Halo Growth and Merger Rates as a Cosmological Test

Dark matter haloes grow at a rate that depends on the value of the cosmological parameters $\sigma_8$ and $\Omega_{\rm m}$ through the initial power spectrum and the linear growth factor. While halo abundance is routinely used to constrain these parameters, through cluster abundance studies, the halo growth rate is not. In recent work, we proposed constraining the cosmological parameters using observational estimates of the overall dynamical "age" of clusters, expressed, for instance, by their half-mass assembly redshift $z_{50}$. Here we explore the prospects for using the instantaneous growth rate, as estimated from the halo merger rate, from the average growth rate over the last dynamical time, or from the fraction of systems with recent episodes of major growth. We show that the merger rate is mainly sensitive to the amplitude of fluctuations $\sigma_8$, while the rates of recent growth provide constraints in the $\Omega_{\rm m}$-$\sigma_8$ plane that are almost orthogonal to those provided by abundance studies. Data collected for forthcoming cluster abundance studies, or studies of the galaxy merger rate in current and future galaxy surveys, may thus provide additional constraints on the cosmological parameters complementary to those already derived from halo abundance.