The ‘V’ is zero when T=0 and

The
string tension density, string energy, scalar expansion and shear scalar become
infinite for T=0 which indicates that the universe starts at T=0. So they
possess initial singularity. However, as T increases these singularities vanish
but the model (30) has no singularities. At initial momentum (T=0), quark
pressure and density are infinite, further both decreases as T increases. The
special volume ‘V’ is zero when T=0 and becomes infinite when T®¥.
The expansion scalar q and
shear scalar s2
tends to infinity as T  = 0. Where as
when T? ¥,
expansion scalar q and
shear scalar s2
tends to zero. Since  , the model does not approach isotropy for large value of T.
The model is expanding, shearing, no-rotating and has no initial singularities.

                           

          The string tension density, string energy, scalar expansion
and shear scalar become infinite for T=0 which indicates that the universe
starts at T=0. So they possess initial singularity. However, as T increases
these singularities vanish but the model (40) has no singularities. At initial
momentum (T=0), quark pressure and density are infinite, further both decreases
as T increases. The special volume ‘V’ is zero when T=0 and becomes infinite
when T®¥. The expansion scalar q and shear scalar s2
tends to infinity as T  = 0. Whereas when
T®¥, expansion scalar q and shear scalar s2
tends to zero. Since  , the model does not approach isotropy for large value of T.
The model is expanding, shearing, no-rotating and has no initial singularities.

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4.   Conclusing  
Remarks:

 

    In
this paper, I have exhibited some exact cosmological solutions of Einstein
field equations which have expansion, rotation and shear besides rotation. The
ratio   for our model considerably greater than its
present value (10-3) obtained from indirect arguments concerning the
isotropy of the primordial black body radiation. This fact indicates that the
early stages of evolution of the universe which is analogous to result obtained
by Yilmaz 40. It is interesting to note that as T gradually increases, the
scalar expansion ? and shear scalar ?2 decreases and finally vanish
when T??.

 My result may have some observational
consequences, in principle at least, for the astrophysical effects of cosmic evolution,
yielding possible relic evidences on the importance of extra dimensions at the
early universe. However, it may be too premature to come to any definite
conclusions in this regard. Hence I am brief on this point.

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