1914:
460:
The particle horizon recedes constantly as time passes and the conformal time grows. As such, the observed size of the universe always increases. Since proper distance at a given time is just comoving distance times the scale factor (with
768:
1505:
646:
1982:
378:
1149:
1398:
239:
2113:
1091:
2020:
1677:
457:
is not a physically meaningful time (this much time has not yet actually passed); though, as we will see, the particle horizon with which it is associated is a conceptually meaningful distance.
1031:
78:(approximately 13.8 billion light-years), but rather the speed of light times the conformal time. The existence, properties, and significance of a cosmological horizon depend on the particular
779:
278:
424:
887:
1228:
2472:
Margalef-Bentabol, Berta; Margalef-Bentabol, Juan; Cepa, Jordi (February 2013). "Evolution of the cosmological horizons in a universe with countably infinitely many state equations".
2152:
971:
1456:
1801:
1590:
505:
807:
455:
682:
1555:
1258:
907:
834:
115:
271:
1284:
689:
305:
1764:
1744:
1720:
1700:
1528:
1304:
1171:
927:
525:
162:
142:
1464:
1458:. Notice that the addition ranges over all possible partial constituents and in particular there can be countably infinitely many. With this notation we have:
782:
cosmological model. In that context, the universe can be approximated as composed by non-interacting constituents, each one being a perfect fluid with density
66:, it represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present epoch defines the size of the
2406:
Margalef-Bentabol, Berta; Margalef-Bentabol, Juan; Cepa, Jordi (2012-12-21). "Evolution of the cosmological horizons in a concordance universe".
2382:
2276:
2249:
2222:
533:
1923:
310:
1784:
The concept of a particle horizon can be used to illustrate the famous horizon problem, which is an unresolved issue associated with the
1098:
1312:
2035:
1042:
170:
2301:
1989:
837:
430:
to travel from where we are located to the furthest observable distance, provided the universe ceased expanding. As such,
1598:
2542:
978:
2570:
2023:
1793:
2302:"Expanding Confusion: Common Misconceptions of Cosmological Horizons and the Superluminal Expansion of the Universe"
391:
2167:
1789:
842:
1176:
274:
2124:
936:
1406:
1909:{\displaystyle H_{p}(t_{\text{CMB}})=c\eta _{\text{CMB}}=284{\text{ Mpc}}=8.9\times 10^{-3}H_{p}(t_{0})}
2491:
2425:
2323:
2183:
1560:
2188:
2159:
385:
71:
67:
59:
51:
2515:
2481:
2449:
2415:
2347:
2313:
79:
468:
2374:
785:
433:
2534:
2507:
2441:
2388:
2378:
2339:
2282:
2272:
2266:
2245:
2218:
2212:
1306:
including the curvature state equation. It can be proved that the Hubble function is given by
462:
91:
2239:
654:
2499:
2433:
2331:
2171:
763:{\displaystyle H_{p}(t_{0})=c\eta _{0}=14.4{\text{ Gpc}}=46.9{\text{ billion light years}}.}
1766:
which are related as stated before. We have an analogous but slightly different result for
1533:
1236:
892:
812:
100:
1779:
247:
1500:{\displaystyle {\text{The particle horizon }}H_{p}{\text{ exists if and only if }}N>2}
1263:
284:
2503:
2495:
2437:
2429:
2327:
2367:
2155:
1749:
1729:
1705:
1685:
1513:
1289:
1156:
912:
510:
147:
127:
122:
75:
43:
1557:(possibly infinite). The evolution of the particle horizon for an expanding universe (
2564:
2519:
2453:
1767:
1723:
1233:
Any function with a zero subscript denote the function evaluated at the present time
2351:
17:
2118:
2027:
2166:
so well is therefore not explained by the standard explanations about the way the
307:. By convention, a subscript 0 indicates "today" so that the conformal time today
55:
1986:
Since we observe the CMB to be emitted essentially from our particle horizon (
2511:
2445:
2392:
2343:
2286:
2271:. Cambridge, UK ; New York: Cambridge University Press. pp. 419–.
2163:
2535:"Understanding the Cosmic Microwave Background Temperature Power Spectrum"
2318:
1785:
118:
465:
normally defined to be equal to proper distance at the present time, so
63:
2217:(2nd ed.). Cambridge: Cambridge University Press. pp. 447–.
641:{\displaystyle a(t)H_{p}(t)=a(t)\int _{0}^{t}{\frac {c\,dt'}{a(t')}}}
427:
2335:
1977:{\displaystyle a_{\text{CMB}}H_{p}(t_{\text{CMB}})=261{\text{ kpc}}}
1726:). Notice that the derivative is made with respect to the FLRW-time
373:{\displaystyle \eta (t_{0})=\eta _{0}=1.48\times 10^{18}{\text{ s}}}
1144:{\displaystyle \Omega ={\frac {\rho }{\rho _{c}}}=\sum \Omega _{i}}
426:. Rather, the conformal time is the amount of time it would take a
2486:
2420:
1393:{\displaystyle H(z)=H_{0}{\sqrt {\sum \Omega _{i0}(1+z)^{n_{i}}}}}
507:
at present), the proper distance to the particle horizon at time
2108:{\displaystyle f={\frac {H_{p}(t_{\text{CMB}})}{H_{p}(t_{0})}}}
2373:. Singapore ; Hackensack, NJ: World Scientific. pp.
70:. Due to the expansion of the universe, it is not simply the
2369:
A primer on the physics of the cosmic microwave background
2265:
Hobson, M. P.; Efstathiou, George; Lasenby, A. N. (2006).
