Redshift-Space Galaxy Clustering from Vlasov Perturbation Theory

A key method to learn about the universe is to use the spatial location of galaxies as distributed in the sky, which are not random but rather clustered due to gravity. These studies allow us to probe critical cosmological questions, such as what were the conditions in the early universe, how much matter is in the universe, and why its expansion is accelerating. The main challenge in extracting such information from astronomical data is the need to precisely compute the effects of gravitational clustering beyond the largest scales. In this project, a team from New York University will develop a new theoretical approach that can incorporate the effects of crossing of the orbits of particles that necessarily happens on small scales, and compute its effect on the observables used to extract cosmological information. This promises to increase the power of galaxy clustering measurements from astronomical data. The project team will integrate aspects of this research into undergraduate and graduate courses and will develop and new cosmology lecture series for the general public. This proposal focuses on extending the formalism of Vlasov Perturbation Theory (VPT), which describes gravitational clustering in cosmology incorporating the effects of orbit crossing that source a velocity dispersion tensor. The major goals of this proposal are to (1) extend the current results of VPT for the matter power spectrum to the matter bispectrum at one-loop order, (2) extend the VPT approach to perturbative redshift-space distortions predictions for the one-loop matter bispectrum, (3) incorporate VPT predictions for matter correlators to predict the one-loop galaxy power spectrum and bispectrum in real space, (4) extend the velocity-difference generating function (VDG) approach to redshift-space distortions to VPT, and (5) build an emulator of VPT to substantially improve the speed of calculations of the galaxy power spectrum and bispectrum in redshift space using the VDG approach for biased tracers. The team will update the publicly available COMET code to use VPT to compute the one-loop galaxy power spectrum and bispectrum in redshift space given a cosmological model that can be used for cosmological parameter estimation through Markov-Chain Monte Carlo. This will be useful to analyze current galaxy redshift surveys such as DESI and Euclid. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.