Related papers: Cosmographic analysis with Chebyshev polynomials

When photons from distant galaxies and stars pass through our neighboring environment, the wavelengths of the photons would be shifted by our local gravitational potential. This local gravitational redshift effect can potentially have an…

We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…

Redshifts have been so easy to measure for so long that we tend to neglect the fact that they too have uncertainties and are susceptible to systematic error. As we strive to measure cosmological parameters to better than 1% it is worth…

In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…

The best polynomial approximation and Chebyshev approximation are both important in numerical analysis. In tradition, the best approximation is regarded as more better than the Chebyshev approximation, because it is usually considered in…

We present a strategy for a statistically rigorous Bayesian approach to the problem of determining cosmological parameters from the results of observations of anisotropies in the cosmic microwave radiation background. We propose the…

Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…

We present a cosmographic study designed to test the simplest type of accelerating cosmology: a flat universe with matter and a cosmological constant ($\Lambda$). Hubble series expansions are fit to the SCP Union2.1 supernova data set to…

The Chebyshev expansion offers a numerically efficient and easy-implement algorithm for evaluating dynamic correlation functions using matrix product states (MPS). In this approach, each recursively generated Chebyshev vector is…

Approximation theorem is one of the most important aspects of numerical analysis that has evolved over the years with many different approaches. Some of the most popular approximation methods include the Lebesgue approximation theorem, the…

Cosmological parameter estimation from forthcoming experiments promise to reach much greater precision than current constraints. As statistical errors shrink, the required control over systematic errors increases. Therefore, models or…

Astrometric calibration of images with a small field of view is often inferior to the internal accuracy of the source detections due to the small number of accessible guide stars. One important experiment with such challenges is the Hubble…

We discuss the problems of applying Maximum Likelihood methods to the CMB and how one can make it both efficient and optimal. The solution is a generalised eigenvalue problem that allows virtually no loss of information about the parameter…

Recently several studies have jointly analysed data from different cosmological probes with the motivation of estimating cosmological parameters. Here we generalise this procedure to take into account the relative weights of various probes.…

We present cosmological parameter constraints as estimated using the Bayesian BeyondPlanck (BP) analysis framework. This method supports seamless end-to-end error propagation from raw time-ordered data to final cosmological parameters. As a…

In the context of cosmography approach and using the data of Hubble diagram for supernovae, quasars and gamma-ray bursts, we study some DE parametrizations and also the concordance $\Lambda$CDM universe. Using the different combinations of…

This paper considers the approximation of a monomial $x^n$ over the interval $[-1,1]$ by a lower-degree polynomial. This polynomial approximation can be easily computed analytically and is obtained by truncating the analytical Chebyshev…

In this work, we perform observational data analysis on Einsteinian cubic gravity and $f(P)$ gravity to constrain the parameter space of the theories. We use the 30-point $z-H(z)$ cosmic chronometer data as the observational tool for our…

In this paper, we study the cosmological constraints from the measurements of Hubble parameters---$H(z)$ data. Here, we consider two kinds of $H(z)$ data: the direct $H_0$ probe from the Hubble Space Telescope (HST) observations of Cepheid…

We present a proof-of-principle determination of the Hubble parameter $H(z)$ from photometric data, obtaining a determination at an effective redshift of $z=0.75$ ($0.65<z<0.85$) of $H(0.75) =105.0\pm 7.9(stat)\pm 7.3(sys)$ km s$^{-1}$…