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Abstract

The early universe provides an opportunity for quantum gravity to connect to
observation by explaining the large-scale structure of the Universe. In the
group field theory (GFT) approach, a macroscopic universe is described as a GFT
condensate; this idea has already been shown to reproduce a semiclassical large
universe under generic conditions, and to replace the cosmological singularity
by a quantum bounce. Here we extend the GFT formalism by introducing additional
scalar degrees of freedom that can be used as a physical reference frame for
space and time. This allows, for the first time, the extraction of correlation
functions of inhomogeneities in GFT condensates: in a way conceptually similar
to inflation, but within a quantum field theory of both geometry and matter,
quantum fluctuations of a homogeneous background geometry become the seeds of
cosmological inhomogeneities. We compute the power spectrum of scalar
cosmological perturbations and find that it is naturally approximately scale
invariant, with a naturally small amplitude. This confirms the potential of GFT
condensate cosmology to provide a purely quantum gravitational foundation for
the understanding of the early universe.