  The Hubble constant proves to be the pseudo-Finsleroid--Landsberg factor. The
covariantly conserved pseudo-Finsleroid--gravitational tensor is explicitly
found after evaluating the respective Finsleroid--case curvature tensor and
required contractions in attentive way. The equations arisen involve one
parameter g of extension which measures the Finslerian deviation of the
curvature of the indicatrix of unit vectors. The vector field b^i(x) of the
axes of the pseudo--Finsleroids is naturally identified to the field of average
velocity vectors of matter of the universe. The consistent (and unique)
continuation of the Robertson--Walker metric, and hence the Friedmann metrics,
in the Finslerian domain with respect to the parameter g is arisen. The
cosmological pressure and energy density prove to be linear functions of g^2,
so that the presence of the negative pressure seems to be not necessary to get
the agreement with the observed negative nature of deceleration parameter. We
clarify the explicit structure of all the involved tensorial objects.
