General Relativity & Quantum Cosmology

If General Relativity emerges from quantum gravity, then general covariance, the gauge invariance of GR, will emerge with it. We can ask, within any approach to the problem of quantum gravity, what is the “precursor” principle or precept that will give rise to — or manifest itself as — general covariance in the large scale semi-classical approximation?
Given how important the understanding of general covariance (or lack of it!) was in the development of GR we might expect that thinking about this question will be similarly important in the development of quantum gravity.
I will explain how general covariance is seen from the perspective of the causal set approach to quantum gravity and describe recent progress in creating a framework for causal set dynamics that is completely covariant and does not refer to any gauge degrees of freedom at all.

In this talk I will report on recent progress in building QFT models on causal sets. The framework I'm using is that of perturbative algebraic quantum field theory (pAQFT). It was developed for rigorous study of perturbative QFT in the continuum, but can also be applied in the situation where spacetime is replaced by a discrete structure. Causality plays a key role in pAQFT, so it is natural to apply it to causets. Construction of models in this framework is purely algebraic and one does not need to specify a state or a Hilbert space representation until the final step, in which correlation functions are computed.

I shall  analyze three specific general-relativistic  problems in which gravitomagnetism plays important role: the dragging of  magnetic fields  around  rotating black holes, dragging inside a collapsing slowly rotating spherical shell of dust, compared with the dragging by rotating gravitational waves (CQG 34, 205006 (2017), Phys. Rev. D 85 124003, (2012) etc). I shall also briefly show how "instantaneous Machian gauges“ can be useful in the cosmological perturbation theory (Phys. Rev. D 76, 063501 (2007)).

We derive an effective Hamiltonian constraint for the Schwarzschild geometry starting from the full loop quantum gravity Hamiltonian constraint and computing its expectation value on coherent states sharply peaked around a spherically symmetric geometry. We use this effective Hamiltonian to study the interior region of a Schwarzschild black hole, where a homogeneous foliation is available. Descending from the full theory, our effective Hamiltonian preserves all relevant information about the graph structure of quantum space and encapsulates all dominant quantum gravity corrections to spatially homogeneous geometries at the effective level. It carries significant differences from the effective Hamiltonian postulated in the context of minisuperspace loop quantization models in the previous literature. We show how, for several geometrically and physically well motivated choices of coherent states, the classical black hole singularity is replaced by a homogeneous expanding Universe. The resultant geometries have no significant deviations from the classical Schwarzschild geometry in the pre-bounce sub-Planckian curvature regime, evidencing the fact that large quantum effects are avoided in these models. In all cases, we find no evidence of a white hole horizon formation. However, various aspects of the post-bounce effective geometry depend on the choice of quantum states. Finally, we show how a de Sitter Universe extending the classical spacetime past the singularity can be recovered by means of the simplicity constraint.