  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
