David Seery
Back reaction and renormalization in cosmological correlation functions
Measurement and inference in cosmology generally depends on a comparison of observed correlations with those predicted by a theoretical model. The sophistication with which we are able to predict such correlations has been slowly increasing. Recently, the unexpected mass distribution of merging black holes detected with LIGO/VIRGO/Kagra has encouraged cosmologists to consider early-universe scenarios in which nontrivial dynamics somehow cause a spike in power over a narrow range of scales. The enhanced fluctuations associated with these scales could collapse to produce the population of black holes observed by LVK.
In these scenarios, back-reaction can cascade power from small scales to large scales. In theoretical calculations this manifests as a sensitivity to loop corrections. These are much the same as the familiar loops in Feynman diagrams that mediate quantum effects for particles scattering in vacuum, although here they can represent a mix of quantum and classical processes. Otherwise there are many points of similarity. In particular, in perturbation theory, the loops need to be regularized and renormalized. There is still considerable ambiguity about how this should be done.
Although activity in this area has been catalysed by the LVK results, but the impact of loops is not limited to these scenarios. Theorists had already been studying them for a variety of applications. Depending on your interests, there could be a number of projects in this area:
Numerical: if you have good computing skills (or want to develop them), then evaluation of the loops is numerically challenging. We are trying to produce high-quality numerical results for the gravitational wave spectrum generated from loops that average over the effect of small-scale structure. This is expected to be a relevant target for LISA and subsequent gravitational wave observatories. To do this we need to build sophisticated High Performance Computing (HPC) codes that deploy on a compute cluster. Sometimes we also leverage tools from data science, including large databases and tools such Arrow for handling out-of-memory datasets.
Theorists: Much progress has been driven by importing (or rediscovering) methods from non-equilibrium quantum field theory. We are exploring the use of these frameworks to write (and solve) evolution equations for cosmological correlation functions beyond tree level. We would like to use these equations to develop improved modelling of gravitational wave production and scalar back-reaction. Non-equilibrium methods have very wide applicability to many phenomena operating over cosmological history. In addition, we are exploring how to correctly regularize and renormalize the resulting correlation functions, so that they can be correctly compared with observation. There would be opportunities to become involved with this effort.
For more information/to apply for these projects, please contact Dr. David Seery (email: D.Seery@sussex.ac.uk).