Cosmological Principle |

**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
distribution.

* __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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