A small universe after all?

Cornish, N.; Spergel, David N.

doi:10.1103/physrevd.62.087304

Cited by 37 publications

(69 citation statements)

References 22 publications

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“…In order to check this, a similar analysis has been carried out for deformed toroidal models whose fundamental cell is described by a rectangular box with sides L 1 = L 2 and L 3 . As shown in figure 6, the "pancake" type models ( In the previous literature, it has also been argued that an increase in the best-fit normalization constant is related to the large-angle suppression owing to the finite size of the spatial section [12]. From our analyses, it is found that inclusion of off-diagonal term can also give a comparable increase in the best-fit normalization constant as well.…”

Section: Fig 5 the Contribution Of Off-diagonal Elements For Cubic supporting

confidence: 72%

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How large is our Universe?

Inoue

Sugiyama

2003

Phys. Rev. D

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We reexamine constraints on the spatial size of closed toroidal models with cold dark matter and the cosmological constant from cosmic microwave background. We carry out Bayesian analyses using the Cosmic Background Explorer (COBE) data properly taking into account the statistically anisotropic correlation, i.e., off-diagonal elements in the covariance. We find that the COBE constraint becomes more stringent in comparison with that using only the angular power spectrum, if the likelihood is marginalized over the orientation of the observer. For some limited choices of orientations, the fit to the COBE data is considerably better than that of the infinite counterpart. The best-fit matter normalization is increased because of large-angle suppression in the power and the global anisotropy of the temperature fluctuations. We also study several deformed closed toroidal models in which the fundamental cell is described by a rectangular box. In contrast to the cubic models, the large-angle power can be enhanced in comparison with the infinite counterparts if the cell is sufficiently squashed in a certain direction. It turns out that constraints on some slightly deformed models are less stringent. We comment on how these results affect our understanding of the global topology of our universe. 98.70.Vc,98.80.Jk

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Section: Fig 5 the Contribution Of Off-diagonal Elements For Cubic supporting

confidence: 72%

“…However, for low matter density models Ω 0 < 1, constraints on the size of the spatial section are less stringent, since the bulk of large-angle temperature fluctuations can be produced in the curvature or Λ dominant era, leading to less stringent suppression in the large-angle power [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

How large is our Universe?

Inoue

Sugiyama

2003

Phys. Rev. D

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“…Should we be able to detect circles if the power spectrum cutoff is due to the size of the largest mode being $ 1= 0 ? While there is no rigorous theorem relating the size of the largest mode to the diameter of the fundamental domain, D, analysis of both negatively curved (Cornish & Spergel 2000) and positively curved (Lehoucq et al 2002) topologies suggest that D $ ð0:6 1Þ . Thus, if the '' peak '' in the power spectrum at ' $ 5 corresponds to the largest mode in the domain, we should be able to detect a pattern of circles in the sky.…”

Section: Intriguing Discrepanciesmentioning

confidence: 99%

First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Determination of Cosmological Parameters

Spergel¹,

Verde²,

Peiris³

et al. 2003

ASTROPHYS J SUPPL S

9,815

500

7,512

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WMAP precision data enable accurate testing of cosmological models. We find that the emerging standard model of cosmology, a flat Ã-dominated universe seeded by a nearly scale-invariant adiabatic Gaussian fluctuations, fits the WMAP data. For the WMAP data only, the best-fit parameters are h ¼ 0:72 AE 0:05, b h 2 ¼ 0:024 AE 0:001, m h 2 ¼ 0:14 AE 0:02, ¼ 0:166 þ0:076 À0:071 , n s ¼ 0:99 AE 0:04, and 8 ¼ 0:9 AE 0:1. With parameters fixed only by WMAP data, we can fit finer scale cosmic microwave background (CMB) measurements and measurements of large-scale structure (galaxy surveys and the Ly forest). This simple model is also consistent with a host of other astronomical measurements: its inferred age of the universe is consistent with stellar ages, the baryon/photon ratio is consistent with measurements of the [D/H] ratio, and the inferred Hubble constant is consistent with local observations of the expansion rate. We then fit the model parameters to a combination of WMAP data with other finer scale CMB experiments (ACBAR and CBI), 2dFGRS measurements, and Ly forest data to find the model's best-fit cosmological parameters: WMAP's best determination of ¼ 0:17 AE 0:04 arises directly from the temperaturepolarization (TE) data and not from this model fit, but they are consistent. These parameters imply that the age of the universe is 13:7 AE 0:2 Gyr. With the Ly forest data, the model favors but does not require a slowly varying spectral index. The significance of this running index is sensitive to the uncertainties in the Ly forest.By combining WMAP data with other astronomical data, we constrain the geometry of the universe, tot ¼ 1:02 AE 0:02, and the equation of state of the dark energy, w < À0:78 (95% confidence limit assuming w ! À1). The combination of WMAP and 2dFGRS data constrains the energy density in stable neutrinos: h 2 < 0:0072 (95% confidence limit). For three degenerate neutrino species, this limit implies that their mass is less than 0.23 eV (95% confidence limit). The WMAP detection of early reionization rules out warm dark matter. Subject headings: cosmic microwave background -cosmological parameterscosmology: observations -early universe On-line material: color figure

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“…Recent works [13][14][15][16] have shown that the angular power spectrum C l is completely consistent with the COBE-DMR data for some compact hyperbolic models which are incompatible with the previous analyses [17]. Because the angular sizes of fluctuations produced at the late epoch are large compared to those on the last scattering for flat or hyperbolic geometry, we expect that the constraints for compact flat models with low-matter-density can be also significantly loosened.…”

Section: Introductionmentioning

confidence: 64%

COBE constraints on a compact toroidal low-density universe

Inoue¹

2001

Class. Quantum Grav.

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In this paper, the cosmic microwave background (CMB) anisotropy in a multiply-connected compact flat 3-torus model with the cosmological constant is investigated. Using the COBE-DMR 4-year data, a full Bayesian analysis revealed that the constraint on the topology of the flat 3-torus model with low-matter-density is less stringent. As in compact hyperbolic models, the large-angle temperature fluctuations can be produced as the gravitational potential decays at the Λ-dominant epoch well after the last scattering. The maximum allowed number N of images of the cell (fundamental domain) within the observable region at present is approximately 49 for Ω m = 0.1 and Ω Λ = 0.9 whereas N ∼ 8 for Ω m = 1.0 and Ω Λ = 0.98.70.Vc,98.80.Hw

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A small universe after all?

Cited by 37 publications

References 22 publications

How large is our Universe?

How large is our Universe?

First‐Year Wilkinson Microwave Anisotropy Probe ( WMAP ) Observations: Determination of Cosmological Parameters

COBE constraints on a compact toroidal low-density universe

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