Averaging in Cosmology  

In General > s.a. cosmological perturbations; friedmann equation.
* Idea: The problem of averaging the observed inhomogeneities and anisotropies in cosmology to produce an FLRW model describing the large-scale evolution of the universe (fitting the parameters of such a model); Because of the non-linearity of the theory, any explicit averaging scheme yields corrections to simply using the Friedmann equation with averaged quantities; The main effect may be that of leading to an acceleration of the expansion rate, a topic that has been the subject of debate.
* Approaches: Buchert & Carfora summarize the effects that quantify the difference between "bare'' and "dressed'' parameters as "curvature backreaction'' and "volume effect''; The "macroscopic gravity" approach modifies the Einstein field equation on cosmological scales by appropriate gravitational correlation terms, that in a homogeneous, isotropic model have the effect of an extra curvature.
@ Reviews: Ellis & Buchert PLA(05)gq [and entropy]; Zalaletdinov gq/07-proc; Célérier a0706-proc; van den Hoogen a1003-MG12.
@ General references: Carfora & Marzuoli PRL(84); Hemmerich A&A(87); Ellis & Stoeger CQG(87); Hellaby GRG(88); Zalaletdinov GRG(92), BASI(97)gq; Zotov & Stoeger CQG(92); Futamase PRD(96); Buchert in(97)ap; Boersma PRD(98)gq/97; Stoeger et al IJMPD(07)gq/99 [linearized]; Sicka et al ap/99-proc [effect of the backreaction term]; Tanimoto gq/99, PTP(99)gq [model]; Buchert & Carfora PRL(03)gq/02 [and scaling]; Paranjape & Singh PRD(07)gq, GRG(08), Paranjape IJMPD(08)-a0705-GRF [corrections to Friedmann equations]; Mattsson & Ronkainen JCAP(08) [scale dependence]; Reiris CQG(08) [k = −1 Friedmann-Lemaître]; Larena PRD(09)-a0902 [for a tilted set of observers]; Paranjape PhD(09)-a0906; Mattsson & Mattsson JCAP(10)-a1007, JCAP(11)-a1012 [role of shear]; Marozzi JCAP(11)-a1011; Wiegand & Schwarz A&A(12)-a1109 [inhomogeneity-induced variance of cosmological parameters].
@ Physical effects and viewpoint: Buchert CQG(11)-a1103 [non-perturbative]; Ellis CQG(11); Wiltshire CQG(11)-a1106, a1311-proc [cosmic structure and timescape scenario]; Preston a1612-PhD [backreaction and effective stress-energy tensor]; Bolejko & Korzyński IJMPD(17)-a1612 [back-reaction].
@ Macroscopic gravity approach: Coley et al PRL(05)gq; Zalaletdinov IJMPA(08)-a0801-conf; van den Hoogen JMP(09)-a0909; Wijenayake et al PRD(16)-a1604 [and available observational data sets].
@ And Ricci flow: Piotrkowska gq/95-conf; Buchert & Carfora CQG(02)gq; Carfora & Buchert in(08)-a0801; > s.a. riemannian geometry.
@ Techniques: Seriu GRG(00)gq [spectral]; Seto ApJ(00)ap [perturbative]; Buchert & Carfora in(02)gq/01 [geometry of scaling]; Buchert GRG(01)gq [effective equation of state]; Behrend PhD(08)-a0812; Coley CQG(10)-a0908, a1001-proc, IJMPD(10) [in terms of scalar curvature invariants]; Baumann et al JCAP(12)-a1004 [perturbations as an effective fluid]; Buchert et al a1012-conf [effective 'morphon' scalar field]; Coley et al JMP(11)-a1102 [approach based on averaging of scalars within unimodular gravity]; Smirnov a1410 [covariant and gauge-invariant averaging formalism for finite volumes]; Visser a1512-MG14 [Buchert coarse-graining and energy conditions]; Buchert et al CQG(18)-a1805 [coordinate-independent averaging formalism]; Heinesen et al CQG(19)-a1811; Deledicque a1907; Fanizza et al JCAP-a1911 [covariant prescriptions]; Brunswic & Buchert a2002 [Gauss-Bonnet-Chern approach]; Ginat a2005 [multiple-scales approach]; > s.a. renormalization.

Types of Theories and Spacetimes > s.a. cosmology; LTB Models; modern cosmological models; general-relativistic models.
@ In Newtonian cosmology: Buchert & Ehlers A&A(97)ap/95; Buchert ASP(96)ap/95, GRG(00)ap.
@ Types of spacetimes: Coley & Pelavas PRD(06)ap, PRD(07)gq/06 [spherical symmetry]; Barrow & Tsagas CQG(07)gq/06 [anisotropic].

Observational Consequences > s.a. cosmological expansion; acceleration and inhomogeneities; observational cosmology.
* Back-reaction: The idea is that, to second order in perturbation theory, the first-order cosmological fluctuations back-react both on the large-scale background geometry and on the perturbations themselves.
* Status: 2007, The question of whether or not these corrections are significant is still a subject of debate, partly due to possible ambiguities in the averaging schemes available, but Paranjape & Singh have shown that not all effects are gauge.
@ Effects: Russ et al PRD(97) [age]; Linder ap/98; Buchert & Carfora in(03)ap; Coley a0704 [and observational cosmology]; Wiltshire PRL(07)-a0709 [and acceleration]; Khosravi et al IJMPD(09)-a0709 [dark-matter-like behavior]; Umeh et al JCAP(11)-a1011 [and expansion rate]; Bagheri & Schwarz JCAP(14)-a1404 [and light propagation].
@ Back-reaction: Buchert et al PRD(00)ap/99; Nambu PRD(02)gq; Brandenberger & Lam ht/04 [and cosmological constant relaxation]; Martineau & Brandenberger PRD(05)ap; Behrend et al JCAP(08)-a0710, Li & Schwarz PRD(08)-a0710 [and FLRW expansion]; Paranjape PRD(08); Gasperini et al JCAP(09)-a0901 [gauge-invariant averages]; Anastopoulos PRD(09); Magni a1202-MS; Clifton et al PRD(12)-a1203 [exact n-body model]; Green & Wald PRD(13)-a1304 [examples]; Ostrowski & Roukema a1512-MG14; Adamek et al CQG(19)-a1706 [in simulations]; Buchert et al CQG(18), CQG+(18) [and choice of foliation]; > s.a. cosmological expansion rate.
@ And evolution, acceleration: Seriu CQG(01)gq; Buchert CQG(06)gq/05 [globally static without cosmological constant], CQG(05) [effective equation of state]; Gruzinov et al JCAP(06)ap [heuristic model, effects \(O(H^2l^2/c^2)\)]; Paranjape & Singh GRG(08)-ap/06, PRL(08)-a0806, Sussman a0807 [no significant effect]; Li et al FdP(08)-a0801-proc; Buchert & Carfora CQG(08)-a0803; Brown et al JCAP(09)-a0811; Coley a0812 [in terms of paths of photons]; Räsänen a1012-proc; Romano & Chen JCAP(11)-a1104 [and apparent value of the cosmological constant]; Clarkson et al RPP(11)-a1109 [growth of structure and dynamics in cosmology]; Clarkson et al PRD(12) [observational constraints]; Brown et al PRD(13)-a1308 [small fractional effect on H, large fractional effect on the deceleration parameter]; Buchert et al CQG(15)-a1505; > s.a. expansion rate [glocal/local discrepancy]; acceleration.

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