PREPRINT

# $\mathrm{S}\mathrm{I}\mathrm{M}\mathrm{B}\mathrm{I}\mathrm{G}$: A Forward Modeling Approach To Analyzing Galaxy Clustering

ChangHoon Hahn, Michael Eickenberg, Shirley Ho, Jiamin Hou, Pablo Lemos, Elena Massara, Chirag Modi, Azadeh Moradinezhad Dizgah, Bruno Régaldo-Saint Blancard, Muntazir M. Abidi

Submitted on 1 November 2022

## Abstract

We present the first-ever cosmological constraints from a simulation-based inference (SBI) analysis of galaxy clustering from the new $\mathrm{S}\mathrm{I}\mathrm{M}\mathrm{B}\mathrm{I}\mathrm{G}$ forward modeling framework. $\mathrm{S}\mathrm{I}\mathrm{M}\mathrm{B}\mathrm{I}\mathrm{G}$ leverages the predictive power of high-fidelity simulations and provides an inference framework that can extract cosmological information on small non-linear scales, inaccessible with standard analyses. In this work, we apply $\mathrm{S}\mathrm{I}\mathrm{M}\mathrm{B}\mathrm{I}\mathrm{G}$ to the BOSS CMASS galaxy sample and analyze the power spectrum, ${P}_{\ell }\left(k\right)$, to ${k}_{\mathrm{m}\mathrm{a}\mathrm{x}}=0.5\phantom{\rule{0.167em}{0ex}}h/\mathrm{M}\mathrm{p}\mathrm{c}$. We construct 20,000 simulated galaxy samples using our forward model, which is based on high-resolution $\mathrm{Q}\mathrm{U}\mathrm{I}\mathrm{J}\mathrm{O}\mathrm{T}\mathrm{E}$ $N$-body simulations and includes detailed survey realism for a more complete treatment of observational systematics. We then conduct SBI by training normalizing flows using the simulated samples and infer the posterior distribution of $\mathrm{\Lambda }$CDM cosmological parameters: ${\mathrm{\Omega }}_{m},{\mathrm{\Omega }}_{b},h,{n}_{s},{\sigma }_{8}$. We derive significant constraints on ${\mathrm{\Omega }}_{m}$ and ${\sigma }_{8}$, which are consistent with previous works. Our constraints on ${\sigma }_{8}$ are $27\mathrm{%}$ more precise than standard analyses. This improvement is equivalent to the statistical gain expected from analyzing a galaxy sample that is $\sim 60\mathrm{%}$ larger than CMASS with standard methods. It results from additional cosmological information on non-linear scales beyond the limit of current analytic models, $k>0.25\phantom{\rule{0.167em}{0ex}}h/\mathrm{M}\mathrm{p}\mathrm{c}$. While we focus on ${P}_{\ell }$ in this work for validation and comparison to the literature, $\mathrm{S}\mathrm{I}\mathrm{M}\mathrm{B}\mathrm{I}\mathrm{G}$ provides a framework for analyzing galaxy clustering using any summary statistic. We expect further improvements on cosmological constraints from subsequent $\mathrm{S}\mathrm{I}\mathrm{M}\mathrm{B}\mathrm{I}\mathrm{G}$ analyses of summary statistics beyond ${P}_{\ell }$.

## Preprint

Comment: 9 pages, 5 figures

Subject: Astrophysics - Cosmology and Nongalactic Astrophysics