  We study the stability of Bose condensates with Rashba-Dresselhaus spin-orbit
coupling in three dimensions against quantum and thermal fluctuations. The
ground state depletion of the plane-wave condensate due to quantum fluctuations
is, as we show, finite, and therefore the condensate is stable. We also
calculate the corresponding shift of the ground state energy. Although the
system cannot condense in the absence of interparticle interactions, we show by
estimating the number of excited particles that interactions stabilize the
condensate even at non-zero temperature. Unlike in the usual Bose gas, the
normal phase is not kinematically forbidden at any temperature; calculating the
free energy of the normal phase at finite temperature, and comparing with the
free energy of the condensed state, we infer that generally the system is
condensed at zero temperature, and undergoes a transition to normal at non-zero
temperature.
