2262:
2455:
1976:
679:
1648:
156:
4268:
2765:
2651:
36:
691:
4860:
1971:{\displaystyle d_{M}(z)={\begin{cases}{\frac {d_{H}}{\sqrt {\Omega _{k}}}}\sinh \left({\frac {{\sqrt {\Omega _{k}}}d_{C}(z)}{d_{H}}}\right)&\Omega _{k}>0\\d_{C}(z)&\Omega _{k}=0\\{\frac {d_{H}}{\sqrt {|\Omega _{k}|}}}\sin \left({\frac {{\sqrt {|\Omega _{k}|}}d_{C}(z)}{d_{H}}}\right)&\Omega _{k}<0\end{cases}}}
3527:
factors out the expansion of the universe, which gives a distance that does not change in time due to the expansion of space (though this may change due to other, local factors, such as the motion of a galaxy within a cluster); the comoving distance is the proper distance at the present time.
1288:
999:
2256:
2875:
for distant objects in that direction by a factor of about 1.0012 and increases it by the same factor for distant objects in the opposite direction. (The speed of the motion of the Earth around the Sun is only 30 km/s.)
1111:
2921:, does not change with time, as comoving distance accounts for the expansion of the universe. Comoving distance is obtained by integrating the proper distances of nearby fundamental observers along the line of sight (
3384:
1639:
1440:
3461:
2458:
A comparison of cosmological distance measures, from redshift zero to redshift of 10,000, corresponding to the epoch of matter/radiation equality. The background cosmology is Hubble parameter 72 km/s/Mpc,
896:
2607:
2413:
4903:
4510:
2055:
793:
280:
4690:
2540:
2346:
3149:
2829:
There are actually two notions of redshift. One is the redshift that would be observed if both the Earth and the object were not moving with respect to the "comoving" surroundings (the
4413:
3776:
3010:
4010:
2490:
2296:
1333:
4198:
3893:
3619:
2132:
4787:
The
Etherington's distance-duality equation is the relationship between the luminosity distance of standard candles and the angular-diameter distance. It is expressed as follows:
4847:
3103:
5250:
1360:
2943:
The comoving distance (with a small correction for our own motion) is the distance that would be obtained from parallax, because the parallax in degrees equals the ratio of an
4772:
4620:
4460:
4438:
4366:
in this distance measure becomes the age of the universe multiplied by the speed of light (1 light year/year), which turns out to be approximately 13.8 billion light years.
3723:
3577:
1498:
2751:
are used to denote both the comoving and the angular diameter distance. Sometimes, the light-travel distance is also called the "lookback distance" and/or "lookback time".
1091:
651:
2634:
2440:
5113:
5003:
4244:
882:
4585:
4546:
4046:
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are two closely related distance measures used by cosmologists to measure distances between objects; the comoving distance is the proper distance at the present time.
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Peebles calls the transverse comoving distance the "angular size distance", which is not to be mistaken for the angular diameter distance. Occasionally, the symbols
4356:
4123:
3814:
3646:
2915:
2729:
1050:
4204:
is the component of the object's peculiar velocity away from us. In this way, the luminosity distance will be equal to the angular diameter distance multiplied by
2873:
3816:
should be corrected for the motion of the solar system by a factor between 0.99867 and 1.00133, depending on the direction. (If one starts to move with velocity
4710:
3950:
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3554:
3030:
2749:
1533:
1019:
830:
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Together with the scale factor it gives the proper distance of the object when the light we see now was emitted by the it, and set off on its journey to us:
1507:. Although for some limited choices of parameters (see below) the comoving distance integral has a closed analytic form, in general—and specifically for the
721:
2947:
to the circumference of a circle at the present time going through the sun and centred on the distant object, multiplied by 360°. However, objects beyond a
3389:
2141:
2265:
A comparison of cosmological distance measures, from redshift zero to redshift of 0.5. The background cosmology is Hubble parameter 72 km/s/Mpc,
5227:
calculates the different distance measures as a function of cosmological model and redshift, and generates plots for the model from redshift 0 to 20.
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1373:
4960:
893:
We first give formulas for several distance measures, and then describe them in more detail further down. Defining the "Hubble distance" as
455:
4782:
4251:
5190:
I.M.H. Etherington, “LX. On the
Definition of Distance in General Relativity”, Philosophical Magazine, Vol. 15, S. 7 (1933), pp. 761-773.
1985:
1283:{\displaystyle E(z)={\frac {H(z)}{H_{0}}}={\sqrt {\Omega _{r}(1+z)^{4}+\Omega _{m}(1+z)^{3}+\Omega _{k}(1+z)^{2}+\Omega _{\Lambda }}}}
5085:
Light travel distance was calculated from redshift value using the UCLA Cosmological
Calculator, with parameters values as of 2018: H
5044:
Light travel distance was calculated from redshift value using the UCLA Cosmological
Calculator, with parameters values as of 2015: H
4307:
4285:
2804:
2782:
2698:
2672:
664:
119:
53:
4125:
should use the measured redshift, and another correction should be made for the peculiar velocity of the object by multiplying by
714:
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297:
100:
4289:
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measures the parallax of the brightest stars with a precision of 7 microarcseconds), so the parallax of galaxies outside our
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659:
373:
72:
57:
2064:
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2351:
1057:
302:
225:
5245:
3783:
79:
5240:
4469:
4416:
770:
707:
683:
230:
2661:
4635:
2833:), defined by the cosmic microwave background. The other is the actual redshift measured, which depends both on the
4940:
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When accounting for the earth's peculiar velocity, the redshift that would pertain in that case should be used for
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When accounting for the earth's peculiar velocity, the redshift that would pertain in that case should be used but
449:
429:
237:
182:
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86:
46:
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275:
3108:
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994:{\displaystyle d_{H}={\frac {c}{H_{0}}}\approx 3000h^{-1}{\text{Mpc}}\approx 9.26\cdot 10^{25}h^{-1}{\text{m}}}
833:
444:
209:
5221:
explains in detail how to calculate the different distance measures as a function of world model and redshift.
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2462:
2268:
1295:
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68:
4128:
3823:
3582:
1515:. Cosmologists commonly use the following measures for distances from the observer to an object at redshift
412:
292:
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In accord with our present understanding of cosmology, these measures are calculated within the context of
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2963:
2846:
1503:
The formula for comoving distance, which serves as the basis for most of the other formulas, involves an
1512:
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1338:
617:
419:
361:
4589:
Note that the comoving distance is recovered from the transverse comoving distance by taking the limit
2261:
4715:
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781:
of the quasar, galaxy, etc.). The distance measures discussed here all reduce to the common notion of
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778:
630:
602:
424:
133:
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3559:
1679:
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1101:
562:
522:
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439:
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383:
287:
177:
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towards an object, at any distance, the angular diameter of that object decreases by a factor of
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Proper distance roughly corresponds to where a distant object would be at a specific moment of
812:. The expressions for these distances are most practical when written as functions of redshift
4956:
4944:
4933:
4515:
4015:
3516:
2944:
2885:
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887:
612:
93:
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of a distant object is known, we can calculate its luminosity distance by measuring the flux
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695:
507:
497:
482:
333:
202:
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4908:
2925:), whereas the proper distance is what a measurement at constant cosmic time would yield.
