Test of Comoving Coordinate Frame by Low Magnitude-Redshift Relation

Abstract

Observational evidence from variety of sources points at an accelerating universewhich is approximately spatially flat and with $(Ω_M,Ω_Λ)_0\approx(0.3,0.7)$. We have shown that for low redshifts, $z\leq 0.2$, the metric of this cosmological model is equivalant to the de Sitter metric within one percent error. Among various coordinate descriptions for the flat de Sitter model two are most widely used, one yields a non-static and FRW type, while the other gives a static and Schwarzschild type metric. We have obtained the magnitude-redshift relation in the second coordinate frame. Our result indicates a slope of 2.5 for small z. This is in disagreement with observation which is close to the slope of 5. this test discards the second and confirms the first coordinate frame as a comoving reference frame for matter in de Sitter space. We anticipate this test disqualifies any other solution of the field equations which asymptotically approaches to the static de Sitter metric, e.g. the Schwarzschild-de Sitter metric for space around a point mass m.