Cosmological Expansion Rate – Issues and Effects  

Global-Local Relationship > s.a. acceleration [variation in time]; friedmann equation.
* Status: 2013, There is a 9% discrepancy between the value for H0 obtained indirectly from global measurements of the cosmic microwave background and baryon acoustic oscillations, \(H_0\) = 67.8 ± 0.9 km/s·Mpc, and the one obtained more directly from local measurements of the relation between redshifts and distances to sources, \(H_0\) = 73.8 ± 2.4 km/s·Mpc; Only part of this seems to be attributable to a cosmic variance of the Hubble parameter.
@ General references: Marra et al PRL(13)-a1303 [and errors]; Verde et al a1306/PDU [quantifying the tension]; Spergel et al PRD(15)-a1312; Bernal et al JCAP(16)-a1607 [comprehensive analysis]; Baryshev a1610-in.
@ Possible explanations: Li et al SCG-a1311; Romano & Vallejo EPL(15)-a1403 [local overdensity?]; Clarkson et al JCAP(14)-a1405 [relativistic corrections remove the tension]; Odderskov et al JCAP(16)-a1601 [inhomogeneities not likely to be the reason]; Bengaly JCAP(16)-a1510 [effect of the bulk flow motion]; Di Valentino et al PLB(16)-a1606 [extended parameter space, with a phantom-like dark-energy component]; Romano a1609; news sn(17)jun [local void].

Isotropy and Spatial Variation of H > s.a. acceleration [variation in time]; friedmann equation.
@ General references: Wiltshire et al PRD(13)-a1201 [and the cmb dipole].
@ Homogeneity: Giovanelli et al ApJ(99)ap [support]; Enqvist & Mattsson JCAP(07) [inhomogeneity and supernova observations]; Ben-Dayan et al PRL(14)-a1401 [effect of inhomogeneities on measurements of H0, fully relativistic treatment]; > s.a. galaxies.
@ Isotropy: Bochner ap/07-TX [mild evidence for anisotropy]; McClure & Dyer NA(07)ap [statistically significant difference of 9 km/s/Mpc seen]; Schwarz & Weinhorst A&A(07)-a0706 [statistically significant N/S difference at z < 0.2]; Quercellini et al PRL(09) [with future missions]; Campanelli PRD(11), Kalus et al A&A(13)-a1212, Cai et al PRD(13), Beltrán et al PLB(14)-a1402 [constraints on anisotropy from supernovae]; Bolejko et al JCAP(16)-a1512 [statistically significant evidence for anisotropy]; Migkas & Plionis RMAA-a1602 [outliers, but no significant evidence for anisotropy]; > s.a. cmb anisotropy.
@ Vorticity and shear: Jaffe et al ApJL(05)ap; Palle ap/05 [results not reliable]; Marozzi & Uzan PRD(12)-a1206 [shear from backreaction, and anisotropy of expansion]; > s.a. cosmological tests of gravity.

Theoretical Effects > s.a. early-universe models [bounce]; gravitational-wave background; Phantom Divide.
* With dark energy: If it is modeled as a perfect fluid with equation of state parameter w > –1, one gets a(t) = a0 (t/t0)2/3(1+w).
* Effect of inhomogeneities: If the length scale at which homogeneity sets in is much smaller than the Hubble length scale, the back-reaction on the expansion rate due to averaging over inhomogeneities is negligible.
@ General references: Sandage & Lubin AJ(01), Lubin & Sandage AJ(01)ap, AJ(01)ap, AJ(01) [Tolman surface brightness test]; Abramo & Woodard PRD(02)ap/01 [covariant]; Carroll & Kaplinghat PRD(02) [during nucleosynthesis]; Wei & Zhang PLB(07)ap/06 [and various models]; Shafieloo MNRAS(07)ap [reconstruction]; Sen & Scherrer PLB(08)ap/07 [and weak energy condition]; Cherkas & Kalashnikov NPCS-a1206 [local variations on the scale factor].
@ Effect of inhomogeneities: Geshnizjani & Brandenberger PRD(02)gq; Kozaki & Nakao PRD(02)gq [swiss-cheese model]; Kolb et al PRD(05)hp/04; Lieu ap/05/ApJL; Zhao & Mathews PRD(11)-a0912 [and structure formation, numerical]; Collins a1011 [theoretical model]; Singh a1105-proc; Tsamis & Woodard a1405 [back-reaction]; Adamek et al PRL(15)-a1408 [backreaction is a small effect]; Romano & Vallejo EPJC(16)-a1502 [local structure]; Tsagas & Kadiltzoglou PRD(15)-a1507 [effect of peculiar motions on measurements of the deceleration parameter]; Roukema et al a1608 [background Hubble constant]; Peñarrubia & Fattahi a1609/MNRAS; Fleury et al a1612 [large-scale structure]; Basu et al a1612 [super-horizon gravitons and the expansion rate].
@ Local effects of the expansion: Ohanian AJP(00)aug; Bolen et al CQG(01)gq/00; Davis et al AJP(03)apr-ap/01 [red-/blueshift]; Domínguez & Gaite EPL(01)ap; Price & Romano AJP(12)may-gq/05 [classical atom]; Carrera & Giulini gq/06; Adkins et al PRD(07)gq/06; Sereno & Jetzer PRD(07)ap [with dark matter and dark energy]; Balaguera-Antolinez & Nowakowski CQG(07)-a0704 [on large-scale structure]; Faraoni & Jacques PRD(07)-a0707; Nandra et al MNRAS(12)-a1104, MNRAS(12)-a1104; Castelo Ferreira a1203 [corrections to planetary motion]; Giulini SHPMP(14)-a1306-proc; Arenas a1309; Iorio Gal(14)-a1312 [with acceleration, orbit expansion]; Kopeikin EPJP(15)-a1407-conf; Widom et al a1507-MG14 [tests of local expansion–within the galaxy]; Dumin a1609 [overview]; Wiens et al PRL(16) [rulers and atomic clocks]; > s.a. cosmology in general relativity.
@ And structure formation: Wetterich PRD(03); Räsänen JCAP(08)-a0801, IJMPD(08)-a0805-GRF.

Other Effects and Theories
blue bullet Overall expansion: see cosmological expansion; friedmann equation.
blue bullet Effect of perturbations: see averaging in cosmology; effect on acceleration; cosmological perturbations.

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