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Desingularization of the Milne Universe
High Energy Physics - Theory · Submitted 28 Nov 2013
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2+1 dimensions.
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The abstract, sentence by sentence
Resolution of cosmological singularities is an important problem in any full theory of quantum gravity. The Milne orbifold is a cosmology with a big-bang/big-crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. It is known however, that some perturbative string amplitudes diverge in the Milne geometry. Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2+1 dimensions. We explain how to reconcile this with the expectation that non-perturbative string effects are required for resolving Milne. Along the way, we introduce a Grassmann realization of the \.{I}n\"on\"u-Wigner contraction to export much of the AdS technology to our flat space computation.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Resolution of cosmological singularities is an important problem in any full theory of quantum gravity. | background 1.00 | 0.03 | 0.02 | asserted 1.00 |
| s1 | The Milne orbifold is a cosmology with a big-bang/big-crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. | background 1.00 | 0.05 | 0.03 | hedged possibility 0.63 |
| s2 | It is known however, that some perturbative string amplitudes diverge in the Milne geometry. | background 0.93 | 0.04 | 0.02 | asserted 0.98 |
| s3 | Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2+1 dimensions. | contribution 0.50 | 0.95 | 0.91 | asserted 1.00 |
| s4 | We explain how to reconcile this with the expectation that non-perturbative string effects are required for resolving Milne. | contribution 0.54 | 0.83 | 0.07 | asserted 0.97 |
| s5 | Along the way, we introduce a Grassmann realization of the \.{I}n\"on\"u-Wigner contraction to export much of the AdS technology to our flat space computation. | method 0.86 | 0.92 | 0.03 | asserted 1.00 |
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The paper
Original abstract
Resolution of cosmological singularities is an important problem in any full theory of quantum gravity. The Milne orbifold is a cosmology with a big-bang/big-crunch singularity, but being a quotient of flat space it holds potential for resolution in string theory. It is known however, that some perturbative string amplitudes diverge in the Milne geometry. Here we show that flat space higher spin theories can effect a simple resolution of the Milne singularity when one embeds the latter in 2+1 dimensions. We explain how to reconcile this with the expectation that non-perturbative string effects are required for resolving Milne. Along the way, we introduce a Grassmann realization of the \.{I}n\"on\"u-Wigner contraction to export much of the AdS technology to our flat space computation.
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References
How the literature uses it
13 arXiv papers cite this in 25 sentences
Papers citing it · 15 sentences without a confident label
Uses its method or tool 1 paper
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Instead of working directly with the $(1,2)$ gauge theory, we will use the language of the $(2)×(2)$ Grassmann valued connection introduced in [ref] : [equation] where $ϵ$ is a formal Grassmann parameter, $ϵ^2=0$. $T_i$ $(i=±1,0)$ are the generators of $(2,R)$ introduced in appendix [ref], $e^i$ is an orthonormal frame for the metric [ref] and $ω^i$ is the Hodge dual of the spin connection[We use the convention $ϵ^012=1$.] [equation]
Strings vs Spins on the Null Orbifold · Chern-Simons Gauge Field · 0.99
Uses its data or values 1 paper
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Milne metric in 2+1 dimensions is [ref] ds^2 = -dT^2 + r_C^2 dX^2 + α^2 T^2 dϕ^2. where the parameters $α$ and $r_C$ in terms of Mass (M) and Spin (J) are [equation] We are setting $8G = 1$.
3D Gravity, Chern-Simons and Higher Spins: A Mini Introduction · Singularity Resolution using Chern-Simons Theory · 0.85
Cites it as support 2 papers
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Evidence for this in the affirmative has been provided in two different regimes for the Milne singularity, which is a boost orbifold of flat pace: in the target space description using higher spin theory [ref] , and in the low tension limit of string scattering amplitudes [ref] .
Strings vs Spins on the Null Orbifold · Introduction and Summary · 0.99
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The answer found in [ref] was that indeed this is possible.
Gauging Away a Big Bang · 2 · 0.98
Cites it as background 6 papers
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This has sparked considerable interest in a better understanding of flat space holography [ref] .
Wilson Lines and Holographic Entanglement Entropy in Galilean Conformal Field Theories · Introduction · 0.96
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Starting from the Barnich–Compère boundary conditions [ref] , some key developments were the BMS/CFT or BMS/GCA correspondences[ BMS stands for Bondi–van der Burg–Metzner–Sachs [ref] , the asymptotic symmetry algebra of flat spacetimes at null infinity, and GCA for Galilean conformal algebra [ref] . ] [ref] , the flat space chiral gravity proposal [ref] , the counting of flat space cosmology microstates [ref] , the existence of phase transitions between flat space cosmologies and hot flat space [ref] and numerous other aspects of flat space holography [ref] .
Flat space (higher spin) gravity with chemical potentials · Introduction · 1.00
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Related results along these lines, including Hamiltonian reduction [ref] , unitarity [ref] , and the analysis of cosmologies endowed with higher spin fields have been discussed in [ref] , [ref] , [ref] , [ref] ).
Brief review on higher spin black holes · Asymptotic conditions with $W_3$ symmetries · 0.94
What it cites · 16 sentences without a confident label
Uses the method or tool of 2 papers
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The spin-3 fields can be computed via [ref] $Φ_μνρ=1/9(E_(μE_νE_ρ))$.
Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields · The Milne Resolution · 0.99
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The corresponding expressions for the triads and spin-connection (dualized using $ϵ_abc$) are, [equation] [equation] So in the Chern-Simons language the $SL(2)$ Grassmann valued connection is [Note that the $1/ℓ$ in the AdS case [ref] has been repleaced with the Grassmann paramter $ϵ$.], [equation] The $φ$-circle holonomy is, [equation] The eigenvalue spectrum of the holonomy matrix, $w_ϕ^±≡2πα(T_1±ϵT T_2)$ is $(0,±2πα)$.
Black Holes and Singularity Resolution in Higher Spin Gravity · Milne: Metric and Connection · 0.88
Compares with 1 paper
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In [ref] a cosmological sinularity resolution was done, but in the context of dS$_3$ (higher spin) gravity.
Higher Spin Cosmology · Introduction and Conclusion · 0.85
Cites as background 3 papers
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Some recent papers dealing with cosmologies and singularities in a higher spin set up can be found in [ref] .
Higher Spin Resolution of a Toy Big Bang · Introduction and Conclusion · 1.00
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Some recent papers dealing with cosmologies and singularities in a higher spin set up can be found in [ref] .
Higher Spin Cosmology · Introduction and Conclusion · 1.00
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Some recent papers dealing with cosmologies and singularities in a higher spin set up can be found in [ref] .
On Resolutions of Cosmological Singularities in Higher-Spin Gravity · Introduction and Conclusion · 1.00
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