v 1 1 1 Ju n 19 99 Tolman - Bondi model , fractal density and Hubble law . 1 . Initial conditions

Properties of Tolman-Bondi (TB) model produced by two set of initial conditions, 1) fractal density and simultaneous bang time and 2) fractal density and linear Hubble law, are studied. It is shown for the first set that for some physical resonable values of parameters of the model, the central density and the cosmological density parameter Ω0, an area of compatibility of initial conditions has the form ξ > ξTB , where ξ is radial Euler coordinate and ξTB is the low limit of the area, where particle has zero velocity. For the second set of initial conditions it is shown that the area of compartibility is trivial, ξ ≥ 0 only for non-simultaneous bang time. A case of an arbitrary bang time is also studied. It is shown that in the frame of the exact nonliner relativistic TB models it is possible to have a linear velocity distance relation of the expanding space when matter distribution is fractal. This requires a non-unique bang time. The bang time τ(ξ) is calculated for the linear Hubble law and fractal matter distribution with fractal dimension D = 2.