  In standard inflationary cosmology, scalar and tensor perturbations grew as
the Universe expanded and froze when their wavelengths exceeded the Hubble
horizon, producing a tell-tale signature in the fluctuation spectrum and
amplitude of the cosmic microwave background (CMB). But there are now very good
reasons to examine whether structure formation could also have begun via the
seeding of quantum fluctuations in a non-inflationary field. In this Letter, we
study and compare the scalar and tensor modes produced in these two scenarios,
and demonstrate that upcoming observations to measure the B-mode polarization
of the CMB may be able to differentiate between them. Whereas both scalar and
tensor modes should be observable if the field was inflationary, only scalar
modes would be present in the CMB if it were not. Should gravity be purely
classical, however, the tensor modes would have avoided canonical quantization
in all cases, resulting in unmeasurably weak gravitational waves. A
non-detection of B-mode polarization would thus not completely rule out
inflation.
