Modeling nonlinear scales for dynamical dark energy cosmologies with COLA

TL;DR

This work demonstrates that a COLA-based emulator, calibrated against a high-precision ΛCDM emulator, can accurately model nonlinear matter clustering in dynamical dark energy cosmologies represented by the $w_0w_a$CDM model. By training a neural network on COLA-derived nonlinear boosts and post-processing them with a ΛCDM baseline (EuclidEmulator2), the authors achieve near N-body accuracy at a fraction of the computational cost. They validate the approach through a LSST-Y1–like cosmic shear analysis, showing unbiased cosmological parameter constraints (within $0.3\sigma$) and competitive Figure of Merit compared to the benchmark, while a ΛCDM projection method produces larger biases. The results establish COLA-based emulators as a practical, scalable tool for extending nonlinear modeling beyond $\Lambda$CDM, enabling robust inference in dynamical dark energy scenarios and potentially other beyond-$\Lambda$CDM theories.

Abstract

Upcoming galaxy surveys will bring a wealth of information about the clustering of matter, but modeling small-scale structure beyond $Λ$CDM remains computationally challenging. While accurate $N$-body emulators exist to model the matter power spectrum for $Λ$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 for the $w_0w_a$ dark energy model. We combine COLA simulations with an existing high-precision $Λ$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 $0.3σ$ shifts in cosmological parameters. We compare our emulator's performance to a commonly used approach: assuming the $Λ$CDM boost can be employed for extended parameter spaces without modification. We find that our emulator yields a significantly smaller $Δχ^2$ 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.

Figures (7)

• Figure 1: From top to bottom:1) Relative errors between the COLA boosts $B^\mathrm{COLA}$ predicted by the emulator versus those obtained from the test set simulations. 2) Relative errors between $\tilde{B}^\mathrm{COLA}$ (see Equation \ref{['eq:inf_refs']}) and the boosts from EE2. 3) Relative errors between $B^{\mathrm{EE2} \; \Lambda \mathrm{CDM}}$ and EE2. Colors in all panels denote the percentile of cosmologies around the mean: blue contours enclose $50\%$ of cosmologies, red contours enclose $90\%$ of cosmologies, and the outer gray lines enclose $100\%$ of cosmologies. All panels show results for $z = 0$, see Appendix \ref{['app:errors_higher_z']} for the equivalent plots at higher redshifts.
• Figure 2: Cosmological parameter constraints (68% and 95%) from the LSST-Y1 simulated analyses assuming the center cosmology from Table \ref{['tab:param_space']} as the fiducial. Green-filled contours denote constraints obtained using EuclidEmulator2 as the nonlinear prescription, orange dashed and dotted contours use our COLA emulator, and blue dashed contours use EE2$\Lambda$CDM prescription. The left, middle, and right panels show constraints using the angular cutoffs C1, C2, and C3, respectively. We observe no shifts between the analyses; however, using cutoffs C2 and C3, the constraints obtained using COLA are slightly tighter than those found with EE2 for $S_8$ and $w_0$. For EE2$\Lambda\mathrm{CDM}$, this effect is amplified.
• Figure 3: Histograms of $\Delta\chi^2_\mathrm{X} = (\mathbf{t}_\mathrm{X} - \mathbf{t}_\mathrm{EE2})^T \cdot C_\mathrm{data}^{-1} \cdot (\mathbf{t}_\mathrm{X} - \mathbf{t}_\mathrm{EE2})$ for prescription $\mathrm{X} \in \{\mathrm{COLA},\mathrm{EE2}\;\Lambda \mathrm{CDM}\}$ compared to EE2 at the full $w_0w_a$ cosmology, with random samples drawn from the prior. The top, middle, and bottom panels show results for angular cutoffs C1, C2, and C3, respectively. The distribution of $\Delta\chi^2$ values demonstrates an order of magnitude difference between theory predictions calculated using our COLA method compared to the traditional EE2$\Lambda$CDM approach, showing an improved fit from modeling the extended parameters using COLA.
• Figure 4: Spatial distribution of $\Delta\chi^2$ in the $\Omega_m \times \sigma_8$ plane. We observe higher values of $\Delta\chi^2$ at higher values of $\Omega_m$ and $\sigma_8$.
• Figure 5: Cosmological parameter constraints (68% and 95%) from the LSST-Y1 simulated analyses assuming a fiducial cosmology with $w_0^\uparrow$ and $w_a^\uparrow$ (see Table \ref{['tab:fiducials']}), keeping the other parameters at their central values. Green-filled contours denote constraints obtained using EuclidEmulator2 as the nonlinear prescription, orange dashed and dotted contours use our COLA emulator, and blue dashed contours use EE2$\Lambda$CDM prescription. The left, middle, and right panels show constraints using the angular cutoffs C1, C2, and C3, respectively. In this case, the EE2$\Lambda$CDM prescription can provide significant biases in $S_8$, which are not present when using COLA.