Related papers: Cosmographic analysis with Chebyshev polynomials
We present general, analytic methods for Cosmological likelihood analysis and solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's Method, while marginalization over nuisance parameters, and parameter errors and…
We present a comprehensive comparison of different Markov Chain Monte Carlo (MCMC) sampling methods, evaluating their performance on both standard test problems and cosmological parameter estimation. Our analysis includes traditional…
Phenomenological models are widely used in cosmology in relation to constraining different cosmological models, with two common examples being cosmographic expansions and modeling the equation-of-state parameter of dark energy. This work…
Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to…
Approximating adequate number of clusters in multidimensional data is an open area of research, given a level of compromise made on the quality of acceptable results. The manuscript addresses the issue by formulating a transductive…
Deviations from the so-called {\it cosmic distance duality relation} may result from systematic errors in distance measurements or, more interestingly, hint at new physics. Further, it can also be related to the Hubble constant tension…
Cosmography provides a direct method to map the expansion history of the Universe in a model-independent way. Recently, different kinds of observations have been used in cosmographic analyses, such as SNe Ia and gamma ray bursts…
Large scale astronomical surveys are going wider and deeper than ever before. However, astronomers, cosmologists and theorists continue to face the perennial issue that their data sets are often incomplete in magnitude space and must be…
The redshift drift provides a kinematic test of the cosmic expansion history through the slow time variation of the redshift of comoving sources. Motivated by the expected Sandage-Loeb measurements from future facilities, we investigate the…
Identifying new observational probes to constrain cosmological parameters has become an important goal in modern cosmology. In this work, we explore the potential of the cosmic star formation rate density (SFRD), compiled over the redshift…
Obtaining the set of cosmological parameters consistent with observational data is an important exercise in current cosmological research. It involves finding the global maximum of the likelihood function in the multi-dimensional parameter…
In this paper we elucidate the advantage of examining the connections between Hilbert-Kamke equations and geometric designs, or Chebyshev-type quadrature, for classical orthogonal polynomials. We first establish that if a $5$-design with…
We challenge the widely held belief that the cosmological principle is an obvious consequence of the observed isotropy of the cosmic microwave background radiation, combined with the Copernican principle. We perform a detailed analysis of a…
A novel evolutionary method is introduced that can be used for constraining the parameters and theoretical models of Cosmology. The newly proposed algorithm, which is inherently parallel by design, is able to obtain the full potential of…
The Hubble constant ${H}_0$ is a crucial parameter in cosmology. However, different cosmic observations have resulted in varying posterior results for ${H}_0$, leading to what is known as the ${H}_0$ tension. In order to address this issue,…
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed…
We study Chebyshev filter diagonalization as a tool for the computation of many interior eigenvalues of very large sparse symmetric matrices. In this technique the subspace projection onto the target space of wanted eigenvectors is…
We consider location problems to find the optimal sites of placement of a new facility, which minimize the maximum weighted Chebyshev or rectilinear distance to existing facilities under constraints on a feasible location domain. We examine…
Given a standard model to test, an experiment can be designed to: (i) measure the standard model parameters; (ii) extend the standard model; or (iii) look for evidence of deviations from the standard model. To measure (or extend) the…
We analyze the convergence of compressive sensing based sampling techniques for the efficient evaluation of functionals of solutions for a class of high-dimensional, affine-parametric, linear operator equations which depend on possibly…