  Analyzing the clustering of galaxies at the field level in principle promises
access to all the cosmological information available. Given this incentive, in
this paper we investigate the performance of field-based forward modeling
approach to galaxy clustering using the effective field theory (EFT) framework
of large-scale structure (LSS). We do so by applying this formalism to a set of
consistency and convergence tests on synthetic datasets. We explore the
high-dimensional joint posterior of LSS initial conditions by combining
Hamiltonian Monte Carlo sampling for the field of initial conditions, and slice
sampling for cosmology and model parameters. We adopt the Lagrangian
perturbation theory forward model from [1], up to second order, for the forward
model of biased tracers. We specifically include model mis-specifications in
our synthetic datasets within the EFT framework. We achieve this by generating
synthetic data at a higher cutoff scale $\Lambda_0$, which controls which
Fourier modes enter the EFT likelihood evaluation, than the cutoff $\Lambda$
used in the inference. In the presence of model mis-specifications, we find
that the EFT framework still allows for robust, unbiased joint inference of a)
cosmological parameters - specifically, the scaling amplitude of the initial
conditions - b) the initial conditions themselves, and c) the bias and noise
parameters. In addition, we show that in the purely linear case, where the
posterior is analytically tractable, our samplers fully explore the posterior
surface. We also demonstrate convergence in the cases of nonlinear forward
models. Our findings serve as a confirmation of the EFT field-based forward
model framework developed in [2-7], and as another step towards field-level
cosmological analyses of real galaxy surveys.
