  We constrain the growth index $\gamma$ by performing a full-shape analysis of
the power spectrum multipoles measured from the BOSS DR12 data. We adopt a
theoretical model based on the Effective Field theory of the Large Scale
Structure (EFTofLSS) and focus on two different cosmologies: $\gamma$CDM and
$\gamma \nu$CDM, where we also vary the total neutrino mass. We explore
different choices for the priors on the primordial amplitude $A_s$ and spectral
index $n_s$, finding that informative priors are necessary to alleviate
degeneracies between the parameters and avoid strong projection effects in the
posterior distributions. Our tightest constraints are obtained with 3$\sigma$
Planck priors on $A_s$ and $n_s$: we obtain $\gamma = 0.647 \pm 0.085$ for
$\gamma$CDM and $\gamma = 0.612^{+0.075}_{-0.090}$, $M_\nu < 0.30$ for $\gamma
\nu$CDM at 68\% c.l., in both cases $\sim 1\sigma$ consistent with the
$\Lambda$CDM prediction $\gamma \simeq 0.55$. Additionally, we produce
forecasts for a Stage-IV spectroscopic galaxy survey, focusing on a DESI-like
sample. We fit synthetic data-vectors for three different galaxy samples
generated at three different redshift bins, both individually and jointly.
Focusing on the constraining power of the Large Scale Structure alone, we find
that forthcoming data can give an improvement of up to $\sim 85\%$ in the
measurement of $\gamma$ with respect to the BOSS dataset when no CMB priors are
imposed. On the other hand, we find the neutrino mass constraints to be only
marginally better than the current ones, with future data able to put an upper
limit of $M_\nu < 0.27~{\rm eV}$. This result can be improved with the
inclusion of Planck priors on the primordial parameters, which yield $M_\nu <
0.18~{\rm eV}$.
