Relaxation times for Bose-Einstein condensation by self-interaction and
  gravity
  In this letter, we study the Bose-Einstein condensation of a scalar field
with attractive self-interaction both with and without gravitational
interactions. We confirm through full dynamical simulation that the
condensation time scale due to self-interaction is inversely proportional to
the square of the number density $n$ and the self-coupling constant $g$ ($\tau
\propto n^{-2} g^{-2}$). Our results disprove the recent prediction by
Kirkpatrick et al. (2020) \cite{Kirkpatrick:2020fwd} that the self-interaction
relaxation time is inversely proportional to $n |g|$. We give an explanation as
to why Kirkpatrick et al. may be wrong. We also investigate the condensation
time scale when self-interaction and gravity are both important by solving the
Gross-Pitaevskii-Poisson equations, comparing our results to theoretical
models.
