# Cosmology PhD projects

Research projects on offer in our Cosmology Group:

**Testing general relativity with galaxy redshift surveys**

- Video: Testing General Relativity with galaxy redshift surveys
- Florian Beutler - Testing General Relativity with galaxy redshift surveys

This project uses data from galaxy redshift surveys to constrain General Relativity and alternative gravity models using the large-scale velocity field as well as relativistic distortions of the observed redshifts. If we want to understand the expansion of the Universe, we need to understand gravity. Modifications of gravity on cosmic scales have been proposed as one solution to explain the presence of dark energy.

This project will develop an analysis pipeline to measure the anisotropic galaxy clustering signal and apply this pipeline to the currently largest galaxy redshift survey datasets namely the Dark Energy Spectroscopic Instrument (DESI) and the Euclid space-satellite. The aim is to extract information about gravity on cosmic scales and compare these observations with theoretical predictions of various gravity models.

- The project could involve theoretical aspects since we need to use perturbation theory to develop a better model for the galaxy power spectrum and bispectrum.
- Alternatively, this project could use neural network-based emulators to model these statistics.
- This project also has computational aspects, since we need to implement estimators for the power spectrum and bispectrum, optimize for performance (e.g. using parallel computing libraries like MPI) and run them on supercomputers.

The student should bring some experience in any higher-order programming language (e.g., C++ or Python). However, using the supercomputer facilities is easy to learn on the fly. The student is expected to work within the international DESI and Euclid collaborations, which will involve attending international collaboration meetings and regular zoom calls with teams all around the world.

Some publications about cosmological analysis with galaxy redshift surveys:

- Alam et al. MNRAS, 470, (2017); The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological analysis of the DR12 galaxy sample, https://arxiv.org/abs/1607.03155
- Eisenstein et al.; ApJ, 633, 560-574 (2005); Detection of the Baryon Acoustic Peak in the Large-Scale Correlation Function of SDSS Luminous Red Galaxies, https://arxiv.org/abs/astro-ph/0501171
- Desjacques, Jeong \& Schmidt; JCAP, 12 (2018); The Galaxy Power Spectrum and Bispectrum in Redshift Space, https://arxiv.org/abs/1806.04015

**Lensing and clustering with the Rubin Observatory**

Combining weak lensing and galaxy clustering statistics yields one of the most powerful probes in cosmology for understanding the distribution of dark matter and the gravitational and cosmic processes that lead to that distribution. We measure and cross-correlate the two-point statistics of each and compare the results to increasingly rich theoretical models. In this project, you'll be part of the Vera Rubin Observatory, the largest upcoming ground-based photometric survey, which will build the largest dark matter maps and statistics over the course of a decade. It will measure the positions and shapes of 10 billion galaxies over the course of its mission You will work with the analysis pipeline that connects our measurements of these galaxies to our theories of physics and cosmology, becoming part of a large international team to do so. You'll help build the supercomputer analysis that will characterise and model Rubin data from core pixel modelling all the way to theoretical modelling, depending on your interests. This will be a heavily computational project, so it would be good to have a strong interest and some experience in that area.

**Hybrid methods for redshift-space clustering and cosmological tests of gravity**

John Peacock & Marcos Pellejero-Ibanez

One of the fundamental goals for cosmological research is to measure the strength of gravity on the largest scales and to test for deviations from Einstein's relativistic theory. A prime tool for this study is Redshift-Space Distortion of clustering (RSD), caused by the pattern of peculiar velocities: material must flow out of voids and onto high-density concentrations. These velocities alter the apparent redshift, so that apparent 3D galaxy clustering is distorted in the radial direction; measuring this distortion tells us the size of the velocities and hence the strength of gravity. New generations of surveys measuring 20-30 million redshifts aim to measure this effect: the ground-based DESI project started its survey at the beginning of 2020; the space-based Euclid project will follow in 2023. These projects offer the hope of measuring the strength of gravity on cosmological scales at the 1 percent level - an order of magnitude improvement on current limits.

