  We develop a field-theoretic description of large-scale structure formation
by taking the non-relativistic limit of a canonically transformed, real scalar
field which is minimally coupled to scalar gravitational perturbations in
longitudinal gauge. We integrate out the gravitational constraint fields and
arrive at a non-local action which is only specified in terms of the dynamical
degrees of freedom. In order to make this framework closer to the classical
particle description, we construct the corresponding 2PI effective action
truncated at two loop order for a non-squeezed state without field expectation
values. We contrast the dynamical description of the coincident time
phase-space density to the standard Vlasov description of cold dark matter
particles and identify momentum and time scales at which linear perturbation
theory will deviate from the standard evolution.
