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Using the halo model to maximise the information gain from forthcoming weak-lensing surveys.

Periodic Reporting for period 2 - Halo modelling (Using the halo model to maximise the information gain from forthcoming weak-lensing surveys.)

Reporting period: 2019-09-01 to 2020-08-31

As the Universe expands, tiny perturbations that are imprinted upon the universe during inflation eventually collapse under their own weight. These then provide the formation sites for the rich structure of the cosmos that is observed today. The details of this collapse process are governed by the constituent parts of the universe: If there is more dark matter then perturbations weigh more and collapse faster; if there is more dark energy the universe expands faster and this slows down structure formation. It follows that by measuring the progress of this collapse process over the history of the cosmos one can learn about the nature of dark matter and dark energy. The collapse can be measured indirectly via weak gravitational lensing, whereby light from distant sources is bent in a spatially coherent way by the spatial coherence of the intervening structure.

This project aims to address one of the main challenges in inference from contemporary cosmological data using weak lensing: On very large scales, the collapse of cosmological structure is driven by gravity and this is the only force that is important. However, on smaller scales, other processes influence the collapse, particularly processes that originate on the scale of galaxies. These are electromagnetic in origin, and the most important of these processes are the heating of galactic gas by both accreting super-massive black holes in the centres of the galaxies and by the supernovae explosions of massive stars. The influence of these complicated electromagnetic (baryonic) processes make ab-initio theoretical calculations of structure formation very difficult. It becomes necessary to run computationally-intensive hydrodynamic simulations to understand how these baryonic processes redistribute gas, and therefore matter, in the cosmos. This project attempts to expand the knowledge of humanity with regards to how gas dynamics affects the distribution of structure in the Universe.

This project has furthered knowledge regarding the fundamental connection between the unobservable dark-matter Universe and the observable visible Universe. Detailed knowledge of this connection is essential to be able to exploit data from current and future surveys to the full extent possible. The project has three main conclusions: First, a completely novel model has been generated that relates the observable gas and star distributions to the dark matter. In the future it will be possible to use a combination of observables, including the observed galaxy distribution and the electron pressure in conjunction with weak gravitational lensing, to learn about the expansion of the Universe. Second, the underlying predictions for the matter distribution in the absence of baryonic feedback processes have been significantly improved via HMcode-2020. It is essential to have this ingredient well calibrated as other state-of-the-art approaches, such as that mentioned in the first conclusion, rely on this keystone. Third, a new technique has been generated to properly incorporate the physics of dark-matter halo clustering within the existing modelling framework. This is important because previously models have been forced to make the assumption of a linear relationship between haloes and dark matter. Including the non-linearity in this relationship removes a bias that would otherwise affect future cosmological constraints and potentially provides a new window into interesting non-linear physics.
The central project that the researcher has finalised during the fellowship has been to develop a new, theoretical model of how dark matter, gas and starts are distributed in the universe and how these combine to determine the overall distribution of matter. Current models make no distinction between these three, physically-distinct, components of the matter and instead lump them together. Considering the three components separately has the advantage of being able to use the model to make predictions for a number of different observables, particularly for two-point correlation functions of any pair of observables. This model has now been published, and will be used in the future for the analysis of the lensing-tSZ cross correlation function.

During the Project, the researcher has kept his public HMcode (https://github.com/alexander-mead/HMcode) up to date, working on its inclusion with the CAMB software package. This involves collaboration with Professor Anthony Lewis of the University of Sussex. Because of this, HMcode is now the de-facto standard for calculating the non-linear cosmological power spectrum in any cosmological data analysis that uses the non-linear matter distribution. This includes all current galaxy weak-gravitational lensing analyses as well as the most recent Planck cosmic-microwave background analyses. The researcher has recently submitted for publication an updated version of HMcode, which he worked on together with a PhD student at UB, and which includes a novel baryonic-feedback model. The model is now accurate at the 2.5% level. The researcher has also continued his involvement with the Kilo Degree Survey (KiDS; http://kids.strw.leidenuniv.nl/) that currently provides some of the best constraints on the standard cosmological model that have been obtained using the technique of weak gravitational lensing. The researcher has fully incorporated HMcode within the KiDS pipelines and this is now a central part of the KiDS analyses.

Recently, the researcher has recently improved the halo model of structure formation by working on a theoretically-consistent method to incorporate non-linear halo bias within the model. This has the potential to revolutionise the modelling of a very wide range of cosmological problems, particularly in the analysis of cross correlations. This also solves a long-standing problem with the model, which was known to under-predict the correlation on intermediate scales. This has far-reaching implications for all corners of cosmology that use the halo model. This work has recently been submitted to a journal.
As with many astrophysics projects, it is difficult to assess the direct socio-economic impact of the research. However, there are many indirect impacts such as training for the researcher and for those he interacted with during the project; both in terms of direct astrophysics training, but also more transferable skills such as computational and programming skills. As always with blue-sky research, there is also the benefit that this has on the community at large: both in terms of inspiring young people to get involved with STEM and also inspiring the public at large by encouraging a focus on something utterly different from the day-to-day. This is particularly important during times of great change, such as that we now find ourselves in.

The wider societal implications of the project are that better and less biased constraints on cosmological parameters will now be possible using data from forthcoming EU funded surveys such as KiDS and Euclid. This has implications for EU money spent on these projects, as durable theoretical models are absolutely necessary in order to extract knowledge about the Universe from otherwise expensive-to-make measurements.