Null tests of the standard model using the linear model formalism

TL;DR

This paper employs a model-independent linear model formalism to reconstruct key cosmological functions and perform null tests, confirming the consistency of the FLRW geometry and DM cosmology with recent data.

Contribution

It introduces a linear model approach for reconstructing cosmological functions and applies multiple null tests to validate standard cosmology independently of specific models.

Findings

All null tests are consistent with the standard DM model within errors.

Reconstructed functions and derivatives align with predictions of the standard cosmological model.

The method provides a robust, model-independent validation of cosmological assumptions.

Abstract

We test both the FLRW geometry and $\Lambda$CDM cosmology in a model independent way by reconstructing the Hubble function $H(z)$, the comoving distance $D(z)$ and the growth of structure $f\sigma_8(z)$ using the most recent data available. We use the linear model formalism in order to optimally reconstruct the latter cosmological functions, together with their derivatives and integrals. We then evaluate four of the null tests available in literature: $Om_{1}$ by Sahni et al., $Om_{2}$ by Zunckel \& Clarkson, $Ok$ by Clarkson et al., and $ns$ by Nesseris \& Sapone. For all the four tests we find agreement, within the errors, with the standard cosmological model.