Arbitrating the S8 discrepancy with growth rate measurements from redshift-space distortions

Within the Lambda cold dark matter (ΛCDM) model, measurements from recent cosmic microwave background (CMB) and weak lensing (WL) surveys have uncovered a -3σ disagreement in the inferred value of the parameter S8 ≡ σ8√Ωm/0.3, quantifying the amplitude of late-time matter fluctuations. Before questioning whether the S8 discrepancy calls for new physics, it is important to assess the view of measurements other than CMB and WL ones on the discrepancy. Here, we examine the role of measurements of the growth rate f(z) in arbitrating the S8 discrepancy, considering measurements of fσ8(z) from redshift-space distortions (RSDs). Our baseline analysis combines RSD measurements with geometrical measurements from baryon acoustic oscillations (BAO) and Type Ia Supernovae (SNeIa), given the key role of the latter in constraining Ωm. From this combination and within the ΛCDM model, we find S8 = 0.762-0.025+0030, and quantify the agreement between RSD + BAO + SNeIa and Planck to be at the 2.2σ level: the mild disagreement is therefore compatible with a statistical fluctuation. We discuss combinations of RSD measurements with other data sets, including the EG statistic. This combination increases the discrepancy with Planck, but we deem it significantly less robust. Our earlier results are stable against an extension where we allow the dark energy equation of state w to vary. We conclude that, from the point of view of combined growth rate and geometrical measurements, there are hints, but no strong evidence yet, for the Planck ΛCDM cosmology overpredicting the amplitude of matter fluctuations at redshifts z ≲ 1. From this perspective, it might therefore still be premature to claim the need for new physics from the S8 discrepancy.