Bias Loop Corrections to the Galaxy Bispectrum
  Combination of the power spectrum and bispectrum is a powerful way of
breaking degeneracies between galaxy bias and cosmological parameters, enabling
us to maximize the constraining power from galaxy surveys. Recent cosmological
constraints treat the power spectrum and bispectrum on an uneven footing: they
include one-loop bias corrections for the power spectrum but not the
bispectrum. To bridge this gap, we develop the galaxy bias description up to
fourth order in perturbation theory, conveniently expressed through a basis of
Galilean invariants that clearly split contributions that are local and
nonlocal in the second derivatives of the linear gravitational potential. In
addition, we consider relevant contributions from short-range nonlocality
(higher-derivative terms), stress-tensor corrections and stochasticity. To
sidestep the usual renormalization of bias parameters that complicates
predictions beyond leading order, we recast the bias expansion in terms of
multipoint propagators, which take a simple form in our split-basis with loop
corrections depending only on bias parameters corresponding to nonlocal
operators. We show how to take advantage of Galilean invariance to compute the
time evolution of bias and present results for the fourth-order parameters for
the first time. We also discuss the possibilities of reducing the bias
parameter space by using the evolution of bias and exploiting degeneracies
between various bias contributions in the large-scale limit. Our baseline model
allows to verify these simplifications for any application to large-scale
structure data sets.