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263:
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is the time that it took light to reach the observer from the object multiplied by the
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3015:
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17:
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are normalized values of the present radiation energy density, matter density, and "
832:, since redshift is always the observable. They can also be written as functions of
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There are a few different definitions of "distance" in cosmology which are all
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between fundamental observers, i.e. observers that are both moving with the
537:
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that would pertain if neither the object nor we had a peculiar velocity.
3379:{\displaystyle d_{C}(z)=d_{H}\Omega _{m}^{-1/3}\Omega _{\Lambda }^{-1/6}}
2929:
1504:
809:
762:
746:
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270:
172:
165:
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There are websites for calculating light-travel distance from redshift.
1435:{\displaystyle \Omega _{k}=1-\Omega _{r}-\Omega _{m}-\Omega _{\Lambda }}
4292: in this section. Unsourced material may be challenged and removed.
2789: in this section. Unsourced material may be challenged and removed.
155:
27:
Definitions for distance between two objects or events in the universe
5149:
4888:
3456:{\displaystyle f(x)\equiv \int _{0}^{x}{\frac {dx}{\sqrt {x^{3}+1}}}}
2251:{\displaystyle d_{T}(z)=d_{H}\int _{0}^{z}{\frac {dz'}{(1+z')E(z')}}}
766:
758:
2822:
In real observations, the movement of the Earth with respect to the
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of the object observed and on their peculiar velocity. Since the
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observable, but is more convenient for calculations (such as the
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4369:
There is a closed-form solution of the light-travel distance if
5108:
4998:
4012:, which turns out to be equivalent to the expression above for
2966:
for the integral in the definition of the comoving distance if
1634:{\displaystyle d_{C}(z)=d_{H}\int _{0}^{z}{\frac {dz'}{E(z')}}}
4261:
3465:
The comoving distance should be calculated using the value of
2758:
2644:
29:
4056:, which were first used to discover the acceleration of the
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made use of galaxies up to a redshift of a bit over 0.003 (
1964:
4622:, such that the two distance measures are equivalent in a
2841:
is moving at around 370 km/s in a direction between
5224:
4976:
David W. Hogg (2000). "Distance measures in cosmology".
890:
is assumed to be negligible unless specified otherwise.
5225:
iCosmos: Cosmology
Calculator (With Graph Generation )
4131:
3958:
3826:
3105:. Our universe now seems to be closely represented by
2442:
chosen so that the sum of Omega parameters is 1.
773:(CMB) power spectrum) to another quantity that is not
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if the cosmological constant has the other sign). If
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1007:
899:
841:
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2602:{\displaystyle \Omega _{\rm {radiation}}=0.266/3454}
2408:{\displaystyle \Omega _{\rm {radiation}}=0.266/3454}
1366:
density", respectively (the latter representing the
769:, or the angular size of the acoustic peaks in the
60:. Unsourced material may be challenged and removed.
5215:compares different cosmological distance measures.
4932:
4841:
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3143:
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3004:
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2743:
2723:
2636:chosen so that the sum of Omega parameters is one.
2628:
2601:
2534:
2484:
2434:
2407:
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2290:
2250:
2126:
2049:
1970:
1633:
1527:
1492:
1434:
1354:
1327:
1282:
1085:
1044:
1013:
993:
876:
824:
5114:International Centre for Radio Astronomy Research
5004:International Centre for Radio Astronomy Research
4048:. This quantity is important for measurements of
4640:
4505:{\displaystyle \Omega _{r}=\Omega _{\Lambda }=0}
2050:{\displaystyle d_{A}(z)={\frac {d_{M}(z)}{1+z}}}
4685:{\displaystyle \lim _{z\to \infty }d_{T}(z)/c}
4926:
4924:
4250:is the measured redshift, in accordance with
3778:. This is commonly used to observe so called
715:
8:
5251:Length, distance, or range measuring devices
4325:
4321:
2951:have parallax too small to be measured (the
2535:{\displaystyle \Omega _{\rm {matter}}=0.266}
2341:{\displaystyle \Omega _{\rm {matter}}=0.266}
2679:. Unsourced material may be challenged and
796:solution is used to describe the universe.
4904:Friedmann–Lemaître–Robertson–Walker metric
3536:Two comoving objects at constant redshift
3144:{\displaystyle \Omega _{r}=\Omega _{k}=0.}
722:
708:
322:
196:
154:
138:
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4833:
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4512:then there is a closed-form solution for
4490:
4477:
4471:
4447:
4445:
4425:
4423:
4408:{\displaystyle \Omega _{r}=\Omega _{m}=0}
4393:
4380:
4374:
4342:
4336:
4308:Learn how and when to remove this message
4227:
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3800:
3794:
3771:{\displaystyle d_{A}(z)=x/\delta \theta }
3757:
3736:
3730:
3707:
3687:
3667:
3632:
3626:
3621:, where the transverse comoving distance
3596:
3584:
3579:on the sky are said to have the distance
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3017:
3005:{\displaystyle \Omega _{r}=\Omega _{m}=0}
2990:
2977:
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2901:
2895:
2854:
2805:Learn how and when to remove this message
2736:
2716:
2699:Learn how and when to remove this message
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120:Learn how and when to remove this message
4005:{\textstyle d_{L}(z)={\sqrt {L/4\pi S}}}
3519:, which can change over time due to the
2826:has an effect on the observed redshift.
