Cosmic Microwave Background Polarization as a Tool to Constrain the Optical Properties of the Universe

We present a novel formalism to describe the $in$ $vacuo$ conversion between polarization states of propagating radiation, also known as generalized Faraday effect (GFE), in cosmological context. Thinking GFE potential tracer new, isotropy- and/or parity-violating physics, we apply our cosmic microwave background (CMB) polarized anisotropy power spectra, providing simple framework easily compute their observed modifications. In so doing, re-interpret previously results, namely rotation linear plane CMB photons (or birefringence) but point out that could lead partial into circular polarization. notice can be seen an light anisotropic chiral medium (a "dark crystal") and recast its parameters components effective "cosmic susceptibility tensor". For wave number-independent tensor, this allows us set observational bound on GFE-induced circularly spectrum, or $VV$, at $C_{\ell}^{VV} < 2 \times 10^{-5} \mu K^2$ (95 \% C.L.), peak $\ell\simeq 370$, which is some 3 orders magnitude better than presently available direct $VV$ measurements. argue that, unless dramatic technological improvements will arise $V$-modes measurements, variance-limited surveys expected within decade should provide, byproduct, superior bounds CMB.