Averaging in Cosmology| 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.
main page
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