Second-order perturbation theory: a covariant approach involving a barotropic equation of state

We present a covariant and gauge-invariant formalism suited to the study of second-order effects associated with higher order tensor perturbations. The analytical method we have developed enables us to characterize pure second-order tensor perturbations about the FLRW model having different kinds of equations of state. Our analysis of the radiation case suggests that it may be feasible to examine the CMB polarization arising from higher order perturbations. (paper)