  We consider linear perturbation equations for long-wavelength scalar metric
perturbations in generalised gravity, applicable to non-singular cosmological
models including a bounce from collapse to expansion in the very early
universe. We present the general form for the perturbation equations which
follows from requiring that the inhomogeneous universe on large scales obeys
the same local equations as the homogeneous Friedmann-Robertson-Walker
background cosmology (the separate universes approach). In a
pseudo-longitudinal gauge this becomes a homogeneous second-order differential
equation for adiabatic perturbations, which reduces to the usual equation for
the longitudinal gauge metric perturbation in general relativity with vanishing
anisotropic stress. As an application we show that the scale-invariant spectrum
of perturbations in the longitudinal gauge generated during an ekpyrotic
collapse are not transferred to the growing mode of adiabatic density
perturbations in the expanding phase in a simple bounce model.
