Exact non-linear equations for cosmological perturbations
  We present a complete set of exact and fully non-linear equations describing
all three types of cosmological perturbations -- scalar, vector and tensor
perturbations. We derive the equations in a thoroughly gauge-ready manner, so
that any spatial and temporal gauge conditions can be employed. The equations
are completely general without any physical restriction except that we assume a
flat homogeneous and isotropic universe as a background. We also comment
briefly on the application of our formulation to the non-expanding Minkowski
background.
