Growth of Cosmic Structure

We review one of the most fruitful areas in cosmology today that bridge theory and data - the temporal growth of large-scale structure. We go over the growth's physical foundations, and derive its behavior in simple cosmological models. While doing so, we explain how measurements of growth can be used to understand theory. We then review how some of the most mature cosmological probes - galaxy clustering, gravitational lensing, the abundance of clusters of galaxies, cosmic velocities, and cosmic microwave background - can be used to probe the growth of structure. We report the current constraints on growth, which are summarized as measurements of the parameter combination $f\sigma_8$ as a function of redshift, or else as the mass fluctuation amplitude parameter $S_8$. We finally illustrate several statistical approaches, ranging from the "growth index" parameterization to more general comparisons of growth and geometry, that can sharply test the standard cosmological model and indicate the presence of modifications to general relativity.