Skewon field and cosmic wave propagation

•We study the propagation of the Hehl–Obukhov–Rubilar skewon field.•We classify it into Type I and Type II skewons.•No dissipation/no amplification condition implies the skewon field must be Type II.•We constrain the Type I cosmic skewon field to less than a few ×10−35×10−35 from CMB.•Constitutive tensor constructed from asymmetric metric is of Type II and allowed.

We study the propagation of the Hehl–Obukhov–Rubilar skewon field in weak gravity field/dilute matter or with weak violation of the Einstein Equivalence Principle (EEP), and further classify it into Type I and Type II skewons. From the dispersion relation we show that no dissipation/no amplification condition implies that the additional skewon field must be of Type II. For Type I skewon field, the dissipation/amplification is proportional to the frequency and the CMB spectrum would deviate from Planck spectrum. From the high precision agreement of the CMB spectrum with 2.755 K Planck spectrum, we constrain the Type I cosmic skewon field |χijkl(SkI)| to ⩽ a few ×10−35×10−35. The skewon part of constitutive tensor constructed from asymmetric metric is of Type II, hence it is allowed. This study may also be applied to macroscopic electrodynamics in the case of laser pumped medium or dissipative medium.