  We outline the content and theoretical support for the proposal of
"hydrodynamics on (mini)superspace" (or a non-linear extension of quantum
cosmology) as an effective framework for quantum gravity in a cosmological
context. The basis for the proposal is a general correspondence between
hydrodynamics and cosmology, and a picture of the universe as a quantum gravity
condensate. The support comes from several directions. One is from mathematical
physics: the hydrodynamics of quantum fluids can be mapped to relativistic
cosmological dynamics, and both share the same conformal symmetries, which can
be unraveled via geometric methods in superspace. The second is that the
proposed framework is realized in quantum gravity formalisms like group field
theory, in which an emergent cosmological dynamics can be extracted from the
hydrodynamics of fundamental quantum simplices in a condensate phase. The same
proposal can be motivated from the idea of 3rd quantization of gravity and from
recent work on quantum cosmology, as an effective way of incorporating topology
changing processes or cosmological inhomogeneities, respectively. A key
conceptual ingredient is the relational understanding of space and time, which
makes superspace the natural arena for gravitational dynamics, as opposed to
the "spacetime" manifold, together with the general idea of emergent spacetime.
The proposal and the results supporting it suggest an exciting dialogue between
quantum gravity, the theory of quantum fluids and cosmology, as well as a new
direction for analogue gravity simulations in the lab.
