Joint reconstructions of growth and expansion histories from stage-IV surveys with minimal assumptions. II. Modified gravity and massive neutrinos

Based on a formalism introduced in our previous work, we reconstruct the phenomenological function ${G}_{\mathrm{eff}}(z)$ describing deviations from general relativity (GR) model-independent manner. In this alternative approach, model $\ensuremath{\mu}\ensuremath{\equiv}{G}_{\mathrm{eff}}/G$ as Gaussian process and use forecasted growth-rate measurements stage-IV survey to its shape for two different toy-models. We follow two-step procedure: (i) first background expansion history supernovae (SNe) baryon acoustic oscillation (BAO) measurements; (ii) then it obtain growth $f{\ensuremath{\sigma}}_{8}$, that fit redshift-space distortions (RSD) ${G}_{\mathrm{eff}}$. find upcoming surveys such dark energy spectroscopic instrument (DESI) might be capable of detecting GR, provided behavior is accurately determined. even able constrain transition redshift $G\ensuremath{\rightarrow}{G}_{\mathrm{eff}}$ some particular models. further assess impact massive neutrinos reconstructions ${G}_{\mathrm{eff}}$ (or $\ensuremath{\mu}$) assuming given, only neutrino mass free vary. Given tight constraints mass, profiles considered recover numerically effect do not alter conclusions. Finally, stress incorrectly $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ leads degraded reconstruction $\ensuremath{\mu}$, and/or non-negligible bias $({\mathrm{\ensuremath{\Omega}}}_{\mathrm{m},0},{\ensuremath{\sigma}}_{8,0})$-plane.