On spherically symmetric singularity-free models in relativistic cosmology

The introduction of time dependence through a scale factor in a non-conform ally flat static cosmological model whose spacetime can be embedded in a fi ve demensional flat spacetime is shown to give rise to two spherical models of universe filled with perfect fluid acompannied with radial heat flux wi thout any Big Bang type singularity. The first model describes an ever exis ting universe which witnesses a transition from state of contraction to tha t of ever expansion. The second model represents a universe oscillating bet ween two regular states.