2485:{\displaystyle \Omega _{\Lambda }=0.732}
2291:{\displaystyle \Omega _{\Lambda }=0.732}
1328:{\displaystyle \Omega _{r},\Omega _{m},}
1104:, we also define a dimensionless Hubble
4920:
4193:{\textstyle {\sqrt {(1+v/c)/(1-v/c)}},}
3888:{\textstyle {\sqrt {(1+v/c)/(1-v/c)}}.}
353:
325:
217:
146:
4692:, and the time elapsed since redshift
3614:{\displaystyle \delta \theta d_{M}(z)}
2127:{\displaystyle d_{L}(z)=(1+z)d_{M}(z)}
1060:, all the distances are asymptotic to
886:In the remainder of this article, the
4632:The age of the universe then becomes
3725:has the angular diameter distance of
3012:or, by substituting the scale factor
745:between two objects or events in the
7:
5213:'The Distance Scale of the Universe'
4842:{\displaystyle d_{L}=(1+z)^{2}d_{A}}
4290:adding citations to reliable sources
3098:{\displaystyle \Omega _{\Lambda }=0}
2787:adding citations to reliable sources
2677:adding citations to reliable sources
58:adding citations to reliable sources
1052:is the Hubble parameter today, and
794:Friedmann–Lemaître–Robertson–Walker
749:. They are often used to tie some
5177:=0.6847 (see Table/Planck2018 at "
5126:ICRAR Cosmology Calculator - Set H
5052:=0.3089 (see Table/Planck2015 at "
4650:
4597:
4491:
4487:
4474:
4390:
4377:
4362:. For instance, the radius of the
3702:that appears to have angular size
3347:
3343:
3328:
3289:
3285:
3270:
3221:
3217:
3191:
3126:
3113:
3084:
3080:
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2974:
2617:
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1946:
1891:
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1696:
1427:
1423:
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1397:
1378:
1355:{\displaystyle \Omega _{\Lambda }}
1347:
1343:
1313:
1300:
1273:
1269:
1234:
1199:
1164:
450:2dF Galaxy Redshift Survey ("2dF")
25:
5165:KEMP Cosmology Calculator - Set H
5134:=0.315 (see Table/Planck2018 at "
5093:=0.315 (see Table/Planck2018 at "
4783:Etherington's reciprocity theorem
4252:Etherington's reciprocity theorem
665:Timeline of cosmological theories
430:Cosmic Background Explorer (COBE)
5219:'Distance measures in cosmology'
4935:Principles of Physical Cosmology
4858:
4776:
4767:{\displaystyle t(z)=d_{T}(z)/c.}
4615:{\displaystyle \Omega _{k}\to 0}
4266:
3782:, for example in the context of
2763:
2649:
741:to give a natural notion of the
689:
678:
677:
34:
4464:inverse trigonometric functions
4455:{\displaystyle {\text{arsinh}}}
4433:{\displaystyle {\text{arcosh}}}
4277:needs additional citations for
3556:that are separated by an angle
2774:needs additional citations for
1535:along the line of sight (LOS):
445:Sloan Digital Sky Survey (SDSS)
298:Future of an expanding universe
45:needs additional citations for
5150:"KEMPNER Cosmology Calculator"
5068:"UCLA Cosmological Calculator"
5027:"UCLA Cosmological Calculator"
4820:
4807:
4777:Etherington's distance duality
4750:
4744:
4728:
4722:
4671:
4665:
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4571:
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4134:
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4100:
4035:
4029:
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3969:
3877:
3857:
3849:
3829:
3748:
3742:
3718:{\displaystyle \delta \theta }
3608:
3602:
3572:{\displaystyle \delta \theta }
3402:
3396:
3373:
3370:
3353:
3324:
3321:
3312:
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3251:
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2155:
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1558:
1493:{\displaystyle H(z)=H_{0}E(z)}
1487:
1481:
1462:
1456:
1442:determines the curvature. The
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1243:
1221:
1208:
1186:
1173:
1142:
1136:
1124:
1118:
868:
856:
660:History of the Big Bang theory
456:Wilkinson Microwave Anisotropy
1:
4879:Comoving and proper distances
2959:is too small to be measured.
1644:Transverse comoving distance:
1511:—we can only find a solution
1058:dimensionless Hubble constant
652:Discovery of cosmic microwave
303:Ultimate fate of the universe
5109:"ICRAR Cosmology Calculator"
4417:inverse hyperbolic functions
3784:baryon acoustic oscillations
3532:Transverse comoving distance
1446:at a given redshift is then
1086:{\displaystyle z\cdot d_{H}}
5179:Lambda-CDM model#Parameters
5136:Lambda-CDM model#Parameters
5095:Lambda-CDM model#Parameters
5054:Lambda-CDM model#Parameters
2629:{\displaystyle \Omega _{k}}
2435:{\displaystyle \Omega _{k}}
771:cosmic microwave background
420:Black Hole Initiative (BHI)
5267:
4941:Princeton University Press
4931:Peebles, P. J. E. (1993).
4780:
4239:{\displaystyle (1+z)^{2},}
3902:
3655:
3648:is defined appropriately.
2883:
1981:Angular diameter distance:
1509:parameters of our universe
877:{\displaystyle a=1/(1+z).}
785:distance at low redshift.
183:Chronology of the universe
131:
4580:{\displaystyle z(d_{T}).}
4058:expansion of the universe
3658:Angular diameter distance
3652:Angular diameter distance
3521:expansion of the universe
808:one to another for small
276:Expansion of the universe
5148:Kempner, Joshua (2022).
4541:{\displaystyle d_{T}(z)}
4041:{\displaystyle d_{L}(z)}
3501:{\displaystyle d=ad_{C}}
440:Planck space observatory
226:Gravitational wave (GWB)
132:Not to be confused with
3151:In this case, we have:
3065:{\displaystyle 1/(1+z)}
2641:Alternative terminology
293:Inhomogeneous cosmology
