Higher Order Clustering

Since my time as a PhD student I have been interested in higher order clustering statistics such as the 3-point correlation function (3PCF), the bispectrum, multifractal analysis and counts-in-cells. It is my hope that in going beyond the usual gaussian statistics we can gain extra information on the cosmological model. I also have interest in numerical simulations, as they are crucial for checking the validity of theoretical models in non-linear regimes (arxiv:0911.4768), and semi-analytic modeling for reproducing observational catalogues (arxiv: 1106.5687).

In the last few years I developed a code (KSTAT) for calculating the 3-point correlation function (3PCF) of a discreet point set. This code can operate on millions of particles in O(NLogN) time and is scale-able through MPI parallelism. It mainly utilizes structures known as kd-trees to do fast querying on large data sets and reducing the number of CPU operations required to uniquely define spatially separated tuples of points in N-dimensional space.

In 2010 Dr Nishimichi and I investigated the Scale Dependence of the Halo Bispectrum from Non-Gaussian Initial Conditions in Cosmological N-body Simulations (arxiv:0911.4768). For this work I ran hundreds of N-body simulations using the UK’s National Grid Service (NGS). The NGS is a massively parallel distributed system of linked computing facilities contributed by partnering Universities.

During my PhD I considered the halo model approach to galaxy biasing. Using many mock galaxy catalogues in combination with 3PCF measurements were were able to place constraints on the parameters of the halo model. This work was featured in several online science and computing websites e.g. https://sciencenode.org/ feature/simulating-multi-verse-grid.php

Using the CMASS DR11 sample of galaxies we were able to place constraints on the DM-galaxy connection, within the halo model framework. Utilizing many hundreds of mock galaxy catalogues as theoretical templates allowed us to simulate, rather than predict, the 3PCF statistics and thus place constraints on the parameters of the halo occupation distribution (arxiv:1409.7389).

Although the 3PCF has the promise of providing more information on the clustering of galaxies, a lack of development on the theoretical side has inhibited the growth of this field of research. However in the couple of years there has been substantial new work on the perturbation theory of the 3PCF. In my view this is now a perfect time to explore the full potential of the third order statistics of the galaxy distribution.

In late 2015, I investigated the possibility of using the 3PCF of the redshift-space halo density field as a probe of modified gravity (arxiv:1603.05750). We found a significant difference between the 3rd order clustering statistics of the various gravity models tested, as can be see in the figure below. Following up this results, I propose that this deviation should be searched for within observational data. For this we used numerous simulations run with the code, Isis (Llinares et al. 2014), which is a modified gravity version of the code Ramses (Teyssier 2002), a particle mesh code which includes adaptive mesh refinements. I hope to follow-up this work with using more detailed N-body simulations.