  This paper is the third in a series of theorems which state how cosmological
observations can provide evidence for an early phase of acceleration in the
universe. Previous theorems demonstrated that the observed power spectrum for
scalar perturbations forces all possible alternative theories of inflation to
theories other than General Relativity. It was shown that generically, without
a phase of accelerated expansion, these alternatives have to break at least one
of the following tenets of classical general relativity: the Null Energy
Condition (NEC), subluminal signal propagation, or sub-Planckian energy
densities. In this paper we prove how detection of primordial gravitational
waves at large scales can provide independent evidence to support a phase of
accelerated expansion. This proof does not rely on the spectral index for
tensor modes but relies on validity of quantum field theory in curved space
time and tensor modes being sourced from adiabatic vacuum fluctuations. Our
approach, like in the case of scalars, is proof by contradiction: we
investigate the possibility of a detectable tensor signal sourced by vacuum
fluctuations in a non-accelerating, sub-Planckian universe using cosmological
perturbation theory and derive contradictory limits on cosmological dynamics.
The contradiction implies that one or more of our axioms for early universe
must have been broken. The bound from tensor perturbations is not only
independent of, but also stronger than the one obtained from scalar power
spectrum.
