  We study the Bose-Einstein condensate phase transition of three-dimensional
ultracold bosons with isotropic Rashba spin-orbit coupling. Investigating the
structure of Ginzburg-Landau free energy as a function of the condensate
density, we show, within the Bogoliubov approximation, that the condensate
phase transition is first order with a jump in the condensate density. We
calculate the transition temperature and the jump in the condensate density at
the transition for large spin-orbit coupling, where the transition temperature
depends linearly on the density of particles. Finally, we discuss the
feasibility of producing the phase transition experimentally.
