Bias in the Effective Field Theory of Large Scale Structures
  We study how to describe collapsed objects, such as galaxies, in the context
of the Effective Field Theory of Large Scale Structures. The overdensity of
galaxies at a given location and time is determined by the initial tidal
tensor, velocity gradients and spatial derivatives of the regions of dark
matter that, during the evolution of the universe, ended up at that given
location. Similarly to what recently done for dark matter, we show how this
Lagrangian space description can be recovered by upgrading simpler Eulerian
calculations. We describe the Eulerian theory. We show that it is
perturbatively local in space, but non-local in time, and we explain the
observational consequences of this fact. We give an argument for why to a
certain degree of accuracy the theory can be considered as quasi time-local and
explain what the operator structure is in this case. We describe
renormalization of the bias coefficients so that, after this and after
upgrading the Eulerian calculation to a Lagrangian one, the perturbative series
for galaxies correlation functions results in a manifestly convergent expansion
in powers of $k/k_{\rm NL}$ and $k/k_{\rm M}$, where $k$ is the wavenumber of
interest, $k_{\rm NL}$ is the wavenumber associated to the non-linear scale,
and $k_{\rm M}$ is the comoving wavenumber enclosing the mass of a galaxy.
