Modeling nonlinear scales with the comoving Lagrangian acceleration method: Preparing for LSST Y1

Year 1 results of the Legacy Survey of Space and Time (LSST) will provide tighter constraints on small-scale cosmology, beyond the validity of linear perturbation theory. This heightens the demand for a computationally affordable prescription that can accurately capture nonlinearities in beyond-$\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ models. The comoving Lagrangian acceleration (COLA) method, a cost-effective $N$-body technique, has been proposed as a viable alternative to high-resolution $N$-body simulations for training emulators of the nonlinear matter power spectrum. In this study, we evaluate this approach by employing COLA emulators to conduct a cosmic shear analysis with LSST-Y1 simulated data across three different nonlinear scale cuts. We use the $w\mathrm{CDM}$ model, for which the euclidemulator2 (ee2) exists as a benchmark, having been trained with high-resolution $N$-body simulations. We primarily utilize COLA simulations with mass resolution ${M}_{\mathrm{part}}\ensuremath{\approx}8\ifmmode\times\else\texttimes\fi{}{10}^{10}{h}^{\ensuremath{-}1}{M}_{\ensuremath{\bigodot}}$ and force resolution ${\ensuremath{\ell}}_{\text{force}}=0.5{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$, though we also test refined settings with ${M}_{\mathrm{part}}\ensuremath{\approx}1\ifmmode\times\else\texttimes\fi{}{10}^{10}{h}^{\ensuremath{-}1}{M}_{\ensuremath{\bigodot}}$ and force resolution ${\ensuremath{\ell}}_{\text{force}}=0.17{h}^{\ensuremath{-}1}\text{ }\text{ }\mathrm{Mpc}$. We find the performance of the COLA emulators is sensitive to the placement of high-resolution $N$-body reference samples inside the prior, which only ensure agreement in their local vicinity. However, the COLA emulators pass stringent criteria in goodness of fit and parameter bias throughout the prior, when existing high-resolution $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ emulators are leveraged alongside the COLA emulators to predict the respective $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ parameters, suggesting a promising template for extensions to $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$.