Modeling nonlinear scales for dynamical dark energy cosmologies with COLA

Upcoming galaxy surveys will bring a wealth of information about the clustering of matter, but modeling small-scale structure beyond $\Lambda$CDM remains computationally challenging. While accurate N-body emulators exist to model the matter power spectrum for $\Lambda$CDM and some limited extensions, it's unfeasible to generate N-body simulation suites for all candidate models. Motivated by recent hints of an evolving dark energy equation of state, we assess the viability of employing the COmoving Lagrangian Acceleration (COLA) method to generate simulation suites assuming the $w_0w_a$ dark energy model. We combine COLA simulations with an existing high-precision $\Lambda$CDM emulator to extend its predictions into new regions of parameter space. We assess the precision of our emulator at the level of the matter power spectrum, finding that our emulator can reproduce the nonlinear boosts from EuclidEmulator2 at less than $2\%$ error. Moreover, we perform an analysis of a simulated cosmic shear survey akin to the Legacy Survey of Space and Time (LSST) first year of observations, assessing the differences in parameter constraints between our COLA-based emulator and the benchmark emulator. We find our emulator to be in excellent agreement with the benchmark, achieving less than $0.3\sigma$ shifts in cosmological parameters. We compare our emulator's performance to a commonly used approach: assuming the $\Lambda$CDM boost can be employed for extended parameter spaces without modification. We find that our emulator yields a significantly smaller $\Delta\chi^2$ distribution, parameter constraint biases, and a more accurate figure of merit compared to this second approach. Our results demonstrate that COLA emulators provide a computationally efficient path forward for modeling nonlinear structure in extended cosmologies, offering a practical alternative to full N-body suites.