Cosmological
Expansion |

**In General** s.a. expansion rate, issues and effects [including global-local discrepancy] and acceleration;
friedmann equation; relativistic cosmology.

* __Hubble's law__: Introduced as the relationship *v* = *H*_{0}*R* between a distant galaxy's recession speed and its distance, it actually relates the distance to the galaxy's redshift *z* observationally, or its comoving distance to the time rate of change of its comoving distance theoretically; *H*_{0} is not really a constant; Alternatively, *H*_{0} can be replaced by its dimensionless counterpart *h* or "little *h*", defined by *H*_{0} = 100 *h* km/s/Mpc.

* __History__: Credit for the discovery is given to Edwin Hubble (1929), but the work of Lemaître (1927) has been neglected; Mechanisms such as Zwicky's 1929 "tired light" were proposed as alternative explanations for the redshift; Hubble was
initially reluctant to accept the expansion as
real! 1970s, Alan Sandage defined cosmology as the search for two numbers, the Hubble parameter \(H_0\) and deceleration parameter \(q_0\).

* __Measurements__: Calculations
of
the
value of Hubble's constant use redshift and distance measurements; Some high-precision
distance-determination methods use Cepheids, the tip of the red
giant
branch, maser galaxies, surface-brightness fluctuations, the Tully-Fisher relation
and Type-Ia supernovae; 2012, Recently proposed methods use galaxy clusters and gravitational waves.

@ __General references__: Criado & Alamo AJP(07)apr
[motion of photons and galaxies]; Linder RPP(08)-a0801 [rev]; Greenhill et al a0902-rp [measurement];
Padmanabhan GRG(10)-a1001 [and gravitational action and thermodynamics]; Wallace & Prather AJP(12)may [use for teaching introductory physics]; Neben & Turner ApJ(13)-a1209 [using time dependence of redshifts]; Croton PASA(13)-a1308 [dealing with little *h* in data analysis]; Sloan & Silk PRD(16)-a1505 [reason for large expansion].

@ __Conceptual__: Silverman AJP(86)dec
[apparent paradoxes]; Page gq/93 [apparent
superluminal expansion]; Peacock a0809; Kaya AJP(11)-a1107; Padmanabhan RAA(12)-a1207 [expansion of the universe as emergence of space]; Toporensky & Popov PU(14)-a1311 [observer perspective]; Hogan a1312 [quantum indeterminacy in local measurement of cosmic expansion]; Pandey a1705 [information-theoretic viewpoint]; > s.a. history of relativistic cosmology.

**Expansion History** > s.a. cosmology [including
future].

* __2016__: The most accurate measurements have been obtained with Type Ia supernovae and Baryon Acoustic Oscillations, providing evidence for the existence of a transition epoch from a decelerated to an accelerated expansion rate.

@ __General references__: Linder PRL(03)ap/02;
Simon et al PRD(05);
Shafieloo et al MNRAS(06)ap/05 [from supernova data]; Wang & Tegmark PRD(05)
[measurement method]; Sethi et al PLB(05)ap [viability
of linearly coasting model]; Linder PRD(05)ap [and
inhomogeneity growth history]; Bonvin et al PRL(06)
[*H*(*z*) from luminosity distance dipole]; Nojiri & Odintsov JPCS(07)ht/06 [and
reconstruction of modified gravity theory]; Schaefer ApJ(07)ap/06 [Hubble diagram to *z* > 6]; Figueroa et al JCAP(08)-a0807 [and
cosmological parameters]; Mörtsell & Clarkson JCAP(09)-a0811 [constraints];
Linder & Smith JCAP(11)-a1009 [excluding early acceleration periods]; Santos et al APP(11)-a1009 [switch from deceleration to acceleration]; Barboza & Carvalho PLB(12) [kinematic probe]; Shchigolev UJPA(13)-a1404 [toy model of complete history]; > s.a. acceleration.

