Landau Levels in the noncommutative AdS2AdS_2

We formulate the Landau problem in the context of the noncommutative analog of a surface of constant negative curvature, that is $AdS_2$ surface, and obtain the spectrum and contrast the same with the Landau levels one finds in the case of the commutative $AdS_2$ space.Comment: 19 pages, Latex, references and clarifications added including 2 figure

The dS/CFT Correspondence and the Big Smash

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.Comment: 22 pages, clarification of triple analytic continuation, additional Comments added in the light of hep-th/020724