Gravitational waves from primordial scalar and tensor perturbations

We investigate the second order gravitational waves induced by the primordial scalar and tensor perturbations during radiation-dominated era. The explicit expressions of the power spectra of the second order GWs are presented. We calculate the energy density spectra of the second order GWs for a monochromatic primordial power spectra. For large $k$ $(k>k_{\ast })$, the effects of the primordial tensor perturbation with tensor-to-scalar ratio $r=A_h\mathrm{/}{A}_{\zeta }=0.2$ lead to an around $50\mathrm{\%}$ increase of the signal-to-noise ratio (SNR) for LISA observations.