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De Sitter Universe from Causal Dynamical Triangulations without Preferred Foliation
High Energy Physics - Theory · Submitted 20 Jul 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim This provides evidence that the distinguished time slicing of the latter is not an essential part of its kinematical set-up.
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
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The abstract, sentence by sentence
We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and causal properties, present details of the numerical set-up and explain how to extract "volume profiles". Extensive Monte Carlo measurements of the system show the emergence of a de Sitter universe on large scales from the underlying quantum ensemble, similar to what was observed previously in standard CDT quantum gravity. This provides evidence that the distinguished time slicing of the latter is not an essential part of its kinematical set-up.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. | contribution 1.00 | 0.78 | 0.08 | asserted 0.94 |
| s1 | Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and causal properties, present details of the numerical set-up and explain how to extract "volume profiles". | method 0.58 | 0.91 | 0.03 | asserted 0.68 |
| s2 | Extensive Monte Carlo measurements of the system show the emergence of a de Sitter universe on large scales from the underlying quantum ensemble, similar to what was observed previously in standard CDT quantum gravity. | result 1.00 | 0.95 | 0.53 | asserted 1.00 |
| s3 | This provides evidence that the distinguished time slicing of the latter is not an essential part of its kinematical set-up. | interpretation 1.00 | 0.70 | 0.75 | hedged possibility 0.52 |
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The paper
Original abstract
We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and causal properties, present details of the numerical set-up and explain how to extract "volume profiles". Extensive Monte Carlo measurements of the system show the emergence of a de Sitter universe on large scales from the underlying quantum ensemble, similar to what was observed previously in standard CDT quantum gravity. This provides evidence that the distinguished time slicing of the latter is not an essential part of its kinematical set-up.
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References
How the literature uses it
17 arXiv papers cite this in 23 sentences
Papers citing it · 18 sentences without a confident label
Uses its method or tool 1 paper
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A natural choice, which can be used to associate a time variable with individual simplices and subsequently to define the notion of a spatial slice of constant time, is an average version of “link distance to the poles" of the three-sphere (see [ref] for details).
Quantum Gravity from Causal Dynamical Triangulations: A Review · Causal structure, Wick rotation, time and all that · 0.91
Cites it as background 4 papers
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In the particular approach known as Causal Dynamical Triangulations (CDT) [ref] , the causal condition of global hyperbolicity [ref] is additionally enforced on triangulations by means of a space-time foliation, with spatial slices characterized by a fixed topology (usually $S^3$), and typically periodic boundary conditions (p.b.c.) in the time direction.
Spectral Methods and Running Scales in Causal Dynamical Triangulations · Introduction · 0.99
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CDT in 2+1 dimensions is so far not solvable, and its properties have also been studied mostly by numerical simulations [ref] , but one can in principle reach larger volumes than in higher dimensions, and furthermore some analytical tools are available [ref] (and others might be developed more likely than in higher dimensions).
Capturing the phase diagram of (2+1)-dimensional CDT using a balls-in-boxes model · Introduction · 0.91
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A less strict version [ref] imposes more directly a regular light cone structure (all spacetime points carry exactly one future-directed light cone and exactly one past-directed light cone) without an obvious slicing into hypersurfaces.
Causal structure and light-conical singularities in Lorentzian simplicial quantum gravity · Introduction · 0.80
What it cites · 19 sentences without a confident label
Uses the method or tool of 1 paper
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Following the strategy of [ref] for foliated CDT triangulations in 3+1 dimensions, we will use finite-size scaling to achieve a best overlap of these curves.
Planckian Birth of the Quantum de Sitter Universe · Evidence for three-dimensionality from finite-size scaling · 0.99
Compares with 1 paper
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As remarked already in the introduction, the same is not true for Hořava-Lifshitz gravity [ref] – to the extent that our nonperturbative, coordinate-free set-up can be compared with this continuum formulation – where a fixed spatial foliation is essential.
Quantum Gravity at a Lifshitz Point · Summary and conclusions · 0.93
Cites as background 5 papers
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The distribution of spatial volume as a function of time is an important large-scale observable, and its analysis has been instrumental in relating CDT quantum gravity to a de Sitter minisuperspace cosmology in 2+1 and 3+1 dimensions [ref] .
Planckian Birth of the Quantum de Sitter Universe · Re-introducing time · 0.87
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In addition, each path integral history has a distinguished discrete foliation and an associated notion of (discrete) proper time, which ensures the presence of a well-defined causal structure globally (see [ref] for details on motivation, construction and results in CDT).
Nonperturbative Quantum Gravity · Introduction · 0.99
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In higher dimensions, information about the behaviour of observables comes primarily from numerical simulations: three-dimensional CDT quantum gravity has only been solved partially and for restricted classes of triangulations [ref] , while in four dimensions analytical methods are mostly unavailable and one must resort to Monte Carlo simulations to extract physical results.
(2+1)-Dimensional Quantum Gravity as the Continuum Limit of Causal Dynamical Triangulations · Review of Causal Dynamical Triangulations · 0.81
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