Thermal history of the early Universe and primordial gravitational waves from induced scalar perturbations

We study the induced primordial gravitational waves (GWs) 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 background. Our result shows that the spectrum of the induced GWs is affected differently by the standard model degrees of freedom than the GWs coming from the 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 1 at small scales or a non-Gaussian curvature power spectrum, this effect can be observed by gravitational wave observatories.