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We study the induced primordial gravitational waves (GW) coming from theeffect of scalar perturbation on the tensor perturbation at the second order ofcosmological perturbation theory. We use the evolution of the standard modeldegrees of freedom with respect to temperature in the early Universe to computethe induced gravitational waves bakcground. Our result shows that the spectrumof the induced GW is affected differently by the standard model degrees offreedom than the GW coming from first order tensor perturbation. Thisphenomenon is due to the presence of scalar perturbations as a source fortensor perturbations and it is effective around the quark gluon deconfinementand electroweak transition. In case of considering a scalar spectral indexlarger than one at small scales or a non-Gaussian curvature power spectrum thiseffect can be observed by gravitational wave observatories.

Thermal History of the Early Universe and Primordial Gravitational Waves from Induced Scalar Perturbations