Is cosmic acceleration proven by local cosmological probes?
  Context: The cosmological concordance model ($\Lambda$CDM) matches the
cosmological observations exceedingly well. This model has become the standard
cosmological model with the evidence for an accelerated expansion provided by
the type Ia supernovae (SNIa) Hubble diagram. However, the robustness of this
evidence has been addressed recently with somewhat diverging conclusions. Aims:
The purpose of this paper is to assess the robustness of the conclusion that
the Universe is indeed accelerating if we rely only on low-redshift
(z$\lesssim$2) observations, that is to say with SNIa, baryonic acoustic
oscillations, measurements of the Hubble parameter at different redshifts, and
measurements of the growth of matter perturbations. Methods: We used the
standard statistical procedure of minimizing the $\chi^2$ function for the
different probes to quantify the goodness of fit of a model for both
$\Lambda$CDM and a simple nonaccelerated low-redshift power law model. In this
analysis, we do not assume that supernovae intrinsic luminosity is independent
of the redshift, which has been a fundamental assumption in most previous
studies that cannot be tested. Results: We have found that, when SNIa intrinsic
luminosity is not assumed to be redshift independent, a nonaccelerated
low-redshift power law model is able to fit the low-redshift background data as
well as, or even slightly better, than $\Lambda$CDM. When measurements of the
growth of structures are added, a nonaccelerated low-redshift power law model
still provides an excellent fit to the data for all the luminosity evolution
models considered. Conclusions: Without the standard assumption that supernovae
intrinsic luminosity is independent of the redshift, low-redshift probes are
consistent with a nonaccelerated universe.
