Spacetime structure and asymmetric metric from the premetric formulation of electromagnetism

•We explore empirically the spacetime structure based on premetric electrodynamics.•In the skewonless case, the spacetime structure is constrained to metric plus axion.•Type II skewon is constrained in the second order to ∼10−19∼10−19 by nonbirefringence.•Asymmetric metric induced constitutive tensor compensates it and is nonbirefringent.•Cosmic polarization rotation constrains 1 degree of freedom of antisymmetric metric.

We address the issue of spacetime structure determined empirically from the premetric formulation of electromagnetism and explore the role of skewons in the construction of spacetime metric. Type II skewon part is not constrained in the first order. In the second order it induces birefringence and is constrained to ∼10−19∼10−19. However, an additional nonmetric induced second-order contribution to the core-metric principal part makes it nonbirefringent. This second-order contribution is just the extra piece to the core-metric principal constitutive tensor induced by the antisymmetric part of the asymmetric metric which is nonbirefringent. The antisymmetric metric induced constitutive tensor has a pseudoscalar part. The variation of this part is constrained by observation on cosmic polarization rotation to <0.03, and gives one constraint on the 6-degree-of-freedom antisymmetric metric.