Ultralight scalar fields and the growth of structure in the Universe

Ultralight scalar fields, with masses of between m=10^-33 eV and m=10^-22 eV, can affect the growth of structure in the Universe. We identify the different regimes in the evolution of ultralight scalar fields, how they affect the expansion rate of the Universe, and how they affect the growth rate of cosmological perturbations. We find a number of interesting effects, discuss how they might arise in realistic scenarios of the early universe, and comment on how they might be observed.