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We investigate a matter dominated navigation cosmological model. Theinfluence of a possible drift (wind) in the navigation cosmological model makesthe spacetime geometry change from Riemannian to Finslerian. The evolution ofthe Finslerian Universe is governed by the same gravitational field equationwith the familiar Friedmann-Robertson-Walker one. However, the change of spacegeometry from Riemannian to Finslerian supplies us a new relation between theluminosity distant and redshift. It is shown that the Hubble diagram based onthis new relation could account for the observations on distant Type Iasupernovae.

A Matter Dominated Navigation Universe in Accordance with the Type Ia Supernova Data