Spherical collapse of fuzzy dark matter
  It has been postulated that Fuzzy Dark Matter (FDM) could be a viable
alternative to Cold Dark Matter (CDM). FDM is comprised of ultralight bosons
which exist as a Bose-Einstein condensate. Due to the very low mass of FDM, the
de Broglie wavelength of these bosons are of the order of kpc and the quantum
effects manifest at those scales. Hence, unlike CDM, FDM experiences quantum
pressure along with gravitational attraction. In this work, we investigate the
gravitational collapse of a spherically symmetric FDM overdensity. We assume a
power law density profile for an overdense region of FDM and derive an
expression for the temporal evolution of a spherical shell in the
non-interacting limit and use it to derive an expression for average
overdensity contained in the spherical shell in an Einstein--de Sitter
universe. Further, we numerically extend the analysis to the case of
interacting bosons. Finally, we discuss the virialization of such an overdense
region of non-interacting FDM and derive an expression for overdensity in the
linear and the full theory. We compare our results with those obtained in the
case of CDM and conclude with a discussion of the results.
