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

Abstract

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.

Figures (14)

• Figure 1: The linear $P(k)$ in the FreePower method is obtained as an interpolation between the 8 best-fit variable parameters $P_i$ (red points). In black, we depict a test $\Lambda$CDM $P_L(k)$, and in blue the corresponding reconstructed $P_L(k)$ through interpolation. In orange (yellow) we show instead the reconstructed $P_L(k)$ with our best-fit $P_i$ for the high (low) redshift bins.
• Figure 2: $68.3\%$ and $95.4\%$ highest-density interval corner plot for the cosmological and bias terms for the red low-$z$ sample ($z_{\rm eff}=0.38$). Orange dots mark the Planck 2018 $\Lambda$CDM values. The orange curve represents the $L_A$ vs. $E$ relation for $\Lambda$CDM for different values of $\Omega_{m0}$.
• Figure 3: Same as Figure \ref{['fig:plot_lowz']} for the high-$z$ sample ($z_{\rm eff}=0.61$).
• Figure 4: Comparison of our model-independent $f(z)$ results with those obtained assuming $\Lambda$CDM in ISZ20 and with BOSS+eBOSS galaxies eBOSS:2020yzd. FreePower measures directly $f(z)$ but conventional analysis measure instead $f(z)\sigma_8(z)$, so we convert the latter using the values of $\sigma_8$ and $\Omega_{m0}$ obtained in ISZ20. The best fit Planck 2018 curves are depicted in dashed gray ($\Lambda$CDM) or long-dashed orange ($\gamma\Lambda$CDM Nguyen:2023fip -- see text).
• Figure 5: Comparison of $E(z)$ results using cosmic chronometers (CC, in gray) and our FreePower result (in red). For the CC data we use the compilation in Moresco:2022phi, limited to $z<1.2$, and use the $H_0$ value obtained from CC data itself with a Gaussian Process extrapolation Gomez-Valent:2018hwc.