Missing one-loop contributions in secondary gravitational waves

Understand

We find several missing one-loop-order contributions in previous considerations about secondary gravitational waves induced at nonlinear order in cosmological perturbations.

• We consider a consistent perturbative expansion to third-order in cosmological perturbations, including higher-order interactions and iterative solutions ignored in the previous literature.
• Tensor fluctuations induced by the source with two scalar and one tensor perturbations are correlated with the first-order tensor fluctuation and thus give a one-loop-order correction to the tensor power spectrum.
• The missing loop correction is \textit{scale-invariant} and \textit{negative} in the superhorion region, which secondarily reduces the initial primordial tensor power spectrum prior to the horizon re-entry.