Quantum Gravity In De Sitter Space

By E. Witten. 2001

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We discuss some general properties of quantum gravity in De Sitter space. It has been argued that the Hilbert space is of finite dimension. This suggests a macroscopic argument that General Relativity cannot be quantized -- unless it is embedded in a more precise theory that determines the value of the cosmological constant. We give a definition of the quantum Hilbert space using the asymptotic behavior in the past and future, without requiring detailed microscopic knowledge. We discuss the difficulties in defining any precisely calculable or measurable observables in an asymptotically de Sitter spacetime, and explore some meta-observables that appear to make mathematical sense but cannot be measured by an observer who lives in the spacetime. This article is an expanded version of a lecture at Strings 2001 in Mumbai.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4f5edb985ba5b2e28c25ffe82e3221e691fe0e69

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Citations in the corpus

Operator Dictionaries and Wave Functions in AdS/CFT and dS/CFT (2011, methodology): “apers. In 2001 Witten showed that the bulk correlator of a conformally-coupled massless scalar, upon extrapolation to the future boundary, becomes a CFT correlator of an operator of dimension (d 1)=2 [3]. The same year, Strominger continued the dS/CFT program by dening a stress tensor, computing a c”
On loops in inflation (2009, background): “For example, in the dS/CFT correspondence [33, 34], it is speculated that the time-dependence of correlation functions, which occurs at perturbative level in theories where spectators scalar fields have a potential term, should be mapped into renormalization group running for some operators in the C”
The Swampland: Introduction and Review (2019, background): “king entropy as the logarithm of the number of microstates of the black hole. This has been made explicit for certain black holes in string theory following the seminal work [446]. It was proposed in [443,447] that a similar interpretation in terms of microstates should be assigned to de Sitter entr”
De Sitter space and eternity (2007, neutral): “September 2007”
Islands in de Sitter space (2020, background): “n the discussion of closed universes. Both of these options are clearly in tension with general beliefs, for example, that the Hilbert space of de Sitter quantum gravity has dimension of order e1=G N [29,35].4 Perhaps a less dramatic interpretation of the general argument in [1] is that the island f”
Multi-Trace Operators, Boundary Conditions, And AdS/CFT Correspondence (2001, background): “6 Existence of more than one de Sitter invariant state, as investigated in [21,22], presumably means that there are different possible Hilbert spaces – inequivalent quantizations of the field – as occurs in flat spacetime in the presence of spontaneous symmetry breaking.”
Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions (2006, background): “For asymptotically flat-spacetimes, the appropriate boundary from a conformal point of view is null infinity [5].”
Inflation in AdS/CFT (2005, background): “scription of inﬂation? More generally, what degrees of freedom are appropriate for a complete description of quantum gravity in this domain? A substantial amount of work has been done on these topics [13,14,15,16,17,18,19]. We will not be able to answer these questions in this paper, but we will try”
The Annular Report on Non-Critical String Theory (2003, methodology): “discussion in the de Sitter context, see [41, 42]).”
Late-time structure of the Bunch-Davies de Sitter wavefunction (2014, result): “art gives G C(;0;k) = 1 2k3‘2 (1 + k20)cos[k( 0)] + k( 0)sin[k( 0)] ; (1.2) which is singular as k!0. One of the main motivations of our approach is to connect our results with the idea [12,35,36] that BD (at late times) is holographically computed by the partition function of a conformal eld theo”
Higher spin realization of the DS/CFT correspondence (2011, background): “Hence it is natural to try to define dS quantum gravity in terms of a CFT living on the future conformal boundary of dS [1, 2, 3, 4, 5, 6].”
Observables in effective gravity (2005, background): “The status of an observable S-matrix in the De Sitter case is more controversial, but see [3,4].”
Lecture notes on holographic renormalization (2002, background): “[ 66 , 67]. Looking for supporting evidence to a possible dS/CFT correspondence, many”