  It is sometimes argued that observation of tensor modes from inflation would
provide the first evidence for quantum gravity. However, in the usual
inflationary formalism, also the scalar modes involve quantised metric
perturbations. We consider the issue in a semiclassical setup in which only
matter is quantised, and spacetime is classical. We assume that the state
collapses on a spacelike hypersurface, and find that the spectrum of scalar
perturbations depends on the hypersurface. For reasonable choices, we can
recover the usual inflationary predictions for scalar perturbations in
minimally coupled single-field models. In models where non-minimal coupling to
gravity is important and the field value is sub-Planckian, we do not get a
nearly scale-invariant spectrum of scalar perturbations. As gravitational waves
are only produced at second order, the tensor-to-scalar ratio is negligible. We
conclude that detection of inflationary gravitational waves would indeed be
needed to have observational evidence of quantisation of gravity.
