Fine-tuning criteria for inflation and the search for primordial gravitational waves

We revisit arguments that simple models of inflation with a small red tilt in the scalar power spectrum generically yield an observable tensor spectrum. We show that criteria for fine-tuning based upon the algebraic simplicity of the potential depend strongly upon the explicit assumptions they incorporate, particularly regarding the end of inflation. In addition, some models with algebraically simple potentials require carefully tuned initial field configurations, and not all types of fine-tuning are identifiable via the algebraic simplicity of the potential. Conversely, in the absence of a strong prior on the mechanism that ends inflation, we demonstrate the existence of potentials with vanishingly small tensor amplitudes which are natural in terms of both their algebraic form and initial conditions. We thus argue that proposed experiments (CMBPol or BBO) which make highly sensitive measurements of the tensor amplitude cannot definitively rule out the inflationary paradigm.