Fully nonlinear and exact perturbations of the Friedmann world model
  In 1988 Bardeen has suggested a pragmatic formulation of cosmological
perturbation theory which is powerful in practice to employ various fundamental
gauge conditions easily depending on the character of the problem. The
perturbation equations are presented without fixing the temporal gauge
condition and are arranged so that one can easily impose fundamental gauge
conditions by simply setting one of the perturbation variables in the equations
equal to zero. In this way one can use the gauge degrees of freedom as an
advantage in handling problems. Except for the synchronous gauge condition, all
the other fundamental gauge conditions completely fix the gauge mode, and
consequently, each variable in such a gauge has a unique gauge invariant
counterpart, so that we can identify the variable as the gauge-invariant one.
Here, we extend Bardeen's linear formulation to fully nonlinear order in
perturbations, with the gauge advantage kept intact. Derived equations are
exact, and from these we can easily expand to higher order perturbations in a
gauge-ready form. We consider scalar- and vector-type perturbations of an ideal
fluid in a flat background; we also present the multiple components of ideal
fluid case. As applications we present fully nonlinear density and velocity
perturbation equations in Einstein's gravity in the zero-pressure medium,
vorticity generation from pure scalar-type perturbation, and fluid formulation
of a minimally coupled scalar field, all in the comoving gauge. We also present
the equation of gravitational waves generated from pure scalar- and vector-type
perturbations.
