Theoretical implications of detecting gravitational waves

Abstract: 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.