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The ‘v’ is zero when t=0 and

Thestring tension density, string energy, scalar expansion and shear scalar becomeinfinite for T= 0 which indicates that the universe starts at T= 0.

So theypossess initial singularity. However, as T increases these singularities vanishbut the model (30) has no singularities. At initial momentum (T= 0), quarkpressure and density are infinite, further both decreases as T increases. Thespecial volume ‘ V’ is zero when T= 0 and becomes infinite when T®¥. The expansion scalar q andshear scalar s2tends to infinity as T  = 0.

Where aswhen T? ¥, expansion scalar q andshear scalar s2tends 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 expansionand shear scalar become infinite for T= 0 which indicates that the universestarts at T= 0. So they possess initial singularity. However, as T increasesthese singularities vanish but the model (40) has no singularities. At initialmomentum (T= 0), quark pressure and density are infinite, further both decreasesas T increases. The special volume ‘ V’ is zero when T= 0 and becomes infinitewhen T®¥. The expansion scalar q and shear scalar s2tends to infinity as T  = 0.

Whereas whenT®¥, expansion scalar q and shear scalar s2tends 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:     Inthis paper, I have exhibited some exact cosmological solutions of Einsteinfield equations which have expansion, rotation and shear besides rotation. Theratio   for our model considerably greater than itspresent value (10-3) obtained from indirect arguments concerning theisotropy of the primordial black body radiation. This fact indicates that theearly stages of evolution of the universe which is analogous to result obtainedby Yilmaz 40. It is interesting to note that as T gradually increases, thescalar expansion ? and shear scalar ? 2 decreases and finally vanishwhen T??.

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

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