Gravitational wave constraints on the observable inflation

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 observable Universe could have expanded during cosmic inflation. The new bound is roughly four orders of magnitude more stringent than previous bounds. 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.