  We identify a class of condensate states in the group field theory (GFT)
approach to quantum gravity that can be interpreted as macroscopic homogeneous
spatial geometries. We then extract the dynamics of such condensate states
directly from the fundamental quantum GFT dynamics, following the procedure
used in ordinary quantum fluids. The effective dynamics is a non-linear and
non-local extension of quantum cosmology. We also show that any GFT model with
a kinetic term of Laplacian type gives rise, in a semi-classical (WKB)
approximation and in the isotropic case, to a modified Friedmann equation. This
is the first concrete, general procedure for extracting an effective
cosmological dynamics directly from a fundamental theory of quantum geometry.
