  Using the recipe of arXiv:0902.4814, where all fake supersymmetric
backgrounds of matter-coupled fake N=2, d=4 gauged supergravity were
classified, we construct dynamical rotating black holes in an expanding FLRW
universe. This is done for two different prepotentials that are both
truncations of the stu model and correspond to just one vector multiplet. In
this scenario, the cosmic expansion is driven by two U(1) gauge fields and by a
complex scalar that rolls down its potential. Generically, the solutions of
arXiv:0902.4814 are fibrations over a Gauduchon-Tod base space, and we make
three different choices for this base, namely flat space, the three-sphere and
the Berger sphere. In the first two cases, the black holes are determined by
harmonic functions on the base, while in the last case they obey a deformed
Laplace equation that contains the squashing parameter of the Berger sphere.
This is the generalization to a cosmological context of the usual recipe in
ungauged supergravity, where black holes are given in terms of harmonic
functions on three-dimensional Euclidean space. The constructed solutions may
be instrumental in addressing analytically questions like black hole collisions
and violation of cosmic censorship.
