  We study the spectrum of cosmological fluctuations in scenarios such as
Galilean Genesis in which a spectator scalar field acquires a scale-invariant
spectrum of perturbations during an early phase which asymptotes in the far
past to Minkowski space-time. In the case of minimal coupling to gravity and
standard scalar field Lagrangian, the induced curvature fluctuations depend
quadratically on the spectator field and are hence non-scale-invariant and
highly non-Gaussian. We show that if higher dimensional operators (the same
operators that lead to the {\eta}-problem for inflation) are considered, a
linear coupling between background and spectator field fluctuations is induced
which leads to scale-invariant and Gaussian curvature fluctuations.
