Cosmography in $f(Q)$ gravity

TL;DR

This paper employs cosmography to analyze $f(Q)$ gravity in a model-independent manner, deriving functions from observational data to constrain cosmic expansion and the Hubble constant.

Contribution

It introduces a method to derive $f(z)$ and its derivatives up to fourth order from cosmography, applied directly to supernova data in $f(Q)$ gravity.

Findings

Constraints on $H_0$ from supernova data.

Dominance of the first two terms in the luminosity distance expansion.

Validation of cosmography as a tool for modified gravity models.

Abstract

Cosmography is an ideal tool to investigate the cosmic expansion history of the Universe in a model-independent way. The equations of motion in modified theories of gravity are usually very complicated; cosmography may select practical models without imposing arbitrary choices a priori. We use the model-independent way to derive $f(z)$ and its derivatives up to fourth order in terms of measurable cosmographic parameters. We then fit those functions into the luminosity distance directly. We perform the MCMC analysis by considering three different sets of cosmographic functions. Using the largest supernovae Ia Pantheon sample, we derive the constraints on the Hubble constant $H_0$ and the cosmographic functions, and find that the former two terms in Taylor expansion of luminosity distance work dominantly in $f(Q)$ gravity.