Quantifying the evidence for the current speed-up of the Universe with low and intermediate-redshift data. A more model-independent approach

We reconstruct in this paper the deceleration and jerk parameters as functions of the cosmological redshift from data on cosmic chronometers (CCH), baryon acoustic oscillations (BAOs), and the Pantheon+MCT compilation of supernovae of Type Ia (SnIa). The reconstruction is carried out with the Weighted Function Regression method, previously introduced by G\'omez-Valent & Amendola (2018). It improves the usual cosmographic approach by automatically implementing Occam's razor criterion. This makes our procedure to be more free of model and parametrization dependencies than many other analyses in the literature. The reconstructed functions are fully compatible with the predictions for the concordance model. In addition, we also discuss the confidence level at which we can claim that the Universe (assumed to be flat, homogeneous and isotropic) is currently accelerating. According to Jeffreys' scale and jargon, we find moderate evidence in favor of such speed-up using the data on SnIa+CCH, and very strong one when we also use data on BAOs. The measured current value of the deceleration parameter in the latter case reads $q_0\sim -0.60\pm 0.10$, and for the deceleration-acceleration transition redshift we find $z_t\sim 0.8\pm 0.10$. The former is $\sim 6\sigma$ away from $0$. This is in stark contrast, for instance, with the $\sim 17\sigma$ that are found in the context of the flat $\Lambda$CDM even without including the BAOs data. This indicates that cosmography and Occam's razor criterion play a crucial role in this discussion, and that estimating the evidence for positive acceleration only in the framework of a particular cosmological model or parametrization is clearly insufficient.