5202:Academic Press (2003).
4999:"Cosmology Calculator"
4899:Cosmic distance ladder
4843:
4768:
4706:
4686:
4616:
4581:
4542:
4506:
4456:
4434:
4409:
4352:
4240:
4194:
4119:
4087:
4086:{\displaystyle d_{M},}
4042:
4006:
3946:
3926:
3889:
3810:
3772:
3719:
3696:
3676:
3642:
3615:
3573:
3550:
3502:
3457:
3380:
3145:
3099:
3066:
3026:
3006:
2964:closed-form expression
2911:
2890:The comoving distance
2869:
2745:
2725:
2637:
2630:
2603:
2536:
2486:
2451:
2436:
2409:
2342:
2292:
2252:
2137:Light-travel distance:
2128:
2051:
1972:
1635:
1529:
1494:
1436:
1356:
1329:
1284:
1087:
1046:
1015:
995:
878:
826:
753:quantity (such as the
4844:
4769:
4707:
4687:
4617:
4582:
4543:
4507:
4457:
4435:
4410:
4353:
4351:{\displaystyle d_{T}}
4258:Light-travel distance
4241:
4195:
4120:
4118:{\displaystyle (1+z)}
4088:
4043:
4007:
3947:
3927:
3890:
3811:
3809:{\displaystyle d_{A}}
3773:
3720:
3697:
3677:
3643:
3641:{\displaystyle d_{M}}
3616:
3574:
3551:
3503:
3458:
3381:
3146:
3100:
3067:
3027:
3007:
2912:
2910:{\displaystyle d_{C}}
2870:
2746:
2726:
2724:{\displaystyle \chi }
2631:
2604:
2537:
2487:
2457:
2437:
2410:
2343:
2293:
2264:
2253:
2129:
2052:
1973:
1636:
1530:
1495:
1437:
1368:cosmological constant
1357:
1330:
1285:
1088:
1047:
1045:{\displaystyle H_{0}}
1016:
996:
879:
827:
384:Large-scale structure
362:Shape of the universe
18:Light travel distance
4791:
4716:
4696:
4636:
4593:
4552:
4516:
4470:
4444:
4422:
4373:
4335:
4286:improve this article
4208:
4129:
4097:
4067:
4016:
3956:
3936:
3916:
3824:
3793:
3729:
3706:
3686:
3666:
3625:
3583:
3560:
3540:
3476:
3390:
3155:
3109:
3076:
3036:
3016:
2970:
2953:Gaia space telescope
2894:
2853:
2783:improve this article
2735:
2715:
2673:improve this section
2613:
2546:
2496:
2463:
2419:
2352:
2302:
2269:
2142:
2065:
2060:Luminosity distance:
1986:
1649:
1545:
1519:
1450:
1374:
1339:
1296:
1112:
1064:
1029:
1005:
897:
839:
816:
779:comoving coordinates
696:Astronomy portal
654:background radiation
631:List of cosmologists
134:Distance measurement
54:improve this article
5246:Physical quantities
4953:1993ppc..book.....P
4884:Friedmann equations
4364:observable universe
3905:Luminosity distance
3899:Luminosity distance
3422:
3241:
3215:
2868:{\displaystyle 1+z}
2191:
1594:
1102:Friedmann equations
396:Structure formation
288:Friedmann equations
178:Age of the universe
142:Part of a series on
5241:Physical cosmology
4983:astro-ph/9905116v4
4894:Physical cosmology
4839:
4764:
4702:
4682:
4654:
4612:
4577:
4538:
4502:
4452:
4430:
4405:
4348:
4236:
4190:
4115:
4083:
4054:type Ia supernovae
4038:
4002:
3942:
3922:
3885:
3806:
3768:
3715:
3692:
3672:
3662:An object of size
3638:
3611:
3569:
3546:
3498:
3453:
3408:
3376:
3216:
3190:
3141:
3095:
3062:
3022:
3002:
2930:standard cosmology
2907:
2865:
2741:
2721:
2638:
2626:
2599:
2532:
2482:
2452:
2432:
2405:
2338:
2288:
2248:
2177:
2124:
2047:
1968:
1963:
1631:
1580:
1540:Comoving distance:
1525:
1490:
1432:
1352:
1325:
1280:
1083:
1042:
1011:
991:
874:
822:
790:general relativity
739:physical cosmology
435:Dark Energy Survey
379:Large quasar group
148:Physical cosmology
69:"Distance measure"
5200:Modern Cosmology.
5173:=0.315, and Omega
4962:978-0-691-01933-8
4705:{\displaystyle z}
4639:
4450:
4428:
4326:lookback distance
4318:
4317:
4310:
4185:
4000:
3945:{\displaystyle S}
3925:{\displaystyle L}
3909:If the intrinsic
3880:
3695:{\displaystyle z}
3675:{\displaystyle x}
3549:{\displaystyle z}
3525:Comoving distance
3517:cosmological time
3451:
3450:
3025:{\displaystyle a}
2945:astronomical unit
2934:comoving distance
2886:Comoving distance
2880:Comoving distance
2849:, this decreases
2835:peculiar velocity
2818:Peculiar velocity
2815:
2814:
2807:
2744:{\displaystyle r}
2709:
2708:
2701:
2246:
2045:
1937:
1905:
1868:
1867:
1765:
1733:
1706:
1705:
1629:
1528:{\displaystyle z}
1278:
1156:
1100:According to the
1014:{\displaystyle c}
989:
952:
928:
888:peculiar velocity
825:{\displaystyle z}
735:Distance measures
732:
731:
403:
402:
245:
244:
130:
129:
122:
104:
16:(Redirected from
5258:
5198:Scott Dodelson,
5191:
5188:
5182:
5164:
5162:
5160:
5145:
5139:
5125:
5123:
5121:
5104:
5098:
5084:
5082:
5080:
5063:
5057:
5048:=67.74 and Omega
5043:
5041:
5039:
5022:
5016:
5015:
5013:
5011:
4994:
4988:
4987:
4985:
4973:
4967:
4966:
4938:
4928:
4868:
4863:
4862:
4861:
4848:
4846:
4845:
4840:
4838:
4837:
4828:
4827:
4803:
4802:
4773:
4771:
4770:
4765:
4757:
4743:
4742:
4711:
4709:
4708:
4703:
4691:
4689:
4688:
4683:
4678:
4664:
4663:
4653:
4621:
4619:
4618:
4613:
4605:
4604:
4586:
4584:
4583:
4578:
4570:
4569:
4547:
4545:
4544:
4539:
4528:
4527:
4511:
4509:
4508:
4503:
4495:
4494:
4482:
4481:
4461:
4459:
4458:
4453:
4451:
4448:
4439:
4437:
4436:
4431:
4429:
4426:
4414:
4412:
4411:
4406:
4398:
4397:
4385:
4384:
4357:
4355:
4354:
4349:
4347:
4346:
4320:(also known as "
4313:
4306:
4302:
4299:
4293:
4270:
4262:
4249:
4245:
4243:
4242:
4237:
4232:
4231:
4203:
4199:
4197:
4196:
4191:
4186:
4178:
4161:
4150:
4133:
4124:
4122:
4121:
4116:
4092:
4090:
4089:
4084:
4079:
4078:
4050:standard candles
4047:
4045:
4044:
4039:
4028:
4027:
4011:
4009:
4008:
4003:
4001:
3990:
3982:
3968:
3967:
3951:
3949:
3948:
3943:
3931:
3929:
3928:
3923:
3894:
3892:
3891:
3886:
3881:
3873:
3856:
3845:
3828:
3819:
3815:
3813:
3812:
3807:
3805:
3804:
3777:
3775:
3774:
3769:
3761:
3741:
3740:
3724:
3722:
3721:
3716:
3701:
3699:
