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 γ 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: γCDM and γνCDM, where we also vary the total neutrino mass. We explore different choices for the priors on the primordial amplitude As and spectral index ns, 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 3σ Planck priors on As and ns: we obtain γ = 0.647 ± 0.085 for γCDM and γ = 0.612+0.075−0.090, Mν < 0.30 for γνCDM at 68% c.l., in both cases ∼ 1σ consistent with the ΛCDM prediction γ ≃ 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 ∼ 85% in the measurement of γ 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 Mν < 0.27 eV. This result can be improved with the inclusion of Planck priors on the primordial parameters, which yield Mν < 0.18 eV.