5 research outputs found
Can Quantum de Sitter Space Have Finite Entropy?
If one tries to view de Sitter as a true (as opposed to a meta-stable)
vacuum, there is a tension between the finiteness of its entropy and the
infinite-dimensionality of its Hilbert space. We invetsigate the viability of
one proposal to reconcile this tension using -deformation. After defining a
differential geometry on the quantum de Sitter space, we try to constrain the
value of the deformation parameter by imposing the condition that in the
undeformed limit, we want the real form of the (inherently complex) quantum
group to reduce to the usual SO(4,1) of de Sitter. We find that this forces
to be a real number. Since it is known that quantum groups have
finite-dimensional representations only for root of unity, this suggests
that standard -deformations cannot give rise to finite dimensional Hilbert
spaces, ruling out finite entropy for q-deformed de Sitter.Comment: 10 pages, v2: references added, v3: minor corrections, abstract and
title made more in-line with the result, v4: published versio
Aspects of Quantum Gravity in de Sitter Spaces
In these lectures we give a review of recent attempts to understand quantum
gravity on de Sitter spaces. In particular, we discuss the holographic
correspondence between de Sitter gravity and conformal field theories proposed
by Hull and by Strominger, and how this may be reconciled with the
finite-dimensional Hilbert space proposal by Banks and Fischler. Furthermore we
review the no-go theorems that forbid an embedding of de Sitter spaces in
string theory, and discuss how they can be circumvented. Finally, some curious
issues concerning the thermal nature of de Sitter space are elucidated.Comment: 36+1 pages, 5 Postscript figures, introduction and section 6
extended, further references, final version to appear in JCA