Phase Spaces for asymptotically de Sitter Cosmologies

Details Phase Spaces for asymptotically de Sitter Cosmologies Phase Spaces for asymptotically de Sitter Cosmologies

2012-02-23

arxiv.org/abs/1202.5347v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

We construct two types of phase spaces for asymptotically de Sitter Einstein-Hilbert gravity in each spacetime dimension $d \ge 3$. One type contains solutions asymptotic to the expanding spatially-flat ($k=0$) cosmological patch of de Sitter space while the other is asymptotic to the expanding hyperbolic $(k=-1)$ patch. Each phase space has a non-trivial asymptotic symmetry group (ASG) which includes the isometry group of the corresponding de Sitter patch. For $d=3$ and $k=-1$ our ASG also contains additional generators and leads to a Virasoro algebra with vanishing central charge. Furthermore, we identify an interesting algebra (even larger than the ASG) containing two Virasoro algebras related by a reality condition and having imaginary central charges $\pm i \frac{3\ell}{2G}$. On the appropriate phase spaces, our charges agree with those obtained previously using dS/CFT methods. Thus we provide a sense in which (some of) the dS/CFT charges act on a well-defined phase space. Along the way we show that, despite the lack of local degrees of freedom, the $d=3, k=-1$ phase space is non-trivial even in pure $\Lambda > 0$ Einstein-Hilbert gravity due to the existence of a family of `wormhole' solutions labeled by their angular momentum, a mass-like parameter $\theta_0$, the topology of future infinity ($I^+$), and perhaps additional internal moduli.

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