  We present a continuum theory of self-propelled particles, without alignment
interactions, in a momentum-conserving solvent. To address phase separation we
introduce a scalar concentration field $\phi$ with advective-diffusive
dynamics. Activity creates a contribution
$\Sigma_{ij}=-\zeta((\partial_i\phi)(\partial_j\phi)-(\nabla\phi)^{2}\delta_{ij}/d)$
to the deviatoric stress, where $\zeta$ is odd under time reversal and $d$ is
the number of spatial dimensions; this causes an effective interfacial tension
contribution that is negative for contractile swimmers. We predict that domain
growth then ceases at a length scale where diffusive coarsening is balanced by
active stretching of interfaces, and confirm this numerically. Thus the
interplay of activity and hydrodynamics is highly nontrivial, even without
alignment interactions.
