Spherically symmetric anisotropic and inhomogeneous cosmological models

Spherically symmetric cosmological models filled with dust (pressure-free fluid) content are analyzed. It has been pointed out that these models are anisotropic (of non-vanishing shear) and inhomogeneous (∂p/ρr ≠ 0), the characteristics related directly to the presence of the free gravitational field. It is demonstrated that when the free gravitational field vanishes these models degenerate to the corresponding Friedmann-Robertson-Walker (FRW) models. It is further shown that the energy density of the free gravitational field can be introduced into observational cosmology as a new parameter since it enters into the expansion and deceleration equations, as well as conservation law for total energy, implying that the present Hubble velocity can be reached in a shorter time from the big bang. Finally, the effect of shear on the redshift is also discussed. This paper is dedicated to my teacher Professor V V Narlikar on the occasion of his 81st birthday.