  We study the induced primordial gravitational waves (GW) coming from the
effect of scalar perturbation on the tensor perturbation at the second order of
cosmological perturbation theory. We use the evolution of the standard model
degrees of freedom with respect to temperature in the early Universe to compute
the induced gravitational waves bakcground. Our result shows that the spectrum
of the induced GW is affected differently by the standard model degrees of
freedom than the GW coming from first order tensor perturbation. This
phenomenon is due to the presence of scalar perturbations as a source for
tensor perturbations and it is effective around the quark gluon deconfinement
and electroweak transition. In case of considering a scalar spectral index
larger than one at small scales or a non-Gaussian curvature power spectrum this
effect can be observed by gravitational wave observatories.
