Unbiased Cosmology Inference from Biased Tracers using the EFT Likelihood

We present updates on the cosmology inference using the effective field theory (EFT) likelihood presented previously in Schmidt et al., 2018, Elsner et al., 2019 [1,2]. Specifically, we add a cutoff to the initial conditions that serve as starting point for the matter forward model. We show that this cutoff, which was not employed in any previous related work, is important to regularize loop integrals that otherwise involve small-scale, non-perturbative modes. We then present results on the inferred value of the linear power spectrum normalization $\sigma_{8}$ from rest-frame halo catalogs using both second- and third-order bias expansions, imposing uniform priors on all bias parameters. Due to the perfect bias-$\sigma_{8}$ degeneracy at linear order, constraints on $\sigma_{8}$ rely entirely on nonlinear information. The results show the expected convergence behavior when lowering the cutoff in wavenumber, $\Lambda$. When including modes up to $k \leq \Lambda = 0.1\,h\,{\rm Mpc}^{-1}$ in the second-order case, $\sigma_{8}$ is recovered to within $\lesssim 6\,\%$ for a range of halo masses and redshifts. The systematic bias shrinks to $4\,\%$ or less for the third-order bias expansion on the same range of scales. Together with additional evidence we provide, this shows that the residual mismatch in $\sigma_{8}$ can be attributed to higher-order bias contributions. We conclude that the EFT likelihood is able to infer unbiased cosmological constraints, within expected theoretical systematic errors, from physical biased tracers on quasilinear scales