Dynamics of cosmological perturbations at first and second order
  In this paper we give five gauge-invariant systems of governing equations for
first and second order scalar perturbations of flat Friedmann-Lema\^{i}tre
universes that are minimal in the sense that they contain no redundant
equations or variables. We normalize the variables so that they are
dimensionless, which leads to systems of equations that are simple and
ready-to-use. We compare the properties and utility of the different systems.
For example, they serve as a starting point for finding explicit solutions for
two benchmark problems in cosmological perturbation theory at second order:
adiabatic perturbations in the super-horizon regime (the long wavelength limit)
and perturbations of $\Lambda$CDM universes. However, our framework has much
wider applicability and serves as a reference for future work in the field.
