 0  0.5  1  1.5  2  0  0.5  1  1.5  2 H(t) t IS fluid non-viscous fluid particular  0  1  2  3  0  0.5  1  1.5  2 a(t) t IS fluid non-viscous fluid particular Fig. 1: Left panel: H ( t ) vs. t for viscous (solid line) and non-viscous fluid (dashed line). Contrary to non-viscous fluid, H ( t ) is our solution shows no singularity. The straight line gives the results from the particular solution, Eq. (29). Double dotted curve represent the particular solution, Eq. (39). Right panel: a ( t ) vs. t . The approximate solution gives finite a ( t ) at t = 0. (solid line). Dotted straight line represents the results from Eq. (30). The particular solution is given by the double dotted line, Eq. (40). Fig. 2: Energy density ρ ( t ) as a function of t (left panel). The dependence of T on t is given in the right panel. The curves are as in Fig. 1. In both case, viscous fluid gives no singularity at vanishing t . Straight curve are from Eq. (31) and (32), respectively. difference between the two cases is obvious at small t . We notice a divergence, or singularity, associated with the ideal non-viscous fluid, Eq. (45). The viscous fluid results in finite H even at vanishing t , as can be seen from Eq. (22). The scale factor a ( t ) also shows differences in both cases. a ( t ) in a Universe with an ideal and non-viscous background matter depends on t according to Eq. (46), which simply implies that a ( t ) is directly proportional to t , and a ( t ) vanishes at t = 0, which shows the existence of a singularity of H . Assuming that the background matter is described by a 11  0  2  4  6  0  0.25  0.5  0.75  1 (t) t IS fluid non-viscous fluid particular  0  0.5  1  1.5  0  0.5  1  1.5  2 T(t) t IS fluid non-viscous fluid particular