Large-Scale Spatial Geometry of the Universe

In General > s.a. cosmological models; expansion [including vorticity and shear].
* Idea: The spatial geometry is approximately flat, homogeneous and isotropic, at least locally; The universe may not be "globally" homogeneous and isotropic.
* Distances: In cosmology, distances are determined based on standard candles (e.g., supernovae) or standard rulers (e.g., baryon oscillations); The two methods agree (duality) if some conditions on the physics are met.
* Radius of curvature: Related to the Hubble parameter and the total mass-energy density by

R = (c/H₀) (1 / |1–_tot|^1/2) .

* Status: 2000, Evidence for zero overall spatial curvature (Boomerang); 2003, Evidence for small positive curvature (WMAP), with radius R = 3.0 × 10⁴ Mpc using current parameter values.
> Related topics: see large-scale topology of the universe; quantum geometry [microscopic scale].

References
@ II: Adams & Shapiro AS(01)sep [10 orientable Euclidean 3-geometries]; Levin 02.
@ General references: Fagundes GRG(92) + GRG(98)gq + rev a0812 [closed spaces]; Manchak SHPMP(09) [global structure is underdetermined].
@ Space curvature: Hu & White ap/96-in [from cmb]; Roos & Harun-or-Rashid ap/00, ap/00 [flatness]; Uzan et al MNRAS(03)ap [and WMAP]; Lieu & Mittaz ApJ(05)ap/03 [exactly 0]; Wang et al PLB(05)ht/04 [from supernovae]; Knox PRD(06)ap/05 [proposal]; Lyth et al JCAP(05)ap/04 [perturbation]; Gu & Khlopov gq/07 [method]; Mersini-Houghton & Kafexhiu APP(08)-a0705 [role of cosmic priors in bounds], comment Räsänen APP(08)-a0705 [analysis]; Araújo & Stoeger MNRAS(09)-a0705 [from supernova luminosity distances]; Vardanyan et al MNRAS-a0901 [model comparison perspective]; Buchert et al GRG(09)-a0906 [and structure formation]; Mortonson a0908/PRD [model-independent tests]; Bozek et al PRD(09) [from causal entropic principle].
@ From lensing: Soucail et al A&A(04)ap [Abell 2218]; Bernstein ApJ(06)ap/05.
@ Distances: Hogg ap/99 [pedagogical]; Jensen et al ap/03-in; Malec et al gq/04 [luminosity distance]; Bassett & Kunz PRD(04), Kunz & Bassett ap/04-in [duality]; Caldwell & Kamionkowski JCAP(04)ap [expansion, geometry and luminosity distance]; Lu & Hellaby CQG(07)-a0705 [determining the metric from observations].
@ Homogeneity, isotropy: Roukema ASR(03)ap/01 [local vs global]; Campanelli et al PRL(06) + pn(06)oct [ellipsoidal shape]; Räsänen PRD(09)-a0903 [and cmb isotropy].
@ Singularities: Szydlowski et al PRD(05)ap [big bang vs bounce, observational tests]; > s.a. types of singularities.
@ Related topics: Quercellini et al PRL(09)-a0809 [geometry from cosmic parallax]; > s.a. rotation.

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