3698:
3693:
3681:
3679:
3678:
3673:
3647:
3645:
3644:
3639:
3637:
3636:
3620:
3618:
3617:
3612:
3601:
3600:
3578:
3576:
3575:
3570:
3555:
3553:
3552:
3547:
3507:
3505:
3504:
3499:
3497:
3496:
3468:
3462:
3460:
3459:
3454:
3452:
3443:
3442:
3433:
3432:
3424:
3421:
3416:
3385:
3383:
3382:
3377:
3369:
3368:
3364:
3351:
3350:
3341:
3336:
3335:
3311:
3310:
3306:
3293:
3292:
3283:
3278:
3277:
3240:
3236:
3224:
3214:
3210:
3198:
3189:
3188:
3167:
3166:
3150:
3148:
3147:
3142:
3134:
3133:
3121:
3120:
3104:
3102:
3101:
3096:
3088:
3087:
3071:
3069:
3068:
3063:
3046:
3031:
3029:
3028:
3023:
3011:
3009:
3008:
3003:
2995:
2994:
2982:
2981:
2916:
2914:
2913:
2908:
2906:
2905:
2874:
2872:
2871:
2866:
2810:
2803:
2799:
2796:
2790:
2767:
2759:
2750:
2748:
2747:
2742:
2730:
2728:
2727:
2722:
2704:
2697:
2693:
2690:
2684:
2653:
2645:
2635:
2633:
2632:
2627:
2625:
2624:
2608:
2606:
2605:
2600:
2595:
2584:
2583:
2582:
2541:
2539:
2538:
2533:
2525:
2524:
2523:
2491:
2489:
2488:
2483:
2475:
2474:
2441:
2439:
2438:
2433:
2431:
2430:
2414:
2412:
2411:
2406:
2401:
2390:
2389:
2388:
2347:
2345:
2344:
2339:
2331:
2330:
2329:
2297:
2295:
2294:
2289:
2281:
2280:
2257:
2255:
2254:
2249:
2247:
2245:
2241:
2224:
2206:
2205:
2193:
2190:
2185:
2176:
2175:
2154:
2153:
2133:
2131:
2130:
2125:
2114:
2113:
2077:
2076:
2056:
2054:
2053:
2048:
2046:
2044:
2033:
2023:
2022:
2012:
1998:
1997:
1977:
1975:
1974:
1969:
1967:
1966:
1954:
1953:
1942:
1938:
1936:
1935:
1926:
1916:
1915:
1906:
1904:
1899:
1898:
1889:
1884:
1881:
1869:
1866:
1861:
1860:
1851:
1846:
1845:
1844:
1835:
1823:
1822:
1802:
1801:
1782:
1781:
1770:
1766:
1764:
1763:
1754:
1744:
1743:
1734:
1732:
1731:
1722:
1719:
1707:
1704:
1703:
1694:
1693:
1692:
1683:
1661:
1660:
1640:
1638:
1637:
1632:
1630:
1628:
1624:
1609:
1608:
1596:
1593:
1588:
1579:
1578:
1557:
1556:
1534:
1532:
1531:
1526:
1499:
1497:
1496:
1491:
1477:
1476:
1444:Hubble parameter
1441:
1439:
1438:
1433:
1431:
1430:
1418:
1417:
1405:
1404:
1386:
1385:
1361:
1359:
1358:
1353:
1351:
1350:
1334:
1332:
1331:
1326:
1321:
1320:
1308:
1307:
1289:
1287:
1286:
1281:
1279:
1277:
1276:
1264:
1263:
1242:
1241:
1229:
1228:
1207:
1206:
1194:
1193:
1172:
1171:
1162:
1157:
1155:
1154:
1145:
1131:
1096:
1092:
1090:
1089:
1084:
1082:
1081:
1055:
1051:
1049:
1048:
1043:
1041:
1040:
1020:
1018:
1017:
1012:
1000:
998:
997:
992:
990:
987:
985:
984:
972:
971:
953:
950:
948:
947:
929:
927:
926:
914:
909:
908:
883:
881:
880:
875:
855:
831:
829:
828:
823:
724:
717:
710:
694:
693:
692:
681:
680:
374:Galaxy formation
334:Lambda-CDM model
323:
315:Components
197:
158:
139:
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
5266:
5265:
5261:
5260:
5259:
5257:
5256:
5255:
5231:
5230:
5209:
5195:
5194:
5189:
5185:
5176:
5172:
5168:
5158:
5156:
5147:
5146:
5142:
5133:
5130:=67.4 and Omega
5129:
5119:
5117:
5106:
5105:
5101:
5092:
5089:=67.4 and Omega
5088:
5078:
5076:
5065:
5064:
5060:
5051:
5047:
5037:
5035:
5024:
5023:
5019:
5009:
5007:
4996:
4995:
4991:
4975:
4974:
4970:
4963:
4930:
4929:
4922:
4917:
4909:Subatomic scale
4864:
4859:
4857:
4854:
4829:
4819:
4794:
4789:
4788:
4785:
4779:
4734:
4714:
4713:
4694:
4693:
4655:
4634:
4633:
4596:
4591:
4590:
4561:
4550:
4549:
4519:
4514:
4513:
4486:
4473:
4468:
4467:
4442:
4441:
4420:
4419:
4389:
4376:
4371:
4370:
4338:
4333:
4332:
4314:
4303:
4297:
4294:
4283:
4271:
4260:
4247:
4223:
4206:
4205:
4201:
4127:
4126:
4095:
4094:
4093:but the factor
4070:
4065:
4064:
4019:
4014:
4013:
3959:
3954:
3953:
3934:
3933:
3914:
3913:
3907:
3901:
3822:
3821:
3817:
3796:
3791:
3790:
3780:standard rulers
3732:
3727:
3726:
3704:
3703:
3684:
3683:
3664:
3663:
3660:
3654:
3628:
3623:
3622:
3592:
3581:
3580:
3558:
3557:
3538:
3537:
3534:
3513:
3511:Proper distance
3488:
3474:
3473:
3466:
3434:
3425:
3388:
3387:
3352:
3342:
3327:
3294:
3284:
3269:
3180:
3158:
3153:
3152:
3125:
3112:
3107:
3106:
3079:
3074:
3073:
3034:
3033:
3014:
3013:
2986:
2973:
2968:
2967:
2938:proper distance
2897:
2892:
2891:
2888:
2882:
2851:
2850:
2820:
2811:
2800:
2794:
2791:
2780:
2768:
2757:
2733:
2732:
2713:
2712:
2705:
2694:
2688:
2685:
2670:
2654:
2643:
2616:
2611:
2610:
2549:
2544:
2543:
2499:
2494:
2493:
2466:
2461:
2460:
2422:
2417:
2416:
2355:
2350:
2349:
2305:
2300:
2299:
2272:
2267:
2266:
2234:
2217:
2207:
2198:
2194:
2167:
2145:
2140:
2139:
2105:
2068:
2063:
2062:
2034:
2014:
2013:
1989:
1984:
1983:
1962:
1961:
1945:
1943:
1927:
1907:
1890:
1882:
1876:
1852:
1836:
1831:
1830:
1814:
1812:
1793:
1790:
1789:
1773:
1771:
1755:
1735:
1723:
1720:
1714:
1695:
1684:
1675:
1652:
1647:
1646:
1617:
1610:
1601:
1597:
1570:
1548:
1543:
1542:
1517:
1516:
1468:
1448:
1447:
1422:
1409:
1396:
1377:
1372:
1371:
1342:
1337:
1336:
1312:
1299:
1294:
1293:
1268:
1255:
1233:
1220:
1198:
1185:
1163:
1146:
1132:
1110:
1109:
1094:
1073:
1062:
1061:
1053:
1032:
1027:
1026:
1003:
1002:
973:
963:
936:
918:
900:
895:
894:
837:
836:
814:
813:
802:
728:
690:
688:
670:
669:
656:
653:
646:
644:Subject history
636:
635:
627:
472:
464:
463:
460:
457:
415:
405:
404:
367:Galaxy filament
320:
308:
307:
259:
254:Expansion
247:
246:
231:Microwave (CMB)
210:Nucleosynthesis
194:
137:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
5264:
5262:
5254:
5253:
5248:
5243:
5233:
5232:
5229:
5228:
5222:
5216:
5208:
5207:External links
5205:
5204:
5203:
5193:
5192:
5183:
5174:
5170:
5166:
5140:
5131:
5127:
5107:Staff (2022).
