Null tests of the standard model using the linear model formalism

We test both the Friedmann-Lema\^tre-Robertson-Walker geometry and cosmology in a model-independent way by reconstructing the Hubble function H (z), the comoving distance D (z), and the growth of structure f₈ (z) using the most recent data available. We use the linear model formalism in order to optimally reconstruct the above cosmological functions, together with their derivatives and integrals. We then evaluate four of the null tests available in the literature that probe both background and perturbation assumptions. For all the four tests, we find agreement, within the errors, with the standard cosmological model.