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Space-like Dp branes: accelerating cosmologies versus conformally de Sitter space-time

We consider the space-like D$p$ brane solutions of type II string theories having isometries ISO$(p+1)$ $\times$ SO$(8-p,1)$. These are asymptotically flat solutions or in other words, the metrics become flat at the time scale $τ\gg τ_0$. On the other hand, when $τ\sim τ_0$, we get $(p+1)+1$ dimensional flat FLRWmetrics upon compactification on a $(8-p)$ dimensional hyperbolic space with time dependent radii. We show that the resultant $(p+1)+1$ dimensional metrics describe transient accelerating cosmologies for all $p$ from 1 to 6, i.e., from $(2+1)$ to $(7+1)$ space-time dimensions. We show how the acceleration changes with the interplay of the various parameters characterizing the solutions in $(3+1)$ dimensions. Finally, for $τ\ll τ_0$, after compactification on $(8-p)$ dimensional hyperbolic space, the resultant metrics are shown to take the form of $(p+1)+1$ dimensional de Sitter spaces upto a conformal transformation. Cosmologies here are decelerating, but, only in a particular conformal frame we get eternal acceleration.