In General > s.a. observational
cosmology [including case against]; Principle of Mediocrity.
* Idea: The universe is homogeneous and isotropic, an extension to the cosmos of the Copernican principle; It can be taken to say that the small-scale degrees of freedom don't need to be taken into account when studying the dynamics of the large-scale ones.
* History: Introduced by Einstein in a 1917 paper; Formulated in its present form by Bondi in 1948, and assumed as simplifying assumption in model building; Questioned for a decade after the discovery of superclusters and voids in 1985 (e.g., fractal universes), but by 1995 there was evidence that at scales larger than 100 Mpc there was no structure.
* Status: 2009, According to SDSS DR6 data, the galaxy distribution is homogeneous at length-scales greater than 70 h–1 Mpc; 2010, Analysis of the cosmic microwave background Sunyaev-Zel'dovich effect confirms the Copernican Principle at Gpc scale; 2013, 4-Gly quasar group challenges its validity; 2016, Deviations from homogeneity are consistent with simulations.
* Conditional cosmological principle: A more subtle version, in which the universe looks the same from every galaxy; Proposed by B Mandelbrot, supported by L Pietronero, it is consistent with non-homogeneity in the fractal sense.
@ General references: Jaakkola Ap(89); Zeng & Zhao gq/05, Zeng gq/05 [and standard cosmology]; Schwarz a0905-in [more precise formulation, tests]; news ras(13)jan [4-Gly Large Quasar Group].
@ Different versions: Mittal & Lohiya Frac(03)ap/02 [conditional, fractal dust]; Sylos Labini AIP(10)-a0910 [relaxed].
@ Tests: Lahav CQG(02); Clifton et al PRL(08) [and supernovae]; Sylos Labini & Baryshev JCAP(10)-a1006 [and galaxy surveys]; Sylos Labini CQG(11)-a1103; Longo a1405 [using galaxy correlations].
> Related topics: see axions [and isotropy]; inflationary universe.
> Online resources: see Wikipedia page.
Homogeneity, Copernican Principle > s.a. Copernican Principle; large-scale geometry
of the universe; matter
* Idea: Violations of the Copernican Principle (for example by a Hubble-scale void) have been suggested as alternatives to dark energy, and fractal models up to the largest scales have been advocated for years by Pietronero, Sylos Labini and others; So far (2013), all observations are consistent with homogeneity.
* 1997: The distribution looks scale-invariant up to 150 Mpc and possibly 1000 Mpc, the observational limit, with fractal D ≈ 2.
* 2009: According to SDSS DR6 data, the galaxy distribution is homogeneous at length-scales greater than 70 h–1 Mpc.
* 2014: Evidence using large quasar groups supporting the validity of the cosmological principle up to scales 200-400 h–1 Mpc.
@ General references: Gaite et al ApJL(99)ap/98 [matter, vs fractal]; Lahav ASP-ap/99, ap/00-proc; Trodden & Vachaspati MPLA(99)gq [problem]; Bolejko & Stoeger GRG(10)-a1005-GRF = IJMPD(10) [initial conditions for spontaneous homogenization]; Akerblom & Cornelissen JMP(12)-a1008 [relative entropy as a measure of inhomogeneity].
@ Tests based on the cmb: Tomita & Inoue PRD(09)-a0903 [integrated Sachs-Wolfe effect]; Zhang & Stebbins PRL(11)-a1009 [kinetic Sunyaev-Zel'dovich effect]; Clifton et al PRL(12); Zibin & Moss a1409 [tight constraints using cmb secondary anisotropies].
@ Galaxy-based tests: Heavens et al JCAP(11)-a1107, Hoyle et al ApJL(13)-a1209 [galaxy fossil record]; Wang & Dai MNRAS(13)-a1304 [orientation of galaxy pairs]; Li & Li a1412 [large quasar groups]; Pandey & Sarkar MNRAS(15)-a1507 [SDSS data using Shannon entropy]; Laurent et al JCAP(16)-a1602 [BOSS quasar sample]; Ntelis a1607 [homogeneity scale, BOSS CMASS galaxy sample]; Sarkar & Pandey MNRAS(16)-a1607 [degree of inhomogeneity at the largest scales].
@ Other tests: Romano PRD(07)ap; Clarkson et al PRL(08)-a0712 [model-independent, and acceleration]; Uzan et al PRL(08) [time-drift of cosmological redshift]; Clifton et al PRL(08)-a0807 [redshift dependence of luminosity distance]; Bolejko & Wyithe JCAP(09)-a0807 [supernovas and cosmic flow]; Jia & Zhang JCAP(08)-a0809 [neutrino background]; Yadav et al MNRAS(10)-a1001 [scale, and fractal dimension]; Maartens PTRS(11)-a1104; Zhang et al PRD(15)-a1210 [using the Hubble parameter]; Longo a1305 [no evidence of a void]; Li & Lin A&A(15)-a1509 [gamma-ray bursts]; Carvalho & Marques A&A(16)-a1512 [angular distribution of cosmological parameters]; > s.a. galaxy distribution; observation [homogeneity].
@ Constraints: Dautcourt ap/99; Valkenburg et al MNRASL(13)-a1209.
@ The case against homogeneity: Clarkson & Barrett CQG(99)ap; Barrett & Clarkson CQG(00)ap/99; Clarkson PhD(99)ap/00; Park et al a1611 [fluctuations larger than random, but homogeneity is not necessary in the standard model].
> Related topics: see cosmology and general relativity [local effects]; cosmological models [inhomogeneous and/or anisotropic]; averaging in cosmology; Homogeneous Manifold; fractals in physics.
Isotropy > s.a. Anisotropy.
@ General references: Marinoni et al JCAP(12) [definition and value of isotropy scale].
@ Observations: news sa(11)dec [evidence of a special direction]; Longo a1112 [angular distribution of quasar spectra]; Appleby & Shafieloo JCAP(14)-a1405 [in the local universe, 2MASS extended source catalog]; news sci(16)sep [no signs of anisotropy]; > s.a. cmb anisotropy; cosmological expansion and acceleration.
> Theoretical models: see bianchi models; bianchi-IX models and brane-world cosmology [anisotropy dissipation]; relativistic cosmology.
> Quantum models: see minisuperspace quantum cosmology.
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