William R. Kelly, Donald Marolf
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.
View original:
http://arxiv.org/abs/1202.5347
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