Cosmological Principle |

**In General** > s.a. observational cosmology [including case against];
Principle of Mediocrity; Typicality.

* __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; 2013,
So far 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];
Jiménez et al JCAP(19)-a1902 [homogeneity].

@ __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 CTP(15)-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-proc [homogeneity scale, BOSS CMASS galaxy sample];
Sarkar & Pandey MNRAS(16)-a1607 [degree of inhomogeneity at the largest scales];
Secrest et al ApJL-a2009 [with quasars].

@ __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 MNRAS(17)-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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