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Dr David Marsh
King’s College London
Research Project Grant

Topology from cosmology: axions, astrophysics and machine learning

David Marsh brings together experts in geometry, string theory, machine learning and axion astrophysics to chart a path through the landscape of string theory to the correct description of our Universe

Graph that plots the number of axions in a string theory model
Representation of the ‘Kreuzer-Skarke database’, a list of topological properties that can be used to construct, and now test experimentally, extra dimensional models. The x and y axes label topological quantities that determine the number of axions in a string theory model. The colour code gives the frequency of elements in the database. But this representation hides a layer of complexity: there is in fact one special location, at the far corner with x-axis value 491, where the number of actual models constructable from this dataset is thought to be maximised. McAllister’s group have developed tools to efficiently construct axion properties explicitly across all of this database and I will use tools from astrophysics and data science to explore it as never before.

The Standard Model of particle physics describes all the particles and forces observed in any laboratory on Earth. However, it does not answer foundational problems in cosmology, such as: what the main constituents of the Universe are and what started the Big Bang. Axions are hypothetical particles that could potentially answer all these questions. There is not ‘one axion to rule them all’, but it is possible to solve each cosmological problem using a different flavour of axion. This hints at a deeper structure, leading to an explosion of interest in searches for axions.

This deeper structure is connected to another question: are there extra dimensions of space? String theory predicts six additional dimensions, along with various flavours of axions resulting from forces in these dimensions. String theory is notoriously hard to test due in part to the vast number of possibilities for the shape and topology of the extra dimensions: a problem known as the ‘landscape’. Recent advances in computation have allowed us to start searching the landscape and subjecting it to tests based on the astrophysics of axions. Together with Liam McAllister, I directed a research team to perform such a test: we constructed 100,000 string theory models. We then used astrophysical data to show that a significant fraction of these models are falsified. 

This Leverhulme Research Project Grant will take our ideas to the next level, involving three step-change advances.

The landscape: the image shows one way of thinking about, and constructing, string theory models. McAllister’s group have developed computational tools that allow models in the most topologically complex part of this landscape, containing 491 axion flavours, to be constructed in milliseconds. These tools can generate vast datasets, which it is my role, as an astroparticle physicist, to test.

Axion astrophysics: I have worked for my whole career on ways to search for axions from their effects on astrophysical systems. I will combine every test available under a unified framework, from X-ray observations to axion ‘helioscopes’, from black holes to dark matter, to test string theory models.

Machine learning: in exploratory work, I have noticed patterns in the relationship between string theory models and the degree to which they are consistent with astrophysical axion searches. However, the complexity of the problem makes it impossible to solve with human ingenuity alone, which is where my two co-investigators Yang-Hui He and Jim Halverson come in. They are experts in applying machine learning to physics problems, particularly string theory. Together, we hope machine learning will help discover underlying patterns in the relationship between topology and astrophysics.

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