5099:
5090:
5086:
5066:Staff (2018).
5058:
5049:
5045:
5025:Staff (2015).
5017:
4997:Staff (2022).
4989:
4968:
4961:
4919:
4918:
4916:
4913:
4912:
4911:
4906:
4901:
4896:
4891:
4886:
4881:
4876:
4870:
4869:
4853:
4850:
4836:
4832:
4826:
4822:
4818:
4815:
4812:
4809:
4806:
4801:
4797:
4781:Main article:
4778:
4775:
4763:
4760:
4756:
4752:
4749:
4746:
4741:
4737:
4733:
4730:
4727:
4724:
4721:
4712:until now is:
4701:
4681:
4677:
4673:
4670:
4667:
4662:
4658:
4652:
4649:
4646:
4642:
4611:
4608:
4603:
4599:
4576:
4573:
4568:
4564:
4560:
4557:
4537:
4534:
4531:
4526:
4522:
4501:
4498:
4493:
4489:
4485:
4480:
4476:
4462:(or involving
4415:involving the
4404:
4401:
4396:
4392:
4388:
4383:
4379:
4360:speed of light
4345:
4341:
4331:This distance
4316:
4315:
4274:
4272:
4265:
4259:
4256:
4235:
4230:
4226:
4222:
4219:
4216:
4213:
4189:
4184:
4181:
4177:
4173:
4170:
4167:
4164:
4160:
4156:
4153:
4149:
4145:
4142:
4139:
4136:
4114:
4111:
4108:
4105:
4102:
4082:
4077:
4073:
4037:
4034:
4031:
4026:
4022:
3999:
3996:
3993:
3989:
3985:
3980:
3977:
3974:
3971:
3966:
3962:
3952:and determine
3941:
3921:
3903:Main article:
3900:
3897:
3884:
3879:
3876:
3872:
3868:
3865:
3862:
3859:
3855:
3851:
3848:
3844:
3840:
3837:
3834:
3831:
3803:
3799:
3767:
3764:
3760:
3756:
3753:
3750:
3747:
3744:
3739:
3735:
3714:
3711:
3691:
3671:
3656:Main article:
3653:
3650:
3635:
3631:
3610:
3607:
3604:
3599:
3595:
3591:
3588:
3568:
3565:
3545:
3533:
3530:
3512:
3509:
3495:
3491:
3487:
3484:
3481:
3449:
3446:
3441:
3437:
3431:
3428:
3420:
3415:
3411:
3407:
3404:
3401:
3398:
3395:
3375:
3372:
3367:
3363:
3359:
3355:
3349:
3345:
3340:
3334:
3330:
3326:
3323:
3320:
3317:
3314:
3309:
3305:
3301:
3297:
3291:
3287:
3282:
3276:
3272:
3268:
3265:
3262:
3259:
3256:
3253:
3250:
3247:
3244:
3239:
3235:
3231:
3228:
3223:
3219:
3213:
3209:
3205:
3202:
3197:
3193:
3187:
3183:
3179:
3176:
3173:
3170:
3165:
3161:
3140:
3137:
3132:
3128:
3124:
3119:
3115:
3094:
3091:
3086:
3082:
3061:
3058:
3055:
3052:
3049:
3045:
3041:
3021:
3001:
2998:
2993:
2989:
2985:
2980:
2976:
2904:
2900:
2884:Main article:
2881:
2878:
2864:
2861:
2858:
2819:
2816:
2813:
2812:
2771:
2769:
2762:
2756:
2753:
2740:
2720:
2707:
2706:
2657:
2655:
2648:
2642:
2639:
2623:
2619:
2598:
2594:
2590:
2587:
2581:
2578:
2575:
2572:
2569:
2566:
2563:
2560:
2557:
2552:
2531:
2528:
2522:
2519:
2516:
2513:
2510:
2507:
2502:
2481:
2478:
2473:
2469:
2429:
2425:
2404:
2400:
2396:
2393:
2387:
2384:
2381:
2378:
2375:
2372:
2369:
2366:
2363:
2358:
2337:
2334:
2328:
2325:
2322:
2319:
2316:
2313:
2308:
2287:
2284:
2279:
2275:
2259:
2258:
2244:
2240:
2237:
2233:
2230:
2227:
2223:
2220:
2216:
2213:
2210:
2204:
2201:
2197:
2189:
2184:
2180:
2174:
2170:
2166:
2163:
2160:
2157:
2152:
2148:
2134:
2123:
2120:
2117:
2112:
2108:
2104:
2101:
2098:
2095:
2092:
2089:
2086:
2083:
2080:
2075:
2071:
2057:
2043:
2040:
2037:
2032:
2029:
2026:
2021:
2017:
2010:
2007:
2004:
2001:
1996:
1992:
1978:
1965:
1960:
1957:
1952:
1948:
1944:
1941:
1934:
1930:
1925:
1922:
1919:
1914:
1910:
1903:
1897:
1893:
1888:
1879:
1875:
1872:
1865:
1859:
1855:
1850:
1843:
1839:
1833:
1832:
1829:
1826:
1821:
1817:
1813:
1811:
1808:
1805:
1800:
1796:
1792:
1791:
1788:
1785:
1780:
1776:
1772:
1769:
1762:
1758:
1753:
1750:
1747:
1742:
1738:
1730:
1726:
1717:
1713:
1710:
1702:
1698:
1691:
1687:
1681:
1680:
1678:
1673:
1670:
1667:
1664:
1659:
1655:
1641:
1627:
1623:
1620:
1616:
1613:
1607:
1604:
1600:
1592:
1587:
1583:
1577:
1573:
1569:
1566:
1563:
1560:
1555:
1551:
1524:
1489:
1486:
1483:
1480:
1475:
1471:
1467:
1464:
1461:
1458:
1455:
1429:
1425:
1421:
1416:
1412:
1408:
1403:
1399:
1395:
1392:
1389:
1384:
1380:
1349:
1345:
1324:
1319:
1315:
1311:
1306:
1302:
1275:
1271:
1267:
1262:
1258:
1254:
1251:
1248:
1245:
1240:
1236:
1232:
1227:
1223:
1219:
1216:
1213:
1210:
1205:
1201:
1197:
1192:
1188:
1184:
1181:
1178:
1175:
1170:
1166:
1160:
1153:
1149:
1144:
1141:
1138:
1135:
1129:
1126:
1123:
1120:
1117:
1080:
1076:
1072:
1069:
1039:
1035:
1023:speed of light
1010:
983:
980:
976:
970:
966:
962:
959:
956:
946:
943:
939:
935:
932:
925:
921:
917:
912:
907:
903:
873:
870:
867:
864:
861:
858:
854:
850:
847:
844:
821:
801:
798:
730:
729:
727:
726:
719:
712:
704:
701:
700:
699:
698:
686:
672:
671:
668:
667:
662:
657:
650:
647:
642:
641:
638:
637:
634:
633:
626:
625:
620:
615:
610:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
555:
550:
545:
540:
535:
530:
525:
520:
515:
510:
505:
500:
495:
490:
485:
