  We demonstrate that the gravity wave background amplitude implies a robust
upper bound on the ratio: \lambda / H^{-1} < e^60, where \lambda is the proper
wavelength of fluctuations of interest and H^{-1} is the horizon at the end of
inflation. The bound holds as long as the energy density of the universe does
not drop faster than radiation subsequent to inflation. This limit implies that
the amount of expansion between the time the scales of interest leave the
horizon and the end of inflation, denoted by e^N, is also bounded from above,
by about e^60 times a factor that involves an integral over the first slow-roll
parameter. In other words, the bound on N is model dependent -- we show that
for vast classes of slow-roll models, N < 67. The quantities, \lambda / H^{-1}
or N, play an important role in determining the nature of inflationary scalar
and tensor fluctuations. We suggest ways to incorporate the above bounds when
confronting inflation models with observations. As an example, this bound
solidifies the tension between observations of cosmic microwave background
(CMB) anisotropies and chaotic inflation with a \phi^4 potential by closing the
escape hatch of large N (< 62).
