The growth rate of cosmic structure is a powerful cosmological probe for extracting information on the gravitational interactions and dark energy. In the late-time Universe, the growth rate becomes nonlinear and is usually probed by measuring the two-point statistics of galaxy clustering in redshift space up to a limited scale, retaining the constraint on the linear growth rate $f$. In this paper, we present an alternative method to analyze the growth of structure in terms of local densities, i.e., $f(\mathrm{\Delta })$. Using $N$-body simulations, we measure the function of $f(\mathrm{\Delta })$ and show that structure grows faster in high-density regions and slower in low-density regions. We demonstrate that $f(\mathrm{\Delta })$ can be modeled using a log-normal Monte Carlo random walk approach, which provides a means to extract cosmological information from $f(\mathrm{\Delta })$. We discuss prospects for applying this approach to galaxy surveys.

• Received 12 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.103502