480:
474:
473:
470:
469:
466:
465:
462:
461:
454:
452:
447:
442:
437:
432:
427:
422:
416:
411:
410:
407:
406:
401:
400:
399:
398:
386:
381:
376:
364:
356:
355:
351:
350:
349:
348:
336:
328:
327:
321:
314:
313:
310:
309:
306:
305:
300:
295:
290:
278:
273:
260:
253:
252:
249:
248:
243:
242:
241:
240:
238:Neutrino (CNB)
228:
220:
219:
215:
214:
213:
212:
195:
193:Early universe
192:
191:
188:
187:
186:
185:
180:
175:
160:
159:
151:
150:
144:
143:
128:
127:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
5263:
5252:
5249:
5247:
5244:
5242:
5239:
5238:
5236:
5226:
5223:
5220:
5217:
5214:
5211:
5210:
5206:
5201:
5197:
5196:
5187:
5184:
5180:
5155:
5151:
5144:
5141:
5137:
5116:
5115:
5110:
5103:
5100:
5096:
5075:
5074:
5069:
5062:
5059:
5055:
5034:
5033:
5028:
5021:
5018:
5006:
5005:
5000:
4993:
4990:
4984:
4979:
4972:
4969:
4964:
4958:
4954:
4950:
4946:
4942:
4937:
4936:
4927:
4925:
4921:
4914:
4910:
4907:
4905:
4902:
4900:
4897:
4895:
4892:
4890:
4887:
4885:
4882:
4880:
4877:
4875:
4872:
4871:
4867:
4856:
4851:
4849:
4834:
4830:
4824:
4816:
4813:
4810:
4804:
4799:
4795:
4784:
4774:
4761:
4758:
4754:
4747:
4739:
4735:
4731:
4725:
4719:
4699:
4679:
4675:
4668:
4660:
4656:
4644:
4630:
4627:
4625:
4624:flat universe
4609:
4601:
4587:
4574:
4566:
4562:
4555:
4532:
4524:
4520:
4499:
4496:
4483:
4478:
4465:
4418:
4402:
4399:
4394:
4386:
4381:
4367:
4365:
4361:
4343:
4339:
4329:
4327:
4323:
4322:lookback time
4312:
4309:
4301:
4291:
4287:
4281:
4280:
4275:This section
4273:
4269:
4264:
4263:
4257:
4255:
4254:(see below).
4253:
4233:
4228:
4220:
4217:
4214:
4187:
4179:
4175:
4171:
4168:
4165:
4158:
4151:
4147:
4143:
4140:
4137:
4109:
4106:
4103:
4080:
4075:
4071:
4061:
4059:
4055:
4051:
4032:
4024:
4020:
3997:
3994:
3991:
3987:
3983:
3978:
3972:
3964:
3960:
3939:
3919:
3912:
3906:
3898:
3896:
3882:
3874:
3870:
3866:
3863:
3860:
3853:
3846:
3842:
3838:
3835:
3832:
3801:
3797:
3787:
3785:
3781:
3765:
3762:
3758:
3754:
3751:
3745:
3737:
3733:
3712:
3709:
3689:
3669:
3659:
3651:
3649:
3633:
3629:
3605:
3597:
3593:
3589:
3586:
3566:
3563:
3543:
3531:
3529:
3526:
3522:
3518:
3510:
3508:
3493:
3489:
3485:
3482:
3479:
3470:
3463:
3447:
3444:
3439:
3435:
3429:
3426:
3418:
3413:
3409:
3405:
3399:
3393:
3365:
3361:
3357:
3338:
3332:
3318:
3315:
3307:
3303:
3299:
3280:
3274:
3260:
3257:
3254:
3245:
3237:
3233:
3229:
3226:
3211:
3207:
3203:
3200:
3195:
3185:
3181:
3177:
3171:
3163:
3159:
3138:
3135:
3130:
3122:
3117:
3092:
3089:
3056:
3053:
3050:
3043:
3039:
3019:
2999:
2996:
2991:
2983:
2978:
2965:
2960:
2958:
2954:
2950:
2946:
2941:
2939:
2935:
2931:
2926:
2924:
2920:
2902:
2898:
2887:
2879:
2877:
2862:
2859:
2856:
2848:
2844:
2840:
2836:
2832:
2827:
2825:
2817:
2809:
2806:
2798:
2788:
2784:
2778:
2777:
2772:This section
2770:
2766:
2761:
2760:
2754:
2752:
2738:
2718:
2703:
2700:
2692:
2682:
2678:
2674:
2668:
2667:
2663:
2658:This section
2656:
2652:
2647:
2646:
2640:
2621:
2596:
2592:
2588:
2585:
2529:
2526:
2479:
2476:
2456:
2449:
2445:
2427:
2402:
2398:
2394:
2391:
2335:
2332:
2285:
2282:
2263:
2238:
2235:
2228:
2221:
2218:
2214:
2211:
2202:
2199:
2195:
2187:
2182:
2178:
2172:
2168:
2164:
2158:
2150:
2146:
2138:
2135:
2118:
2110:
2106:
2099:
2096:
2093:
2087:
2081:
2073:
2069:
2061:
2058:
2041:
2038:
2035:
2027:
2019:
2015:
2008:
2002:
1994:
1990:
1982:
1979:
1958:
1955:
1950:
1939:
1932:
1928:
1920:
1912:
1908:
1895:
1877:
1873:
1870:
1857:
1841:
1837:
1827:
1824:
1819:
1806:
1798:
1794:
1786:
1783:
1778:
1767:
1760:
1756:
1748:
1740:
1736:
1728:
1715:
1711:
1708:
1700:
1689:
1685:
1676:
1671:
1665:
1657:
1653:
1645:
1642:
1621:
1618:
1611:
1605:
1602:
1598:
1590:
1585:
1581:
1575:
1571:
1567:
1561:
1553:
1549:
1541:
1538:
1537:
1536:
1522:
1514:
1510:
1506:
1501:
1484:
1478:
1473:
1469:
1465:
1459:
1453:
1445:
1419:
1414:
1406:
1401:
1393:
1390:
1387:
1382:
1369:
1365:
1322:
1317:
1309:
1304:
1290:
1265:
1260:
1252:
1249:
1246:
1238:
1230:
1225:
1217:
1214:
1211:
1203:
1195:
1190:
1182:
1179:
1176:
1168:
1158:
1151:
1147:
1139:
1133:
1127:
1121:
1115:
1107:
1103:
1098:
1078:
1074:
1070:
1067:
1059:
1037:
1033:
1024:
1008:
981:
978:
974:
968:
964:
960:
957:
954:
944:
941:
937:
933:
930:
923:
919:
915:
910:
905:
901:
891:
889:
884:
871:
865:
862:
859:
852:
848:
845:
842:
835:
819:
811:
807:
799:
797:
795:
791:
786:
784:
780:
776:
772:
768:
765:of a distant
764:
760:
757:of a distant
756:
752:
748:
744:
740:
736:
725:
720:
718:
713:
711:
706:
705:
703:
702:
697:
