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Scalar induced gravitational waves contribute to the cosmologicalgravitational wave background. They can be related to the primordial densitypower spectrum produced towards the end of inflation and therefore are aconvenient new tool to constrain models of inflation. These waves are sourcedby terms quadratic in perturbations and hence appear at second order incosmological perturbation theory. While the focus of research so far was onpurely scalar source terms we also study the effect of including first ordertensor perturbations as an additional source. This gives rise to two additionalsource terms: a term quadratic in the tensor perturbations and a cross terminvolving mixed scalar and tensor perturbations. We present full analyticalexpressions for the spectral density of these new source terms and discusstheir general behaviour. To illustrate the generation mechanism we study twotoy models containing a peak on small scales. For these models we show that thescalar-tensor contribution becomes non-negligible compared to the scalar-scalarcontribution on smaller scales. We also consider implications for futuregravitational wave surveys.

Induced gravitational waves: the effect of first order tensor perturbations