Cosmological Evidence Modelling: a new simulation-based approach to constrain cosmology on non-linear scales

Abstract

Extracting accurate cosmological information from galaxy-galaxy and galaxy-matter correlation functions on non-linear scales ( < ∼ 10 h −1 Mpc) requires cosmological simulations. Additionally, one has to marginalise over several nuisance parameters of the galaxy-halo connection. However, the computational cost of such simulations prohibits naive implementations of stochastic posterior sampling methods like Markov chain Monte Carlo (MCMC) that would require of order O(10 6 ) samples in cosmological parameter space. Several groups have proposed surrogate models as a solution: a so-called emulator is trained to reproduce observables for a limited number of realisations in parameter space. Afterwards, this emulator is used as a surrogate model in an MCMC analysis. Here, we demonstrate a different method called Cosmological Evidence Modelling (CEM). First, for each simulation, we calculate the Bayesian evidence marginalised over the galaxy-halo connection by repeatedly populating the simulation with galaxies. We show that this Bayesian evidence is directly related to the posterior probability of cosmological parameters. Finally, we build a physically motivated model for how the evidence depends on cosmological parameters as sampled by the simulations. We demonstrate the feasibility of CEM by using simulations from the Aemulus simulation suite and forecasting cosmological constraints from BOSS CMASS measurements of redshift-space distortions. Our analysis includes an exploration of how galaxy assembly bias affects cosmological inference. Overall, CEM has several potential advantages over the more common approach of emulating summary statistics, including the ability to easily marginalise over highly complex models of the galaxy-halo connection and greater accuracy, thereby reducing the number of simulations required.

On the halo-mass and radial scale dependence of the lensing is low effect

“…We see highly significant deviations from the expected unity ratio and find ∆Σ obs /∆Σ mod ∼ 0.60 − 0.65 instead. We also show, as a guidance, the 6% systematic uncertainty coming from the lensing systematics, the 1σ uncertainty from not modelling galaxy assembly bias (Lange et al 2019b) and the impact of baryonic feedback whereby the band show the range between the predictions from Illustris and IllustrisTNG (Lange et al 2019c).…”

“…Finally, combining galaxygalaxy lensing signals with constraints from redshift-space clustering on non-linear scales is another promising avenue. First, redshift-space clustering could constrain the amount of galaxy assembly bias (Lange et al 2019c;Yuan et al 2020a) and further reduce the uncertainty in the lensing predictions on non-linear scales. Additionally, redshift-space clustering is sensitive to the cosmological parameter combination f σ8 where f is the growth rate.…”

Large-scale dark matter simulations

“…An alternative could be to formulate these with automatic differentiation, for which several optimization algorithms can be employed speeding up parameter sampling considerably. Another option is to split the cosmological and galaxy formation parameters and emulate directly the ''Bayesian evidence'' of a given cosmology (Lange et al 2019(Lange et al , 2022.…”

Predicting halo occupation and galaxy assembly bias with machine learning

“…If the GAB is significant in the real universe, neglecting it would have direct implications for interpreting galaxy clustering and the inferred galaxy-halo connection and cosmological constraints (Zentner et al 2014;McEwen & Weinberg 2018;McCarthy et al 2019;Lange et al 2019). Some extensions to include environment or other halo properties have been suggested (e.g., Hearin et al 2016;McEwen & Weinberg 2018;Contreras et al 2021;Xu et al 2021).…”