Bound on induced gravitational waves during inflation era

We put the upper bound on gravitational waves (GWs) induced by scalar-field fluctuations during inflation. In particular, we focus case where scalar get amplified within some subhorizon scales mechanism Since energy conservation law leads to density of fluctuations, amplitudes are constrained and therefore GWs also. Taking into account this, derive GWs. As a result, find that GW power spectrum must be $\mathcal P_h \lesssim \mathcal O(\epsilon^2 (k/k_*)^2)$ up logarithmic factor, $\epsilon$ is slow-roll parameter $k_*$ peak scale fluctuations.