Abstract
The primordial perturbations will inevitably generate higher order
perturbations. We study the second order scalar perturbations generated by the
primordial curvature and tensor perturbations in the radiation-dominated era.
After presenting all the possible second-order source terms, we obtain the
explicit expressions of the kernel functions and the power spectra of the
second order scalar perturbations. The contributions from the initial
second-order perturbations are considered. We calculate the power spectra of
second order scalar perturbations for different tensor-to-scalar ratio $r$.
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