A major challenge at the interface of quantum gravity and cosmology is to
explain how the large-scale structure of the Universe emerges from physics at
the Planck scale. In this letter, we take an important step in this direction
by extracting the dynamics of scalar isotropic cosmological perturbations from
full quantum gravity, as described by the causally complete Barrett-Crane group
field theory model. From the perspective of the underlying quantum gravity
theory, cosmological perturbations are represented as nearest-neighbor two-body
entanglement of group field theory quanta. Their effective dynamics is obtained
via mean-field methods and described relationally with respect to a physical
Lorentz frame causally coupled to the quantum geometry. We quantitatively study
these effective dynamical equations and show that at low energies they are
perfectly consistent with those of General Relativity, while for
trans-Planckian scales quantum effects become important. These results
therefore not only provide crucial insights into the potentially purely quantum
gravitational nature of cosmological perturbations, but also offer rich
phenomenological implications for the physics of the early Universe.Comment: 6+1 pages, 2 figure