Recent observations suggest that the cosmological equation-of-state parameter w is close to −1. To say this is to imply that w could be slightly less than −1, which leads to R.Caldwell's "Phantom cosmologies". These often have the property that they end in a "Big Smash", a final singularity in which the Universe is destroyed in a finite proper time by excessive expansion. We show that, classically, this fate is not inevitable: there exist Smash-free Phantom cosmologies, obtained by a suitable perturbation of the deSitter equation of state, in which the spacetime is in fact asymptotically deSitter. [ Contrary to popular belief, such cosmologies, which violate the Dominant Energy Condition, do not necessarily violate causality.] We also argue, however, that the physical interpretation of these classically acceptable spacetimes is radically altered by "holography", as manifested in the dS/CFT correspondence. It is shown that, if the boundary CFTs have conventional properties, then recent ideas on "time as an inverse renormalization group flow" can be used to rule out these cosmologies. Very recently, however, it has been argued that the CFTs in dS/CFT are of a radically unconventional form, and this opens up the possibility that Smash-free Phantom spacetimes offer a simple model of a "bouncing" cosmology in which the quantum-mechanical entanglement of the field theories in the infinite past and future plays an essential role.

One of the main virtues of string gas cosmology is that it resolves cosmological singularities. Since the Universe can be approximated by a locally asymptotically de Sitter spacetime by the end of the inflationary era, a singularity theorem implies that these cosmologies effectively violate the Null Energy Condition [not just the Strong Energy Condition]. We stress that this is an extremely robust result, which does not depend on assuming that the spatial sections remain precisely flat in the early Universe. This means, however, that it must be possible for string cosmologies to cross the recently much-discussed phantom divide [from w < −1 to w > −1, where w is the equation-ofstate parameter]. This naturally raises the question as to whether the phantom divide can be crossed again, to account for recent observations suggesting that w < −1 at the present time. We argue that non-perturbative string effects rule out this possibility, even if the NEC violation in question is only "effective".

When de Sitter first introduced his celebrated spacetime, he claimed, following Schwarzschild, that its spatial sections have the topology of the real projective space IRP 3 (that is, the topology of the group manifold SO(3)) rather than, as is almost universally assumed today, that of the sphere S 3 . (In modern language, Schwarzschild was disturbed by the non-local correlations enforced by S 3 geometry.) Thus, what we today call "de Sitter space" would not have been accepted as such by de Sitter. There is no real basis within classical cosmology for preferring S 3 to IRP 3 , but the general feeling appears to be that the distinction is in any case of little importance. We wish to argue that, in the light of current concerns about the nature of de Sitter space, this is a mistake. In particular, we argue that the difference between "dS(S 3 )" and "dS(IRP 3 )" may be very important in attacking the problem of understanding horizon entropies. In the approach to de Sitter entropy via Schwarzschild-de Sitter spacetime, we find that the apparently trivial difference between IRP 3 and S 3 actually leads to very different perspectives on this major question of quantum cosmology.

Inflation allows the problem of the Arrow of time to be understood as a question about the structure of spacetime: why was the intrinsic curvature of the earliest spatial sections so much better behaved than it might have been? This is really just the complement of a more familiar problem: what mechanism prevents the extrinsic curvature of the earliest spatial sections from diverging, as classical General Relativity suggests? We argue that the stringy version of "creation from nothing", sketched by Ooguri, Vafa, and Verlinde, solves both of these problems at once. The argument, while very simple, hinges on some of the deepest theorems in global differential geometry. These results imply that when a spatially toral spacetime is created from nothing, the earliest spatial sections are forced to be [quasi-classically] exactly locally isotropic. This local isotropy, in turn, forces the inflaton into its minimal-entropy state. The theory explains why the Arrow does not reverse in black holes or in a cosmic contraction, if any.

AdS black holes with planar event horizon topology play a central role in AdS/CFT holography, and particularly in its applications. Generalizations of the known planar black holes can be found by considering the Plebański-Demiański metrics, a very general family of exactly specified solutions of the Einstein equations. These generalized planar black holes may be useful in applications. We give a concrete example of this in the context of the holographic description of the Quark-Gluon Plasma (QGP). We argue that our generalized planar black holes allow us to construct a model of the internal shearing motion generated when the QGP is produced in peripheral heavy-ion collisions. When embedded in string theory, the bulk physics is in fact unstable. We find however that this instability may develop too slowly to affect the evolution of the plasma, except possibly for high values of the quark chemical potential, such as will be studied in experimental scans of the quark matter phase diagram.