On a robust analysis of the growth of structure

Current cosmological tensions show that it is crucial to test the predictions from the canonical $\Lambda$CDM paradigm at different cosmic times. One very appealing test of structure formation in the universe is the growth rate of structure in our universe $f$, usually parameterized via the growth index $\gamma$, with $f\equiv \Omega_m(a)^\gamma$ and $\gamma \simeq 0.55$ in the standard $\Lambda$CDM case. Recent studies have claimed a suppression of the growth of structure from a variety of cosmological observations, characterized by $\gamma>0.55$. By employing different self-consistent growth parameterizations schemes, we show here that $\gamma<0.55$, obtaining instead \emph{an enhanced growth of structure today}. This preference reaches the $3\sigma$ significance using Cosmic Microwave Background observations, Supernova Ia and Baryon Acoustic Oscillation measurements. The addition of Cosmic Microwave Background lensing data relaxes such a preference to the $2\,\sigma$ level, since a larger lensing effect can always be compensated with a smaller structure growth, or, equivalently, with $\gamma>0.55$. We have also included the lensing amplitude $A_{\rm L}$ as a free parameter in our data analysis, showing that the preference for $A_{\rm L}>1$ still remains, except for some particular parameterizations when lensing observations are included. We also not find any significant preference for a multipole dependence of $A_{\rm L}$. To further reassess the effects of a non-standard growth, we have computed by means of N-body simulations the dark matter density fields, the dark matter halo mass functions and the halo density profiles for different values of $\gamma$. Future observations from the Square Kilometer Array, reducing by a factor of three the current errors on the $\gamma$ parameter, could finally settle the issue.