A model-independent measurement of the expansion and growth rates from BOSS using the FreePower method

In this work we provide a data analysis of the BOSS galaxy clustering data with the recently proposed FreePower method, which adopts as parameters the power spectrum band-powers, the expansion rate, and the growth rate instead of specific cosmological parametrizations. It relies on the Alcock-Paczyński effect and redshift-space distortions, and makes use of one-loop perturbation theory for biased tracers. In this way, we obtain for the first time constraints on the linear growth rate, on the Hubble parameter, as well as on the dimensionless distance $H_0 D_A$ and various bias functions, that are independent of a model for the power spectrum shape and thus of both the early and late-time cosmological modelling. Using weakly-informative priors, requiring basically that $σ_8 \in [0.67, 1.07]$ at 95% CI, we find at $z_{\rm eff}=0.38$, $f=0.67^{+0.20}_{-0.19}$, $H/H_0=1.033^{+0.13}_{-0.081}$, $H_0 D_A = 0.264^{+0.026}_{-0.039}$ and at $z_{\rm eff}=0.61$, $f=0.82^{+0.25}_{-0.20}$, $H/H_0=1.085^{+0.16}_{-0.067}$, $H_0 D_A = 0.390^{+0.036}_{-0.046}$. We find lower $H/H_0$ results than expected from Planck 2018 $Λ$CDM results at a confidence level of 1.7$σ$ ($2.1σ$) for low-$z$ (high-$z$). These results form a proof-of-principle of the FreePower method. We also get constraints on the bias parameters which are in agreement with constraints from previous BOSS analyses, which serves as a cross-check of our pipeline.