  Gravitational waves (GW) produced in the early Universe contribute to the
number of relativistic degrees of freedom, $N_{\rm eff}$, during Big Bang
Nucleosynthesis (BBN). By using the constraints on $N_{\rm eff}$, we present a
new bound on how much the Universe could have expanded between horizon exit of
the largest observable scales today and the end of inflation. We discuss the
implications on inflationary models and show how the new constraints affect
model selection. We also discuss the sensitivities of the current and planned
GW observatories such as LIGO and LISA, and show that the constraints they
could impose are always less stringent than the BBN bound.
