Evidence for suppression of structure growth in the concordance cosmological model

Abstract

We present evidence for a suppressed growth rate of large-scale structure during the dark-energy dominated era. Modeling the growth rate of perturbations with the ``growth index'' $\gamma$, we find that current cosmological data strongly prefer a higher growth index than the value $\gamma=0.55$ predicted by general relativity in a flat $\Lambda$CDM cosmology. Both the cosmic microwave background data from Planck and the large-scale structure data from weak lensing, galaxy clustering, and cosmic velocities separately favor growth suppression. When combined, they yield $\gamma=0.633^{+0.025}_{-0.024}$, excluding $\gamma=0.55$ at a statistical significance of 3.7$\sigma$. The combination of $f\sigma_8$ and Planck measurements prefers an even higher growth index of $\gamma=0.639^{+0.024}_{-0.025}$, corresponding to a 4.2$\sigma$-tension with the concordance model. In Planck data, the suppressed growth rate offsets the preference for nonzero curvature and fits the data equally well as the latter model. A higher $\gamma$ leads to a higher matter fluctuation amplitude $S_8$ inferred from galaxy clustering and weak lensing measurements, and a lower $S_8$ from Planck data, effectively resolving the $S_8$ tension.