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

TL;DR

This paper introduces an anisotropic cosmological model based on very special relativity, modifies the FRW metric, and analyzes supernova data to identify a preferred cosmic axis, finding results consistent with isotropy within uncertainties.

Contribution

It proposes a Randers-Finsler type anisotropic cosmological model inspired by very special relativity and constrains it using supernova data to identify a privileged axis.

Findings

Identified a privileged axis close to previous anisotropy claims.

Found the anisotropic magnitude to be consistent with zero within 1 sigma.

Constrained the anisotropy parameter D to 0.03 ± 0.03.

Abstract

Based on Cohen \& Glashow's very special relativity [A. G. Cohen and S. L. Glashow, Phys. Rev. Lett. {\bf 97} (2006) 021601], 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 \((l,b)=({304^\circ}\pm{43^\circ},{-27^\circ}\pm{13^\circ})\) (\(68\%~\rm{C.L.}\)). 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 \(1\sigma\) level since the anisotropic magnitude is \(D=0.03\pm 0.03\).