Related papers: Cosmographic analysis with Chebyshev polynomials
Using a new sub-sample of observed strong gravitational lens systems, for the first time, we present the equation for the angular diameter distance in the $y$-redshift scenario for cosmography and use it to test the cosmographic parameters.…
There are many different approaches to using observations to constrain or determine the global cosmological parameters that describe our universe. Methods that rely upon a determination of the coordinate distance to high-redshift sources…
In this study, we used geometric distances at high redshifts (both luminosity and angular) to perform a cosmographic analysis with the Pad\'e method, which stabilizes the behaviour of the cosmographic series in this redshift regime.…
This paper develops a computational method for studying stable/unstable manifolds attached to periodic orbits of differential equations. The method uses high order Chebyshev-Taylor series approximations in conjunction with the…
We introduce a novel approach, a Dense Shell Method (DSM), for measuring distances for cosmology. It is based on original Baade idea to relate absolute difference of photospheric radii with photospheric velocity. We demonstrate that this…
A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of…
As the statistical power of imaging surveys grows, it is crucial to account for all systematic uncertainties. This is normally done by constructing a model of these uncertainties and then marginalizing over the additional model parameters.…
We analyze decay of Chebyshev coefficients and local Chebyshev approximations for functions of finite regularity on finite intervals, focusing on the framework where the interval length tends to zero while the number of approximation nodes…
Photometric redshift uncertainties are a major source of systematic error for ongoing and future photometric surveys. We study different sources of redshift error caused by choosing a suboptimal redshift histogram bin width and propose…
[Abridged] We seek approximations to the cosmic shear covariance that are as easy to use as the common approximations based on normal statistics, but yield more accurate covariance matrices and parameter errors. We derive expressions for…
The accumulation of redshifts provides a significant observational bottleneck when using galaxy cluster surveys to constrain cosmological parameters. We propose a simple method to allow the use of samples where there is a fraction of the…
There is growing interest in using 3-dimensional neutral hydrogen mapping with the redshifted 21 cm line as a cosmological probe, as it has been argued to have a greater long-term potential than the cosmic microwave background. However, its…
Perturbation theory is a powerful tool for studying large-scale structure formation in the universe and calculating observables such as the power spectrum or bispectrum. However, beyond linear order, typically this is done by assuming a…
Markov-chain Monte Carlo sampling has become a standard technique for exploring the posterior distribution of cosmological parameters constrained by observations of CMB anisotropies. Given an infinite amount of time, any MCMC sampler will…
We address the problem of the best uniform approximation by linear combinations of a finite system of functions. If the system is Chebyshev and the problem is unconstrained, then the classical Remez algorithm provides a fast and precise…
Given a compact subset of a Banach space, the Chebyshev center problem consists of finding a minimal circumscribing ball containing the set. In this article we establish a numerically tractable algorithm for solving the Chebyshev center…
The cosmological model is at present not tested between the redshift of the farthest observed supernovae (z ~ 1.4) and that of the Cosmic Microwave Background (z ~ 1,100). Here we introduce a new method to measure the cosmological…
In the last dozen years a wide and variegated mass of observational data revealed that the universe is now expanding at an accelerated rate. In the absence of a well-based theory to interpret the observations, cosmography provides…
Cosmology constraints serve as a crucial criterion in discriminating cosmological models. The traditional combined method to constrain the cosmological parameters designates the corresponding theoretical value and observational data as…
We introduce a new method to propagate uncertainties in the beam shapes used to measure the cosmic microwave background to cosmological parameters determined from those measurements. The method, which we call Markov Chain Beam…