Averaging and nonlinearity in quantum cosmology

One of the most important questions in fundamental science concerns the beginning of the Universe. In classical general relativity,
this beginning is described by the Big Bang singularity, but we expect this picture to be different in quantum gravity. Quantum gravity could indeed influence the initial conditions for the Universe and thus our understanding of fundamental cosmology.

In studying the impact of quantum gravity on cosmology, one often studies symmetry-reduced models in which the Universe is exactly homogeneous and isotropic, with small linear perturbations added on top. It is often not clear whether this is a valid approximation to the full dynamics, which is complicated and nonlinear.

In this project we want to assess the impact of nonlinearities in quantum cosmology and quantum gravity on the effective description on large scales. The approximation of a homogeneous universe should fundamentally arise from an averaging over the physics at smaller
scales. This becomes particularly pertinent in discrete approaches to quantum gravity in which a macroscopic universe arises from a large
number of “spacetime quanta”.

We will extend the linearised perturbation theory which has been well-studied in quantum cosmology to nonlinear order, and use coarse graining techniques in quantum gravity and quantum cosmology to define a notion of quantum averaging for the cosmological setting. The latter will require developing numerical tools together with some analytical work. We will work within the group field theory approach to quantum gravity and neighbouring fields, such as loop quantum gravity and loop quantum cosmology.

Informal enquiries regarding the project and its practical aspects are encouraged. If you are interested, please contact the proposed
supervisor, Dr Steffen Gielen.

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