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Observing the Dimensionality of Our Parent Vacuum
High Energy Physics - Theory · Submitted 1 Mar 2010
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Such signals could reveal our history of decompactification, providing evidence for the existence of vastly different vacua.
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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
It seems generic to have vacua with lower dimensionality than ours. We consider the possibility that the observable universe originated in a transition from one of these vacua. Such a universe has anisotropic spatial curvature. This may be directly observable through its late-time effects on the CMB if the last period of slow-roll inflation was not too long. These affect the entire sky, leading to correlations which persist up to the highest CMB multipoles, thus allowing a conclusive detection above cosmic variance. Further, this anisotropic curvature causes different dimensions to expand at different rates. This leads to other potentially observable signals including a quadrupolar anisotropy in the CMB which limits the size of the curvature. Conversely, if isotropic curvature is observed it may be evidence that our parent vacuum was at least 3+1 dimensional. Such signals could reveal our history of decompactification, providing evidence for the existence of vastly different vacua.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | It seems generic to have vacua with lower dimensionality than ours. | background 1.00 | 0.08 | 0.07 | hedged possibility 0.67 |
| s1 | We consider the possibility that the observable universe originated in a transition from one of these vacua. | contribution 0.91 | 0.29 | 0.06 | hedged possibility 0.75 |
| s2 | Such a universe has anisotropic spatial curvature. | result 0.78 | 0.29 | 0.09 | asserted 1.00 |
| s3 | This may be directly observable through its late-time effects on the CMB if the last period of slow-roll inflation was not too long. | interpretation 0.64 | 0.14 | 0.10 | hedged possibility 1.00 |
| s4 | These affect the entire sky, leading to correlations which persist up to the highest CMB multipoles, thus allowing a conclusive detection above cosmic variance. | interpretation 0.55 | 0.30 | 0.15 | asserted 0.97 |
| s5 | Further, this anisotropic curvature causes different dimensions to expand at different rates. | result 0.82 | 0.33 | 0.05 | asserted 0.99 |
| s6 | This leads to other potentially observable signals including a quadrupolar anisotropy in the CMB which limits the size of the curvature. | result 0.64 | 0.38 | 0.11 | asserted 0.68 |
| s7 | Conversely, if isotropic curvature is observed it may be evidence that our parent vacuum was at least 3+1 dimensional. | interpretation 0.95 | 0.12 | 0.22 | hedged possibility 1.00 |
| s8 | Such signals could reveal our history of decompactification, providing evidence for the existence of vastly different vacua. | interpretation 1.00 | 0.09 | 0.37 | hedged possibility 1.00 |
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The paper
Original abstract
It seems generic to have vacua with lower dimensionality than ours. We consider the possibility that the observable universe originated in a transition from one of these vacua. Such a universe has anisotropic spatial curvature. This may be directly observable through its late-time effects on the CMB if the last period of slow-roll inflation was not too long. These affect the entire sky, leading to correlations which persist up to the highest CMB multipoles, thus allowing a conclusive detection above cosmic variance. Further, this anisotropic curvature causes different dimensions to expand at different rates. This leads to other potentially observable signals including a quadrupolar anisotropy in the CMB which limits the size of the curvature. Conversely, if isotropic curvature is observed it may be evidence that our parent vacuum was at least 3+1 dimensional. Such signals could reveal our history of decompactification, providing evidence for the existence of vastly different vacua.
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References
How the literature uses it
22 arXiv papers cite this in 33 sentences
Papers citing it · 26 sentences without a confident label
Builds on it 1 paper
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We have gone beyond previous work [ref] by considering not only the temperature, but also the polarisation power spectra, and also by performing full cosmological perturbation theory at early times in order to investigate the effect not only on the scalar, but also the tensor perturbation modes.
An anisotropic universe due to dimension-changing vacuum decay · Conclusions · 1.00
Cites it as background 6 papers
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While many studies have imposed bounds on the possible presence of universal rotation [ref] and of shear [ref] , the cosmological and astrophysical implications of solely anisotropic curvature have not been worked out (see however [ref] and references therein for some pioneering work).
On the Possibility of Anisotropic Curvature in Cosmology · Introduction · 0.95
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Note added: We very recently became aware of interesting work by another group, which computes the effect of late-time spatial curvature and expansion anisotropy on photon free-streaming from the surface of last scattering [ref] .
Observable effects of anisotropic bubble nucleation · Discussion · 0.85
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The consequences of this have only just begun to be explored [ref] .
A signature of anisotropic bubble collisions · Introduction · 0.87
What it cites · 53 sentences without a confident label
Uses the method or tool of 3 papers
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Following [ref] , we express the temperature $(P⃗)$ at any point $P⃗ = łR, β, ϕ$̊ on$Σ$by the expansion [equation] The Fourier components$T̃_rec(k⃗)$represent the power spectrum at recombination.
Testing gaussianity, homogeneity and isotropy with the cosmic microwave background · Statistical Anisotropy · 1.00
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We follow the bipolar power spectrum analysis proposed by [ref] and adopt their notation (note that the normalization convention adopted by [ref] is different from that used by the WMAP team [ref] ).
Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Are There Cosmic Microwave Background Anomalies? · Statistical Anisotropy · 0.99
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We follow the bipolar power spectrum analysis proposed by [ref] and adopt their notation (note that the normalization convention adopted by [ref] is different from that used by the WMAP team [ref] ).
Measuring Statistical isotropy of the CMB anisotropy · Statistical Anisotropy · 0.99
Uses data or values from 2 papers
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Current limits from the WMAP data require the topology scale to be greater than 24 Gpc [ref] .
Constraining the Topology of the Universe · Compact Topology · 0.95
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In fact, the measured quadrupole in our universe has significantly less power than expected from a conventional $Λ$CDM model [ref] .
Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Power Spectra and WMAP-Derived Parameters · The Quadrupole · 0.93
Compares with 2 papers
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This effect is different from other signatures of anisotropy considered in the literature [ref] .
Inflationary perturbations in anisotropic backgrounds and their imprint on the CMB · Discussion · 0.96
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This effect is different from other signatures of anisotropy considered in the literature [ref] .
Gravity Waves Signatures from Anisotropic pre-Inflation · Discussion · 0.96
Cites as support 7 papers
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This may be reasonable because this is very near a catastrophic boundary: large scale structures such as galaxies would not form if inflation did not last long enough to dilute curvature sufficiently [ref] .
Probability Distribution for $\Omega$ in Open-universe Inflation · Introduction and Summary · 0.98
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This may be reasonable because this is very near a catastrophic boundary: large scale structures such as galaxies would not form if inflation did not last long enough to dilute curvature sufficiently [ref] .
The density parameter and the Anthropic Principle · Introduction and Summary · 0.98
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This may be reasonable because this is very near a catastrophic boundary: large scale structures such as galaxies would not form if inflation did not last long enough to dilute curvature sufficiently [ref] .
Observational Consequences of a Landscape · Introduction and Summary · 0.98
Cites as background 3 papers
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The normal eternal inflation picture makes it appear that space should be very large or infinite in all directions [ref] .
What does inflation really predict? · Compact Topology · 0.87
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note that topologies like ours $R^2$ x $S^1$ and $T^2$ x $R$ have been considered before for the case that the curvature is undetectably tiny [ref] and you sit in a horn or cusp region.
What do very nearly flat detectable cosmic topologies look like? · Compact Topology · 0.88
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While this work was in progress we became aware of interesting work by another group working on different signals of a similar general framework [ref] .
Observable effects of anisotropic bubble nucleation · Acknowledgments · 0.84
Discussion
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