Modified gravity and massive neutrinos: constraints from the full shape analysis of BOSS galaxies and forecasts for Stage IV surveys

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 $M_\nu < 0.18~{\rm eV}$.
Comment: updated with accepted version