Massive neutrinos in nonlinear large scale structure: A consistent
  perturbation theory
  A consistent formulation to incorporate massive neutrinos in the perturbation
theory of the effective CDM+baryons fluid is introduced. In this formulation
all linear k dependence in the growth functions of CDM+baryons perturbations,
as well as all consequent additional mode coupling at higher orders, are taken
into account to any desirable accuracy. Our formulation regards the neutrino
fraction, which is constant in time after the non-relativistic transition of
neutrinos, and much smaller than unity, as the coupling constant of the theory.
Then the "bare" perturbations are those in the massless neutrino case when the
neutrino fraction vanishes, and we consider the backreaction corrections due to
the gravitational coupling of neutrinos. We derive the general equations for
the "bare" perturbations, and backrecation corrections. Then, by employing
exact time evolution with the proper analytic Green's function we explicitly
derive the leading backreaction effect, and find precise agreement at the
linear level. We proceed to compute the second order beackreaction correction,
and derive the leading order matter bispectrum in the presence of massive
neutrinos, suggesting the squeezed limit of the matter bispectrum as a
sensitive probe of neutrino mass. Notably, the generic neutrino fraction
formulation in this work may be similarly applied for the consistent inclusion
of massive neutrinos within any perturbative approach.
