Chebyshev cosmography in the framework of extended symmetric teleparallel theory

TL;DR

This paper introduces a novel Chebyshev polynomial-based method to reconstruct $f(Q,T)$ gravity theories, constraining unknown functions with cosmographic parameters and demonstrating excellent agreement with observational data.

Contribution

It develops a new Chebyshev polynomial approach for reconstructing extended symmetric teleparallel gravity theories using cosmography, which is a novel methodological advancement.

Findings

Reconstructed the $f(Q,T)$ functional form using Chebyshev polynomials.

Achieved a luminosity distance expression consistent with standard cosmology.

Data analysis shows excellent agreement with observational datasets.

Abstract

Cosmography has been extensively utilized to constrain the kinematic state of the Universe using measured distances. In this work, we propose a new method to reconstruct coupling theories using the first kind of Chebyshev polynomial for two variables in which the functional form of the $f(Q,T)$ theory has been obtained. Further, the unknowns that appeared in the series are constrained using the cosmographic parameters. We find the explicit form of the luminosity distance in terms of cosmographic parameters to perform MCMC analysis using the PANTHEON+SH0ES data set. Through the distance modulus function, we observe that the result comes out to be an excellent match to the standard cosmological model and data.