  We derive an effective dynamics for scalar cosmological perturbations from
quantum gravity, in the framework of group field theory (GFT) condensate
cosmology. The emergent spacetime picture is obtained from the mean field
hydrodynamic regime of the fundamental theory, and physical observables are
defined using a relational strategy applied at the same level of approximation,
in terms of suitable collective states of the GFT field. The dynamical
equations we obtain for volume and matter perturbations lead to the same
solutions as those of classical general relativity in the long-wavelength,
super-horizon limit, but differ in other regimes. These differences could be of
phenomenological interest and make contact between fundamental quantum gravity
models and cosmological observations, indicating new physics or limitations of
the fundamental models or of the approximations leading to the effective
cosmological dynamics.
