Abstract
One of the fundamental challenges for quantum cosmology is to explain the emergence of our macroscopic Universe from physics at the Planck scale. In the group field theory (GFT) approach to quantum gravity, such a macroscopic universe results from the formation of a “condensate” of fundamentally discrete degrees of freedom. It has been shown that the effective dynamics of such GFT condensates follows the classical Friedmann dynamics at late times, while avoiding the classical singularity by a bounce akin to the one of loop quantum cosmology (LQC). It was also shown how quantum fluctuations in a GFT condensate provide an initial power spectrum of volume fluctuations around exact homogeneity. Here we connect the results for quantum fluctuations in GFT to the usual formalism for cosmological perturbations within quantum field theory in curved spacetime. We consider a bouncing universe filled with a massless scalar field, in which perturbations are generated by vacuum fluctuations in the contracting phase. Matching conditions at the bounce are provided by working within LQC. We then compare the results to the GFT condensate scenario for quantum gravity with massless scalar matter. Here, instead, an initial quantum phase described by a GFT condensate generates initial scalar perturbations through quantum fluctuations. We show general agreement in the predictions of both approaches, suggesting that GFT condensates can provide a physical mechanism for the emergence of a slightly inhomogeneous universe from full quantum gravity.
Highlights
On the largest observable scales, the structure of our Universe appears to show great simplicity: far from requiring the complications of full general relativity, it can be described by linear perturbations on a homogeneous and isotropic background spacetime
Showing the emergence of a realistic universe from a theory of quantum gravity is an outstanding challenge for fundamental physics, addressing which will be crucial in order to complete our understanding of the origins of space and time
We showed some progress towards addressing it in the group field theory approach to quantum gravity: we showed how a condensate of discrete “building blocks” of geometry, a candidate for a semiclassical macroscopic geometry, is capable of producing the correct dynamics of an exactly homogeneous and isotropic background spacetime, and of generating a power spectrum of primordial scalar perturbations that is consistent with expectations coming from the semiclassical approach of standard cosmology in terms of quantum fields on a curved spacetime background
Summary
On the largest observable scales, the structure of our Universe appears to show great simplicity: far from requiring the complications of full general relativity, it can be described by linear perturbations on a homogeneous and isotropic background spacetime. This sets an initial power spectrum for scalar perturbations that is propagated into the semiclassical universe.. This sets an initial power spectrum for scalar perturbations that is propagated into the semiclassical universe.3 This GFT condensate scenario bears some resemblance to string gas cosmology [24] where perturbations generated in a quantum-gravity phase (there given by a string gas) propagate according to the standard Einstein equations.
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