@ __Reconstruction__: Ishida & de Souza A&A(11)-a1012; Shafieloo JCAP(12)-a1204 [high-precision];
Samsing et al PRD(12)-a1208 [model-independent, from cmb observations]; Song PRD(13)-a1210 [using redshift distortions];
Shafieloo et al PRD(13)-a1211 [model-independent, from supernova data]; news sn(12)nov [BOSS finds expansion was slowing down 11 Gyr ago]; Hamaus et al JCAP(14)-a1409 [using the clustering statistics of cosmic voids];
Li et al PRD(16)-a1504 [*H*(*z*) as a function of redshift];
Vitenti & Penna-Lima JCAP(15)-a1505; Hamaus et al JCAP(15)-a1507 [using redshift-space distortions]; Moresco et al JCAP(16)-a1601 [evidence for transition from decelerated to accelerated expansion]; Crevecoeur a1603 [in light of Planck data]; Feng & Li ApJ(16)-a1604 [from SN and GRB measurements]; Wang & Meng PDU-a1709 [from galaxy cluster surveys].

@ __And gravitational waves__: Izquierdo AIP(06)gq [relic gravitational waves];
Linder JCAP(08)-a0711, Nishizawa et al PRD(11) [sirens];
Messenger & Read PRL(12) [from binary neutron star coalescence].

@ __In f(R) gravity__: Amarzguioui
et al A&A(06)ap/05 [Palatini];
Fairbairn & Rydeck JCAP(07)ap.

**Other References** > s.a. doppler effect
global geometry[including distance-redshift relation].

@ __Distance measurements__:
Feast ASP-ap/04; Allen et al a1307 [rev]; Fakhouri et al ApJ(15)-a1511 [using "twin" Type Ia supernovae].

@ __Related topics__: Goldhaber et al ap/96-in
[cosmological time dilation];
Scott & Frolop ap/06 [(not
CJP) coincidences]; Cooray & Caldwell PRD(06)
[complications from bulk motions]; Coley et al IJMPD(06)gq [observer
dependence]; Cattoën & Visser CQG(07)-a0710 [expansions
in powers of *z*]; Uzan et al PRL(08)
[time drift of cosmological redshift]; Guzzo et al nat(08)jan
+ news pw(08)jan
[redshift distortion]; Qi & Lu a1001 [direct
measurement proposal]; Christiansen & Siver AJP(12)may-a1204 [brightness and angular size in an expanding universe];
López-Corredoira PoS-a1501 [tests of expansion].

@ __Arguments against expansion__: Petry ASS(97)
[redshift]; Sumner ap/04 [contraction!];
Whiting Obs-ap/04;
Moret-Bailly ap/04;
Chodorowski ONCP(07)ap/06;
Bunn & Hogg AJP(09)-a0808
[Doppler shift
as opposed to stretching]; Chodorowski a0812;
Crawford a0901 [no
evidence of time dilation in GRBs], a0901 [supernovae];
López-Corredoira IJMPD(10)
[angular-size test]; Rebhan PRD(12)-a1211 [expansion of space is just an interpretation]; Janzen a1303-FQXi; Kragh a1507 [Jacob Halm's 1935 paper].

@ __The universe does expand__:
Lineweaver & Davis SA(05)mar; Abramowicz et
al ap/06, a0812 [expansion
vs motion of galaxies is verifiable]; Faraoni GRG(10)-a0908.

@ __Other unconventional views__: Leffert ap/05 [spatial
condensation]; Grøn
& Elgarøy AJP(07)feb-ap/06 [response];
He ap/06 [flat
spacetime]; Francis et al PASA(07)-a0707;
Lewis et al MNRAS(07)-a0707
[counterargument]; Tomozawa a0710 [center
of expansion, from cmb dipole]; Cook & Burns AJP(09)-a0803
[FLRW model with different interpretation]; Baryshev a0810-proc
["paradoxes"];
Christensen a0810;
Farley PRS(10)-a1005 [no gravity between galaxies and no dark energy]; Chernin a1107; Jain MPLA(12) [no expansion, increasing particle masses]; Lewis AusP-a1605; > s.a. FLRW
models.

I awoke on Friday and because the universe is expanding it took me longer than usual to find my robe...

– Woody Allen, in "Strung Out" The New Yorker, 18 Jul 2003.

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