Two-Scalar Bose-Einstein Condensates: From Stars to Galaxies
  We study the properties of Bose-Einstein Condensate (BEC) systems consisting
of two scalars, focusing on both the case where the BEC is stellar scale as
well as the case when it is galactic scale. After studying the stability of
such systems and making contact with existing single scalar limits, we
undertake a numerical study of the two interacting scalars using
Einstein-Klein-Gordon (EKG) equations, including both non-gravitational
self-interactions and interactions between the species. We show that the
presence of extra scalars and possible interactions between them can leave
unique imprints on the BEC system mass profile, especially when the system
transitions from being dominated by one scalar to being dominated by the other.
At stellar scales (nonlinear regime,) we observe that a repulsive interaction
between the two scalars of the type $+\phi_1^2 \phi_2^2$ can stabilize the BEC
system and support it up to high compactness, a phenomenon only known to exist
in the $+\phi^4$ system. We provide simple analytic understanding of this
behavior and point out that it can lead to interesting gravitational wave
signals at LIGO-Virgo. At galactic scales, on the other hand, we show that
two-scalar BECs can address the scaling problem that arises when one uses
ultralight dark matter mass profiles to fit observed galactic core mass
profiles. In the end, we construct a particle model of two ultralight scalars
with the repulsive $\phi_1^2 \phi_2^2$ interaction using collective symmetry
breaking. We develop a fast numerical code that utilizes the relaxation method
to solve the EKG system, which can be easily generalized to multiple scalars.
