Ultra-Light Scalar Fields and the Growth of Structure in the Universe

Ultra-light 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 ultra-light 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.