensing tomography with the bispectrum and power spectrum can constrain cosmological parameters and the equation of state of dark energy. Our analysis uses the full information at the two- and three-point level from angular…
We examine the power spectrum of the energy level fluctuations of a family of critical power-law random banded matrices with properties similar to those of a disordered conductor at the Anderson transition. It is shown both analytically and…
One approach to extracting the global 21-cm signal from total-power measurements at low radio frequencies is to parametrize the different contributions to the data and then fit for these parameters. We examine parametrizations of the 21-cm…
The absence of large-angle correlations in the temperature of the cosmic microwave background (CMB), confirmed by three independent satellite missions, creates significant tension with the standard model of cosmology. Previous work has…
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…
The drift sequential parameter estimation problems for the Cox-Ingersoll-Ross (CIR) processes under the limited duration of observation are studied. Truncated sequential estimation methods for both scalar and {two}-dimensional parameter…
Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…
The normal parameters are a non--linear transformation of the cosmological parameters whose likelihood function is very well--approximated by a normal distribution. This transformation serves as an extreme form of data compression allowing…
We seek to improve estimates of the power spectrum covariance matrix from a limited number of simulations by employing a novel statistical technique known as shrinkage estimation. The shrinkage technique optimally combines an empirical…
We study the evolution of density perturbations for a class of $f(R)$ models which closely mimic $\Lambda$CDM background cosmology. Using the quasi-static approximation, and the fact that these models are equivalent to scalar-tensor…
Recent theoretical work has established connections between over-parametrized neural networks and linearized models governed by he Neural Tangent Kernels (NTKs). NTK theory leads to concrete convergence and generalization results, yet the…
We analyze the problem of global reconstruction of functions as accurately as possible, based on partial information in the form of a truncated power series at some point, and additional analyticity properties. This situation occurs…
Light degrees of freedom that modify gravity on cosmological scales must be "screened" on solar system scales in order to be compatible with data. The Vainshtein mechanism achieves this through a breakdown of classical perturbation theory,…
We introduce a power-law parameterized quintessence model for the dark energy which accelerate universe at the low redshifts while behaves as an ordinary matter for the early universe. We construct a unique scalar potential for this…
Features during inflation and reionization leave corresponding features in the temperature and polarization power spectra that could potentially explain anomalies in the Planck 2015 data but require a joint analysis to disentangle. We study…
In solar physics, especially in exploratory stages of research, it is often necessary to compare the power spectra of two or more time series. One may, for instance, wish to estimate what the power spectrum of the combined data sets might…
We discuss the parameterized post-Newtonian (PPN) limit of Horndeski's theory of gravity, also known under the name generalized G-inflation or $\text{G}^2$-inflation, which is the most general scalar-tensor theory of gravity with at most…