  In this paper we have given a generalisation of the earlier work by Prigogine
et al. who have constructed a phenomenological model of entropy production via
particle creation in the very early universe generated out of the vacuum rather
than from a singularity, by including radiation also as the energy source and
tried to develop an alternative cosmological model in which particle creation
prevents the big bang. We developed Radiation dominated model of the universe
which shows a general tendency that (i) it originates from instability of
vacuum rather than from a singularity. (ii) Up to a characteristic time
cosmological quantities like density, pressure, Hubble constant and expansion
parameter vary rapidly with time. (iii) After the characteristic time these
quantities settles down and the models are turned into de-sitter type model
with uniform matter, radiation, creation densities and Hubble's constant H. The
de-sitter regime survives during a decay time then connects continuously to a
usual adiabatic matter radiation RW universe.The interesting thing in the paper
is that we have related the phenomenological radiation dominated model to
macroscopic model of quantum particle creation in the early universe giving
rise to the present observed value of cosmic background radiation . It is also
found that the dust filled model tallies exactly with that of the Prigogine's
one, which justifies that our model is generalized Prigogine's model. Although
the model originates from instability of vacuum rather than from a singularity,
still there is a couple of unavoidable singularities in the model.
