Gravitational waves from primordial scalar and tensor perturbations

We investigate the second order gravitational waves induced by the primordial scalar and tensor perturbations during a 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 the monochromatic primordial power spectra P-zeta = A(zeta)k(*)delta(k - k(*)) and P-h = A(h)k(*)delta(k - k(*)). For large k (k > k(*)), the primordial tensor perturbation will affect the total power spectrum of second order GWs significantly. For f(*) = 1.3 x 10(-3) and A(zeta) = 0.02, the effects of the primordial tensor perturbation will lead to an around 100% increase of the signal-to-noise ratio (SNR) for LISA observations if the tensor-to-scalar ratio r = A(h)/A(zeta) > 0.4.

Automated summary

We study the second order gravitational waves produced by the primordial scalar and tensor perturbations in a radiation-dominated era. We provide explicit expressions for the power spectra of the second order GWs. The energy density spectra of the second order GWs are calculated for the monochromatic primordial power spectra P-zeta = A(zeta)k(*)delta(k - k(*)) and P-h = A(h)k(*)delta(k - k(*)). The primordial tensor perturbation significantly affects the total power spectrum of second order GWs for large k (k > k(*)). For f(*) = 1.3 x 10(-3) and A(zeta) = 0.02, the effects of the primordial tensor perturbation result in an approximately 100% increase in the signal-to-noise ratio (SNR) for LISA observations if the tensor-to-scalar ratio r = A(h)/A(zeta) > 0.4.