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Renormalisation Group methods for discrete Quantum Gravity

Periodic Reporting for period 1 - RGDQG (Renormalisation Group methods for discrete Quantum Gravity)

Reporting period: 2016-09-01 to 2018-08-31

"The project ""Renormalisation Group methods for discrete Quantum Gravity"" has searched for numerical methods to relate quantum gravity theories at small scales to larger scales. Understanding quantum gravity requires us to bridge a large gap of scales. The fundamental theory we are searching for is a theory of spacetime at the shortest distances and highest energies. There are many competing proposals for what type of structure best describes this regime. We can not currently generate these high energies in the lab, and hence the most likely method of observing quantum gravity effects are large scale, i.e. astronomical and cosmological observations. To make phenomenological predictions for these large structures, from short scale quantum gravity models, we need to use a renormalisation procedure.
In solid state physics, it is common to use real space renormalisation, in which systems at different sizes are directly related. An example of this is block spin renormalisation of the Ising model, by summarising several spins into one block the system is rescaled, leading to an effective description at larger scales. Applying a similar blocking renormalisation to discrete theories of quantum gravity can help us understand their scaling behaviour. This scaling behaviour can then be used to generalise from small scale simulations to larger scale structures, and to identify universal characteristics arising in these models.
"During this project we have numerically explored how different theories of quantum gravity scale.
This work is an important step in trying to connect the high energy modesl of quantum gravity with experimentally testable predictions.
While the goal of deriving phenomenology from these results is still far in the future the simulations were sucessful and helped us better understand the models.
Some particularly interesting findings of these investigations were that a 2d model of causal set quantum gravity dynamically generates dark energy and that the phase transitions in non-commutative geometry are of higher order.
These results have been published in academic journals, and presented at several conferences.

In addition I have participated in outreach activities to present the basic ideas of numerical quantum gravity to the general public.
The most successful of these was my appearance on the Netflix show ""Bill Nye saves the world"", where I talk about my work, and about the twin paradox of special relativity at the end of episode 5 in season 2."
Before this project the scaling of neither causal set theory nor non-commutative geometry was understood, so the research has pushed the state of the art further.
The research in this project was highly theoretical and mathematical, and has no socio-economic or societal impact.