Emulating the Non-Linear Matter Power-Spectrum in Mixed Axion Dark Matter Models

TL;DR

The study tackles predicting the non-linear matter power-spectrum in mixed axion dark matter models to enable weak-lensing constraints. It leverages fast COLA simulations with axion physics encoded only in the initial conditions, and trains a neural-network emulator for the ratio $r = P_{ m ax}/P_{ m Lambda{CDM}}$, which can be combined with existing $ abla ext{ΛCDM}$ emulators. The emulator achieves roughly $<10^{-2}$ mean-squared error on training and test data and offers a ~4500× speed-up over full simulations, showing reasonable agreement with axionHMCode and HMCode for suppression but not capturing all small-scale enhancements. This approach provides a practical tool for rapid inference of axion mass and abundance from power-spectrum observations, though it awaits validation against full axion simulations and incorporation of quantum-pressure effects for small-scale features.

Abstract

In order to constrain ultra light dark matter models with current and near future weak lensing surveys we need the predictions for the non-linear dark matter power-spectrum. This is commonly extracted from numerical simulations or from using semi-analytical methods. For ultra light dark matter models such numerical simulations are often very expensive due to the need of having a very low force-resolution often limiting them to very small simulation boxes which do not contain very large scales. In this work we take a different approach by relying on fast, approximate $N$-body simulations. In these simulations, axion physics are only included in the initial conditions, allowing us to run a large number of simulations with varying axion and cosmological parameters. From our simulation suite we use machine learning tools to create an emulator for the ratio of the dark matter power-spectrum in mixed axion models - models where dark matter is a combination of CDM and axion - to that of $Λ$CDM. The resulting emulator only needs to be combined with existing emulators for $Λ$CDM to be able to be used in parameter constraints. We compare the emulator to semi-analytical methods, but a more thorough test to full simulations to verify the true accuracy of this approach is not possible at the present time and is left for future work.

Figures (12)

• Figure 1: An example of the non-linear power-spectrum ratio $r$ for varying axion abundance (top panel) and axion mass (bottom panel). We use axion mass $m_{\rm ax} = 10^{-26}$ eV in the top panel, and axion abundance $f_{\rm ax} = 0.5$ in the bottom panel. The data in this figure was generated using the trained axion emulator described in this paper.
• Figure 2: Tests of how the power-spectrum ratio $r$ changes with varying simulation parameters: box-size, number of time-steps and grid-size (force resolution). A control simulation with parameters $N_{\rm time-steps} = 30$, $N_{\rm mesh-size} = 640$ and $B = 350$ Mpc/h was used.
• Figure 3: Comparison of the power-spectrum ratio $r$ as calculated with COLA to what is found with RAMSES. The top left panel shows the raw power-spectrum found using COLA and RAMSES, while the bottom left panel shows the relative difference between the two. The top right panel shows the ratio between the power-spectrum from $\Lambda$CDM and axions, and the bottom right panel shows the relative difference of these.
• Figure 4: The variation of the power-spectrum ratio $r$ as function of cosmological parameters. The dashed line indicates a relative difference of $1\%$. Only $A_s$ and $\Omega_m$ have significant ($\gtrsim 1\%$) deviations. An axion abundance of $f_{\rm ax} =0.2$ and axion mass of $m_{\rm ax} = 10^{-24}$ eV was used.
• Figure 5: Distribution of samples in our Latin hypercube. We increase the sample density at some of the edges in order to improve the performance of the emulator in these regions.