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Circular polarization of the cosmic microwave background (CMB) can be inducedby Faraday conversion of the primordial linearly polarized radiation as itpropagates through a birefringent medium. Recent work has shown that thedominant source of birefringence from primordial density perturbations is theanisotropic background CMB. Here we extend prior work to allow for theadditional birefringence that may arise from primordial vector and tensorperturbations. We derive the formulas for the power spectrum of the inducedcircular polarization and apply those to the standard cosmology. We find theroot-variance of the induced circular polarization to be $\sqrt{<V^2>}\sim3\times 10^{-14}$ for scalar perturbations and $\sqrt{<V^2>}\sim 7\times10^{-18} (r/0.06)$ for tensor perturbations with a tensor-to-scalar ratio $r$.

Circular polarization of the cosmic microwave background from vector and tensor perturbations