Non-linear CMB lensing with neutrinos and baryons: FLAMINGO simulations versus fast approximations

Weak lensing of the cosmic microwave background is rapidly emerging as a powerful probe of neutrinos, dark energy, and new physics. We present a fast computation of the non-linear CMB lensing power spectrum that combines non-linear perturbation theory at early times with power spectrum emulation using cosmological simulations at late times. Comparing our calculation with light-cones from the FLAMINGO 5.6 Gpc cube dark-matter-only simulation, we confirm its accuracy to $1{{\ \rm per\ cent}}$ ($2{{\ \rm per\ cent}}$) up to multipoles L = 3000 (L = 5000) for a νΛCDM cosmology consistent with current data. Clustering suppression due to small-scale baryonic phenomena such as feedback from active galactic nuclei can reduce the lensing power by $\sim 10{{\ \rm per\ cent}}$. To our perturbation theory and emulator-based calculation, we add SP(k), a new fitting function for this suppression, and confirm its accuracy compared to the FLAMINGO hydrodynamic simulations to $4{{\ \rm per\ cent}}$ at L = 5000, with similar accuracy for massive neutrino models. We further demonstrate that scale-dependent suppression due to neutrinos and baryons approximately factorize, implying that a careful treatment of baryonic feedback can limit biasing neutrino mass constraints.