On the Statistics of Biased Tracers in the Effective Field Theory of
  Large Scale Structures
  With the completion of the Planck mission, in order to continue to gather
cosmological information it has become crucial to understand the Large Scale
Structures (LSS) of the universe to percent accuracy. The Effective Field
Theory of LSS (EFTofLSS) is a novel theoretical framework that aims to develop
an analytic understanding of LSS at long distances, where inhomogeneities are
small. We further develop the description of biased tracers in the EFTofLSS to
account for the effect of baryonic physics and primordial non-Gaussianities,
finding that new bias coefficients are required. Then, restricting to dark
matter with Gaussian initial conditions, we describe the prediction of the
EFTofLSS for the one-loop halo-halo and halo-matter two-point functions, and
for the tree-level halo-halo-halo, matter-halo-halo and matter-matter-halo
three-point functions. Several new bias coefficients are needed in the
EFTofLSS, even though their contribution at a given order can be degenerate and
the same parameters contribute to multiple observables. We develop a method to
reduce the number of biases to an irreducible basis, and find that, at the
order at which we work, seven bias parameters are enough to describe this
extremely rich set of statistics. We then compare with the output of $N$-body
simulations. For the lowest mass bin, we find percent level agreement up to
$k\simeq 0.3\,h\,{\rm Mpc}^{-1}$ for the one-loop two-point functions, and up
to $k\simeq 0.15\,h\,{\rm Mpc}^{-1}$ for the tree-level three-point functions,
with the $k$-reach decreasing with higher mass bins. This is consistent with
the theoretical estimates, and suggests that the cosmological information in
LSS amenable to analytical control is much more than previously believed.
