  Motivated by recent experiments, we investigate the system of
isotropically-interacting bosons with Rashba spin-orbit coupling. At the
non-interacting level, there is a macroscopic ground-state degeneracy due to
the many ways bosons can occupy the Rashba spectrum. Interactions treated at
the mean-field level restrict the possible ground-state configurations, but
there remains an accidental degeneracy not corresponding to any symmetry of the
Hamiltonian, indicating the importance of fluctuations. By finding analytical
expressions for the collective excitations in the long-wavelength limit and
through numerical solution of the full Bogoliubov- de Gennes equations, we show
that the system condenses into a single momentum state of the Rashba spectrum
via the mechanism of order by disorder. We show that in 3D the quantum
depletion for this system is small, while the thermal depletion has an infrared
logarithmic divergence, which is removed for finite-size systems. In 2D, on the
other hand, thermal fluctuations destabilize the system.
