General Relativity & Quantum Cosmology

In approaches to quantum gravity, where smooth spacetime is an emergent approximation of a discrete Planckian fundamental structure, any standard effective field theoretical description will miss part of the degrees of freedom and thus break unitarity. Here we show that these expectations can be made precise in loop quantum cosmology. Concretely, even when loop quantum cosmology is unitary at the fundamental level, when microscopic degrees of freedom, irrelevant to low-energy cosmological observers, are suitably ignored, pure states in the effective description evolve into mixed states due to decoherence with the Planckian microscopic structure. When extrapolated to black hole formation and evaporation, this concrete example provides a key physical insight for a natural resolution of Hawking's information paradox.

Cosmological perturbation theory has a long tradition for describing the early phases of the Universe. As the observations of the CMB radiation suggest, it is reasonable, at least as a first approximation, to implement cosmological inhomogeneities as small perturbations around homogeneous and isotropic FRW solutions. In these approaches, backreactions between the inhomogeneities and the background are usually neglected. There is an ongoing debate about how and to which extend these backreactions affect the large scale structure of the Universe. Even at a purely classical level, there is no conclusive answer to this question yet.

In my talk, I am going to present a new systematic formalism for implementing backreactions in cosmological perturbation theory, in which both, the perturbations and the homogeneous degrees of freedom are considered as quantum degrees of freedom. As a more realistic theory of quantum fields on quantum cosmological space times, it can help to close the gap between a full theory of quantum gravity and symmetry-reduced models of quantum cosmology, and to confront these theories with observations. Our results show that quantum backreactions imply non-trivial corrections that are potentially phenomenologically significant.

I will explain how dark energy in cosmology could arise from the

noisy diffusion of energy from the low energy degrees of freedom of matter (described in terms of QFT)

to the fundamental Planckian granularity (expected from quantum gravity). This

perspective leads to a natural model resolving the fine tuning problem associated to the small

value of the cosmological constant. However, recent observations suggest that the dark energy

component in our universe might not be constant and should  instead have grown from the recombination time to the present.

I will present new ideas suggesting a possible explanation within the same framework.

It has long been argued that combining the uncertainty principle with gravity will lead to an effective minimum length at the Planck scale. A particular challenge is to model the presence of a smallest length scale in a manner which respects continuous spacetime symmetries. One path for deriving low-energy descriptions of an invariant minimum length in quantum field theory is based on generalized uncertainty principles. Here I will consider the question how this approach enables one to retain Euclidean or even Lorentzian symmetries. The Euclidean case yields a ultraviolet cutoff in the form of a bandlimit, and this then allows one to apply the powerful Shannon sampling theorem of classical information theory which establishes the equivalence between continuous and discrete representations of information. As a consequence, one obtains discrete representations of fields which are more subtle than a simple discretization of space, and are in fact equivalent to a continuum representation. Quantum fields in this model exhibit a finite density of information and a corresponding regularization of the entanglement of the vacuum, as I will demonstrate in detail. We then examine the Lorentzian symmetry generalization. This case leads to a Lorentz-invariant analogue of bandlimitation, and we discuss the nature of the corresponding sampling theory.

Simulations that numerically solve Einstein's equations are the only means to accurately predict the outcome of the merger of two black holes. The most important outputs from these simulations are the gravitational waveforms, and the mass and spin of the final black hole formed after the merger. The waveforms are used in extracting astrophysical information from detections, while the final mass and spin are used in testing general relativity. Unfortunately, these simulations are too expensive for direct use in data analysis; each simulation can take a month on a supercomputer. Surrogate modeling is a data-driven approach to modeling, that uses machine learning like techniques to interpolate between hundreds of existing simulations. In this talk, I will discuss some recent developments in surrogate modeling, including a new 7-dimensional model that fully captures the effects of precession; the wobbling of the orbit caused when the black holes’ spin axes aren’t perpendicular to the plane of the orbit. This model reproduces the waveform as well as the final black hole's mass and spin as accurately as the simulations themselves, while taking only a fraction of a second to evaluate on a laptop.

We study dimensionally restricted non-perturbative causal set quantum dynamics in two and three spacetime dimensions with non-trivial global spatial topology.  The causal set sample space is generated from causal embeddings into latticisations of flat background spacetimes with global spatial topology  and  in two and three dimensions, respectively. The quantum gravity partition function over these sample spaces is studied using Markov Chain Monte Carlo (MCMC) simulations via an analytic continuation of a parameter  analogous to an inverse temperature. In both two and three dimensions we find a phase transition that separates the dominance of the action from that of the entropy. The action dominated phase is characterised by "layered" posets with a high degree of connectivity, while the causal sets in the entropy dominated phase are manifold-like. These results are similar in character to those obtained for topologically trivial causal set dynamics over the sample space of 2-orders. The current simulations use a newly developed framework for causal set MCMC calculations, and provide the first implementation of a three-dimensional causal set dynamics.

arXiv paper: https://arxiv.org/abs/1908.11647