Mitigating baryon feedback bias in cosmic shear through a theoretical error covariance in the matter power spectrum

Forthcoming cosmic shear surveys will make precise measurements of the matter density field down to very small scales, scales which are dominated by baryon feedback. The modelling of baryon feedback is crucial to ensure unbiased cosmological parameter constraints; the most efficient approach is to use analytic models, but these are limited by how well they can capture the physics of baryon feedback. We investigate the fitting and residual errors of various baryon feedback models to a suite of hydrodynamic simulations, and propagate these to cosmological parameter constraints for cosmic shear. We present an alternative formalism to binary scale-cuts through the use of a theoretical error covariance, which is a well-motivated alternative using errors in the power spectrum modelling itself. We depart from previous works by modelling baryonic feedback errors directly in the matter power spectrum, which is the natural basis to do so and thus preserves information in the lensing kernels. When including angular multipoles up to $\ell_{\mathrm{max}} = 5000$, and assuming Euclid-like survey properties, we find that even multi-parameter models of baryon feedback can introduce significant levels of bias. In contrast, our theoretical error reduces the bias in $\Omega_{\mathrm{m}}$ and $S_{8}$ to acceptable levels, with only a modest increase in parameter variances. The theoretical error approach bypasses the need to directly determine the per-bin $\ell_{\mathrm{max}}$ values, as it naturally suppresses the biassing small-scale information. We also present a detailed study of how flexible HMCode-2020, a widely-used non-linear and baryonic feedback model, is at fitting a range of hydrodynamical simulations.