Arbitrating the $S_8$ discrepancy with growth rate measurements from Redshift-Space Distortions

Abstract

Within the 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 f σ8(z) from Redshift-Space Distortions (RSD). 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 +0.030 −0.025 , 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 datasets, 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 over-predicting 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.

Minimal theory of massive gravity in the light of CMB data and the $S_8$ tension

“…5. On the other hand, these data are known to be in tension (∼ 3σ) within ΛCDM [30]. Thus, we can combine CMB and RSD in MTMG scenario.…”

“…Additionally, the authors in [24] identified a large tension between RSD and CMB measurements. Disagreement between CMB and combinations of RSD measurements with other datasets, including the E G statistic, is discussed in [30], pointing out a tension up to 5σ, depending on the datasets.…”

Model-independent constraints on $Ω_m$ and $H(z)$ from the link between geometry and growth

“…Riess et al 2021;Freedman et al 2020;Pesce et al 2020) or the density-weighted amplitude of fluctuations, 𝑆 8 ≡ 𝜎 8 (Ω 𝑚 /0.3) 0.5 (e.g. Asgari et al 2021;DES Collaboration et al 2021a;Alsing et al 2017;Nunes & Vagnozzi 2021;Heymans et al 2021;Ruiz-Zapatero et al 2021;García-García et al 2021;White et al 2021), where 𝜎 8 is the variance of 𝛿, in spheres of radius 8 ℎ −1 Mpc.…”

Gravitational waves in higher-order $R^{2}$ gravity

“…J 1 is the Bessel function of the first kind. Plugging (35) into (34) and manipulating with respect to t , leads to [55]:…”