SOLUTIONS OF GAUGE-INVARIANT COSMOLOGICAL PERTURBATIONS IN THE LONG-WAVELENGTH LIMIT

We investigate gauge-invariant cosmological perturbations in a spatial ly Bat Friedmann-Robertson-Walker universe with scalar fields. It is w ell known that the evolution equation for the gauge-invariant quantiti es has exact solutions in the long-wavelength limit. We find that thes e gauge-invariant solutions can be obtained by differentiating the bac kground solution with respect to parameters contained in the backgroun d system. This method is very useful when we analyse the long-waveleng th behaviour of cosmological perturbations with multiple scalar fields .