But these statistically precise measurements demand an equally precise theory. The RSD anisotropy generates an elegant analytic distortion of clustering on scales where linear perturbation theory is valid (10-100 Mpc), but more information is gained by using measurements at smaller scales, down to 1 Mpc. Here we need to allow for nonlinearities in gravitational collapse and in the galaxy-formation process. We also need to allow for non-local effects of tidal gravitational fields on galaxy properties ('assembly bias'). A purely analytic theory in this regime is challenging, motivating 'hybrid' approaches that use numerical simulations of structure formation in combination with a parameterised approach to galaxy bias. We have developed two distinct methods: Lagrangian Bias and Halo Streaming (see references below). These differ according to whether astrophysical effects are treated via the initial fluctuation field, or via the late-time population of dark-matter haloes and their properties. The aim of this PhD project is to compare these different theoretical approaches, with the aim of developing a novel integrated approach that includes the strengths of each method. A particularly important extension of existing work will be to cover the 'multitracer' regime where different classes of galaxy inhabit the same region of space: apart from testing the robustness of conclusions regarding the strength of gravity, the multitracer approach offers the possibility of more precise measurement through the partial cancellation of cosmic variance.

This science case lies at the frontier of Large Scale Structure modelling and has as its primary scientific objective precise cosmological measurements that can result in the discovery of new physics in the Universe. The student will collaborate with internationally renowned scientists as a member of the DESI and Euclid teams and will have the opportunity to travel to international conferences and visit foreign institutions. The project makes use of machine learning techniques and cutting-edge simulations, and thus comes with access to supercomputing resources. Cosmology at Edinburgh provides an inclusive environment in which students are encouraged to display creativity and innovation.

References

- RSD review: https://arxiv.org/abs/0808.0003
- Multitracers and assembly bias: https://arxiv.org/abs/1910.05095
- Nonlinear RSD in GAMA: https://arxiv.org/abs/2006.05383
- Lagrangian bias in redshift space: https://arxiv.org/abs/2109.08699
- Halo streaming model: https://arxiv.org/abs/2206.05065
- DESI: https://www.desi.lbl.gov
- Euclid: https://www.euclid-ec.org

**Probing the distribution of dark matter haloes with galaxy groups**

It is now well established that structure in our universe formed by gravitational instability, which magnifies initial density fluctuations and concentrates matter (predominantly dark matter) into nonlinear clumps called dark matter "haloes". Galaxies form within these structures, and a central task for cosmology is to understand how the resulting galaxy populations depend on the properties of the haloes that they inhabit. Next-generation galaxy surveys aim to use the galaxy distribution as a proxy for the overall mass density, in order to study fundamental issues such as the nature of gravity and the properties of the "dark energy" that drives accelerating cosmic expansion. In this work, it is therefore essential to have a detailed knowledge of the mapping between dark and visible matter. One way of approaching this is to study galaxy groups and clusters, since these systems must correspond to individual dark matter haloes. The state of the art in galaxy groups is the catalogue created from the GAMA spectroscopic survey (https://arxiv.org/abs/1106.1994), but the opportunity now exists to improve on this in two ways: increasing the range of halo masses probed and also increasing the range of redshifts studied, so that the evolution of the group population can be measured. New spectroscopic data are now arriving from the DESI survey (https://www.desi.lbl.gov), which will increase the GAMA sample by about a factor 100. But most galaxies will still lack a spectroscopic redshift, and so it is important to use the lower precision "photometric redshifts" that can be estimated from the colours of fainter galaxies. A great resource here exists in the form of the Legacy Survey imaging (https://www.legacysurvey.org), which we have recently exploited to create a new catalogue of photometric redshifts (https://arxiv.org/abs/2010.00466). By combining this information with spectroscopy, it should be possible to construct a new group catalogue that surpasses all existing work in terms of fidelity and coverage in mass and redshift. Once this catalogue is in place, it will open the door to many follow-up projects in cosmology. The total masses of the groups can be estimated by gravitational lensing, and Edinburgh is a world leader in this work (https://arxiv.org/abs/1507.00735), both in using ground-based data, but also in the revolutionary results expected from space with the 2023 launch of the Euclid satellite (https://www.euclid-ec.org). The DESI survey will be underway until the end of 2025, and this is a project in which Edinburgh researchers will be making leading contributions to the analysis. A particularly interesting project will be to probe the strength of gravity on cosmological scales by measuring the amplitude of infall velocities onto haloes, via the "redshift-space distortions" of the cross-correlations between groups and the general galaxy distribution (https://arxiv.org/abs/2006.05383). There are many other possible lines of research, and this project will form an effective introduction to forefront issues in statistical cosmology, including both the theory of large-scale structure and handling of large datasets from surveys and numerical simulations.