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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Theory, hep-th
Abstract:
We study the dynamics of perturbations representing deviations from perfect
isotropy in the context of the emergent cosmology obtained from the group field
theory formalism for quantum gravity. Working in the mean field approximation
of the group field theory formulation of the Lorentzian EPRL model, we derive
the equations of motion for such perturbations to first order. We then study
these equations around a specific simple isotropic background, characterised by
the fundamental representation of $\mbox{SU(2)}$, and in the regime of the
effective cosmological dynamics corresponding to the bouncing region replacing
the classical singularity, well approximated by the free GFT dynamics. In this
particular example, we identify a region in the parameter space of the model
such that perturbations can be large at the bounce but become negligible away
from it, i.e. when the background enters the non-linear regime. We also study
the departures from perfect isotropy by introducing specific quantities, such
as the surface-area-to-volume ratio and the effective volume per quantum, which
make them quantitative.
