The FLAMINGO project: the coupling between baryonic feedback and cosmology in light of the $S_8$ tension

Large-scale structure surveys have reported measurements of the density of matter, $\Omega_\mathrm{m}$, and the amplitude of clustering, $\sigma_8$, that are in tension with the values inferred from observations of the cosmic microwave background. While this may be a sign of new physics that slows the growth of structure at late times, strong astrophysical feedback processes could also be responsible. In this work, we argue that astrophysical processes are not independent of cosmology and that their coupling naturally leads to stronger baryonic feedback in cosmological models with suppressed structure formation or when combined with a mechanism that removes dark matter from halos. We illustrate this with two well-motivated extensions of the Standard Model known to suppress structure formation: massive neutrinos and decaying dark matter. Our results, based on the FLAMINGO suite of hydrodynamical simulations, show that the combined effect of baryonic and non-baryonic suppression mechanisms is greater than the sum of its parts, particularly for decaying dark matter. We also show that the dependence of baryonic feedback on cosmology can be modelled as a function of the ratio $f_\mathrm{b}/c^2_\mathrm{v}\sim f_\mathrm{b}/(\Omega_\mathrm{m}\sigma_8)^{1/4}$ of the universal baryon fraction, $f_\mathrm{b}$, to a velocity-based definition of halo concentration, $c^2_\mathrm{v}$, giving an accurate fitting formula for the baryonic suppression of the matter power spectrum. Although the combination of baryonic and non-baryonic suppression mechanisms can resolve the tension, the models with neutrinos and decaying dark matter are challenged by constraints on the expansion history.