  We investigate the growth rate of structures in the local Universe. For this,
we use as a cosmological tracer the HI line extra-galactic sources from the
Arecibo Legacy Fast ALFA (ALFALFA) survey to obtain a measurement of the
normalized growth rate parameter, $f \sigma_{8}$, considered a powerful tool to
constrain alternative models of gravity. For these analyses, we calculate the
Local Group velocity due to the matter structures distribution in the ALFALFA
catalogue and compare it with the Local Group velocity relative to the Cosmic
Microwave Background frame to obtain the velocity scale parameter, $\beta$.
Using Monte Carlo realizations and log-normal simulations, our methodology
quantifies the errors introduced by shot-noise and partial sky coverage of the
analysed data. The measurement of the velocity scale parameter $\beta$, and the
calculation of the matter fluctuation of the cosmological tracer,
$\sigma_{8}^{\text{tr}}$, lead us to $f \sigma_{8} = 0.46 \pm 0.06$ at $\bar{z}
= 0.013$, in good agreement (at $1 \sigma$ level) with the value expected in
the $\Lambda$CDM concordance model. In addition, our analyses of the ALFALFA
sample also provide a measurement of the growth rate of structures $f \,=\,
0.56 \pm 0.07$, at $\bar{z} = 0.013$.