687:
685:
676:
675:
674:
673:
666:
663:
661:
658:
655:
649:
648:
645:
640:
639:
632:
629:
628:
624:
621:
619:
616:
614:
611:
609:
606:
604:
601:
599:
596:
594:
591:
589:
586:
584:
581:
579:
576:
574:
571:
569:
566:
564:
561:
559:
556:
554:
551:
549:
546:
544:
541:
539:
536:
534:
531:
529:
526:
524:
521:
519:
516:
514:
511:
509:
506:
504:
501:
499:
496:
494:
491:
489:
486:
484:
481:
479:
476:
475:
468:
467:
459:
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
423:
421:
418:
417:
414:
409:
408:
397:
394:
390:
387:
385:
382:
380:
377:
375:
372:
368:
365:
363:
360:
359:
358:
357:
352:
347:
344:
340:
337:
335:
332:
331:
330:
329:
324:
318:
312:
311:
304:
301:
299:
296:
294:
291:
289:
286:
282:
279:
277:
274:
272:
269:
265:
262:
261:
257:
251:
250:
239:
236:
232:
229:
227:
224:
223:
222:
221:
216:
211:
208:
204:
201:
200:
199:
198:
190:
189:
184:
181:
179:
176:
174:
171:
167:
164:
163:
162:
161:
157:
153:
152:
149:
145:
141:
140:
135:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
5199:
5186:
5169:=67.4, Omega
5157:. Retrieved
5153:
5143:
5118:. Retrieved
5112:
5102:
5077:. Retrieved
5071:
5061:
5036:. Retrieved
5030:
5020:
5008:. Retrieved
5002:
4992:
4971:
4934:
4866:Space portal
4786:
4631:
4628:
4588:
4548:but not for
4368:
4330:
4319:
4304:
4295:
4284:Please help
4279:verification
4276:
4062:
3908:
3788:
3682:at redshift
3661:
3535:
3524:
3514:
3471:
3464:
2961:
2942:
2937:
2933:
2927:
2922:
2889:
2839:Solar System
2828:
2821:
2801:
2792:
2781:Please help
2776:verification
2773:
2710:
2695:
2686:
2671:Please help
2659:
2444:Edwin Hubble
2136:
2059:
1980:
1643:
1539:
1502:
1291:
1105:
1099:
892:
885:
834:scale factor
803:
792:, where the
787:
774:
750:
737:are used in
734:
733:
458:Probe (WMAP)
392:
389:Reionization
370:
342:
316:
284:
267:
264:Hubble's law
255:
234:
206:
169:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
5154:Kempner.net
4943:. pp.
2962:There is a
2957:Local Group
2919:Hubble flow
2831:Hubble flow
2824:Hubble flow
1513:numerically
1364:dark energy
413:Experiments
346:Dark matter
339:Dark energy
281:FLRW metric
218:Backgrounds
5235:Categories
4915:References
4200:where now
3911:luminosity
2949:megaparsec
2448:Messier 60
1093:for small
806:asymptotic
755:luminosity
751:observable
493:Copernicus
471:Scientists
326:Components
80:newspapers
4651:∞
4648:→
4607:→
4598:Ω
4492:Λ
4488:Ω
4475:Ω
4391:Ω
4378:Ω
4169:−
3995:π
3864:−
3766:θ
3763:δ
3713:θ
3710:δ
3590:θ
3587:δ
3567:θ
3564:δ
3410:∫
3406:≡
3348:Λ
3344:Ω
3329:Ω
3316:−
3290:Λ
3286:Ω
3271:Ω
3227:−
3222:Λ
3218:Ω
3201:−
3192:Ω
3127:Ω
3114:Ω
3085:Λ
3081:Ω
2988:Ω
2975:Ω
2719:χ
2660:does not
2618:Ω
2551:Ω
2501:Ω
2472:Λ
2468:Ω
2424:Ω
2357:Ω
2307:Ω
2278:Λ
2274:Ω
2179:∫
1947:Ω
1892:Ω
1874:
1854:Ω
1816:Ω
1775:Ω
1725:Ω
1712:
1697:Ω
1582:∫
1428:Λ
1424:Ω
1420:−
1411:Ω
1407:−
1398:Ω
1394:−
1379:Ω
1348:Λ
1344:Ω
1314:Ω
1301:Ω
1274:Λ
1270:Ω
1235:Ω
1200:Ω
1165:Ω
1106:parameter
1071:⋅
979:−
961:⋅
955:≈
942:−
931:≈
810:redshifts
783:Euclidean
623:Zeldovich
523:Friedmann
498:de Sitter
425:BOOMERanG
354:Structure
319:Structure
203:Inflation
5159:6 August
5120:6 August
5079:6 August
5038:6 August
5010:4 August
4874:Big Bang
4852:See also
4298:May 2024
2795:May 2024
2689:May 2024
2239:′
2222:′
2203:′
1622:′
1606:′
1505:integral
800:Overview
775:directly
763:redshift
747:universe
743:distance
684:Category
603:Suntzeff
563:Lemaître
513:Einstein
478:Aaronson
271:Redshift
173:Universe
166:Big Bang
110:May 2024
4949:Bibcode
4945:310–320
2755:Details
2681:removed
2666:sources
1370:), and
1056:is the
1021:is the
608:Sunyaev
593:Schmidt
583:Penzias
578:Penrose
553:Huygens
543:Hawking
528:Galileo
94:scholar
4959:
4889:Parsec
4449:arsinh
4427:arcosh
4324:" or "
4246:where
3386:where
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2609:, and
2415:, and
1292:Here,
1001:where
767:galaxy
761:, the
759:quasar
682:
618:Wilson
613:Tolman
573:Newton
568:Mather
558:Kepler
548:Hubble
508:Ehlers
488:Alpher
483:Alfvén
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258:Future
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4978:arXiv
4052:like
3072:, if
2589:0.266
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2480:0.732
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2286:0.732
598:Smoot
588:Rubin
533:Gamow
518:Ellis
503:Dicke
101:JSTOR
87:books
5161:2022
5122:2022
5081:2022
5073:UCLA
5040:2022
5032:UCLA
5012:2022
4957:ISBN
3032:for
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