  It is known that purely repulsive self-propelled colloids can undergo bulk
liquid-vapor phase separation. In experiments and large scale simulations,
however, more complex steady states are also seen, comprising a dynamic
population of dense clusters in a sea of vapor, or dilute bubbles in a liquid.
Here we show that these microphase-separated states should emerge generically
in active matter, without any need to invoke system-specific details. We give a
coarse-grained description of them, and predict transitions between regimes of
bulk phase separation and microphase separation. We achieve these results by
extending the $\phi^4$ field theory of passive phase separation to allow for
all local currents that break detailed balance at leading order in the gradient
expansion. These local active currents, whose form we show to emerge from
coarse-graining of microscopic models, include a mixture of irrotational and
rotational contributions, and can be viewed as arising from an effective
nonlocal chemical potential. Such contributions influence, and in some
parameter ranges reverse, the classical Ostwald process that would normally
drive bulk phase separation to completion.
