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.

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.