Eur. Phys. J. C (2013) 73: 2459
https://doi.org/10.1140/epjc/s10052-013-2459-x

Regular Article - Theoretical Physics

Cosmological model with local symmetry of very special relativity and constraints on it from supernovae

¹ Institute of High Energy Physics, Chinese Academy of Sciences, 100049, Beijing, China
² Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, 100049, Beijing, China

^* e-mail: wangsai@ihep.ac.cn

Received: 26 February 2013
Revised: 21 May 2013
Published online: 4 June 2013

Abstract

Based on Cohen & Glashow’s very special relativity (Cohen and Glashow in Phys. Rev. Lett. 97:021601, 2006), we propose an anisotropic modification to the Friedmann–Robertson–Walker (FRW) line element. An arbitrarily oriented 1-form is introduced and the FRW spacetime becomes of the Randers–Finsler type. The 1-form picks out a privileged axis in the universe. Thus, the cosmological redshift as well as the Hubble diagram of the type Ia supernovae (SNe Ia) becomes anisotropic. By directly analyzing the Union2 compilation, we obtain the privileged axis pointing to (l,b)=(304^∘±43^∘,−27^∘±13^∘) (68 % C.L.). This privileged axis is close to those obtained by comparing the best-fit Hubble diagrams in pairs of hemispheres. It should be noticed that the result is consistent with isotropy at the 1σ level since the anisotropic magnitude is D=0.03±0.03.