Mitigation of nonlinear galaxy bias with a theoretical-error likelihood

Stage-IV galaxy surveys will measure correlations at small cosmological scales with high signal-to-noise ratio. One of the main challenges of extracting information from small scales is devising accurate models, as well as characterizing the theoretical uncertainties associated with any given model. In this work, we explore the mitigation of theoretical uncertainty due to nonlinear galaxy bias in the context of photometric 2$\times$2-pt analyses. We consider linear galaxy bias as the fiducial model and derive the contribution to the covariance matrix induced by neglected higher-order bias. We construct a covariance matrix for the theoretical error in galaxy clustering and galaxy-galaxy lensing using simulation-based relations that connect higher-order parameters to linear bias. We test the modified likelihood in 2$\times$2-pt analyses based on two sets of mock data vectors: (1) simulated data vectors, constructed from those same relations between bias parameters, and (2) data vectors based on the AbacusSummit simulation suite. We then compare the performance of the theoretical-error approach to the commonly employed scale cuts. We find most theoretical-error configurations yield results equivalent to the scale cuts in terms of precision and accuracy, in some cases producing significantly stronger bounds on cosmological parameters. These results are independent of the maximum scale $k_\mathrm{max}$ in the analysis with theoretical error. The scenarios where linear bias supplemented by theoretical error is unable to recover unbiased cosmology are connected to inadequate modeling of the $gg$-$g\kappa$ covariance of theoretical error. In view of its removing the ambiguity in the choice of $k_\mathrm{max}$, as well as the possibility of attaining higher precision than the usual scale cuts, we consider this method to be promising for analyses of LSS in upcoming photometric galaxy surveys.