Horizon ratio bound for inflationary fluctuations

We demonstrate that the gravity wave background amplitude implies a robust upper bound on the wavelength-to-horizon ratio at the end of inflation: lambda/H(-1)less than or similar toe(60), as long as the cosmic energy density does not drop faster than radiation subsequent to inflation. This limit implies that N, the number of e-folds between horizon exit and the end of inflation for wave modes of interest, is less than or similar to60 plus a model-dependent factor-for vast classes of slow-roll models, Nless than or similar to67. As an example, this bound solidifies the tension between observations of the cosmic microwave background anisotropies and chaotic inflation with a phi(4) potential by closing the escape hatch of large N (<62).