The complex processes of baryonic feedback associated with galaxy evolution are still poorly understood, and their impact on the clustering of matter on small scales remains difficult to quantify. While many fitting functions and emulators exist to model the matter power spectrum, their input parameters are not directly observable. However, recent studies using hydrodynamical simulations have identified a promising correlation between the gas content of halos and changes to the matter power spectrum from feedback. Building on these findings, we create the first fully data-driven power spectrum emulator. We utilize the kinematic Sunyaev-Zel’dovich (kSZ) effect, a secondary anisotropy in the cosmic microwave background, as a tracer of free electrons in and around halos. We train a neural network to learn the mapping between the suppression of the matter power spectrum and the shape of the kSZ power spectrum extracted with a radial velocity template. We train and validate our algorithm using the FLAMINGO suite of hydrodynamical simulations, which encompasses a wide range of feedback models. Our emulator can reconstruct the matter power spectrum at the subpercent level for scales $k\le 5h/\mathrm{Mpc}$ and $0.2\le z\le 1.25$ directly from the data. Our model is robust and retains percent-level accuracy even for feedback models and cosmological parameter values not seen during training (except in a few extreme cases drastically different from the fiducial model). Due to its robustness, our algorithm offers a new way to identify the sources of suppression in the matter power spectrum, breaking the degeneracies between baryonic feedback and new physics. Finally, we present a forecast for reconstruction of the matter power spectrum combining maps of the microwave background anisotropies from a Simons Observatory-like experiment and galaxy catalogs from the Dark Energy Spectroscopic Instrument.

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• Cosmic microwave background
• Cosmological parameters
• Dark matter
• Large scale structure of the Universe
• Sky surveys