Third-order scalar-tensor correlations suppress the induced gravitational wave background, and some of these new contributions diverge in the ultraviolet.
Practical tools for third order cosmological perturbations
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abstract
We discuss cosmological perturbation theory at third order, deriving the gauge transformation rules for metric and matter perturbations, and constructing third order gauge invariant quantities. We present the Einstein tensor components, the evolution equations for a perfect fluid, and the Klein-Gordon equation at third order, including scalar, vector and tensor perturbations. In doing so, we also give all second order tensor components and evolution equations in full, exhilarating generality.
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Suppression of the induced gravitational wave background due to third-order perturbations
Third-order scalar-tensor correlations suppress the induced gravitational wave background, and some of these new contributions diverge in the ultraviolet.