1086:{\displaystyle \Omega _{i}={\frac {\rho _{i}}{\rho _{c}}}}
2170:
proceeds. The most popular resolution to this problem is
1796:(CMB) was emitted, we obtain a particle horizon of about
2244:. Cambridge: Cambridge University Press. pp. 24–.
234:{\displaystyle \eta =\int _{0}^{t}{\frac {dt'}{a(t')}}}
2306:
2127:
2038:
2015:{\displaystyle 284{\text{ Mpc}}\ll 14.4{\text{ Gpc}}}
1992:
1926:
1804:
1752:
1732:
1708:
1688:
1601:
1563:
1536:
1516:
1467:
1409:
1315:
1292:
1266:
1239:
1179:
1159:
1101:
1045:
981:
939:
915:
895:
845:
815:
788:
692:
657:
536:
513:
471:
436:
394:
313:
287:
250:
173:
150:
130:
103:
1918:
which corresponds to a proper size at that time of:
1746:, while the functions are evaluated at the redshift
144:. In general, the conformal time at a certain time
1672:{\displaystyle {\frac {dH_{p}}{dt}}=H_{p}(z)H(z)+c}
2366:
2268:General relativity: an introduction for physicists
2206:
2204:
2146:
2107:
2026:(CMB) that are separated by about a fraction of a
2014:
1976:
1908:
1758:
1738:
1714:
1694:
1671:
1584:
1549:
1522:
1499:
1450:
1392:
1298:
1278:
1252:
1222:
1165:
1143:
1085:
1026:{\displaystyle \rho _{c}={\frac {3}{8\pi G}}H^{2}}
1025:
965:
921:
901:
881:
828:
801:
762:
676:
640:
519:
499:
449:
418:
372:
299:
265:
233:
156:
136:
109:
2300:Davis, Tamara M.; Lineweaver, Charles H. (2004).
2241:Cosmological inflation and large-scale structure
50:) is the maximum distance from which light from
2474:Journal of Cosmology and Astroparticle Physics
2408:Journal of Cosmology and Astroparticle Physics
889:, such that they add up to the total density
1702:is the speed of light and can be taken to be
929:. Let us now define the following functions:
419:{\displaystyle 4.35\times 10^{17}{\text{ s}}}
8:
2467:
2465:
2463:
2158:with each other. That the entire CMB is in
2238:Liddle, Andrew R.; Lyth, David H. (2000).
882:{\displaystyle p_{i}=\omega _{i}\rho _{i}}
281:, and we have taken the Big Bang to be at
279:Friedmann–Lemaître–Robertson–Walker metric
2485:
2419:
2317:
2138:
2126:
2093:
2080:
2065:
2052:
2045:
2037:
2007:
1996:
1991:
1969:
1954:
1941:
1931:
1925:
1897:
1884:
1871:
1853:
1841:
1822:
1809:
1803:
1788:model. Extrapolating back to the time of
1751:
1731:
1707:
1687:
1636:
1612:
1602:
1600:
1565:
1564:
1562:
1541:
1535:
1515:
1483:
1477:
1468:
1466:
1439:
1414:
1408:
1380:
1375:
1350:
1341:
1335:
1314:
1291:
1265:
1244:
1238:
1223:{\displaystyle 1+z={\frac {a_{0}}{a(t)}}}
1198:
1192:
1178:
1158:
1135:
1117:
1108:
1100:
1075:
1065:
1059:
1050:
1044:
1017:
995:
986:
980:
948:
946:
938:
914:
894:
873:
863:
850:
844:
820:
814:
793:
787:
752:
741:
729:
710:
697:
691:
668:
656:
604:
598:
592:
587:
553:
535:
512:
482:
470:
441:
435:
411:
405:
393:
365:
359:
340:
324:
312:
286:
249:
195:
189:
184:
172:
149:
129:
102:
2147:{\displaystyle \theta \sim 1.7^{\circ }}
2022:), our expectation is that parts of the
2200:
966:{\displaystyle H={\frac {\dot {a}}{a}}}
94:, the particle horizon is equal to the
86:Conformal time and the particle horizon
2214:Cosmology: the science of the universe
1451:{\displaystyle n_{i}=3(1+\omega _{i})}
27:Distance measurement used in cosmology
7:
1286:). The last term can be taken to be
1039:-th dimensionless energy density
1347:
1132:
1102:
1047:
380:. Note that the conformal time is
25:
1485: exists if and only if
1095:The dimensionless energy density
774:Evolution of the particle horizon
778:In this section we consider the
2533:Tojero, Rita (March 16, 2006).
1585:{\displaystyle {\dot {a}}>0}
2099:
2086:
2071:
2058:
1960:
1947:
1903:
1890:
1828:
1815:
1660:
1654:
1648:
1642:
1445:
1426:
1372:
1359:
1325:
1319:
1214:
1208:
716:
703:
632:
621:
580:
574:
565:
559:
546:
540:
488:
475:
330:
317:
260:
254:
225:
214:
1:
2504:10.1088/1475-7516/2013/02/015
2438:10.1088/1475-7516/2012/12/035
62:. Much like the concept of a
2543:Royal Observatory, Edinburgh
2365:Giovannini, Massimo (2008).
2211:Harrison, Edward R. (2000).
1403:where the dilution exponent
388:, which is estimated around
2024:cosmic microwave background
1794:cosmic microwave background
54:could have traveled to the
2587:
1777:
1470:The particle horizon
500:{\displaystyle a(t_{0})=1}
117:that has passed since the
2168:expansion of the universe
802:{\displaystyle \rho _{i}}
754: billion light years
450:{\displaystyle \eta _{0}}
1173:given by the formula
975:The critical density
677:{\displaystyle t=t_{0}}
2148:
2109:
2016:
1978:
1910:
1760:
1740:
1716:
1696:
1673:
1586:
1551:
1524:
1501:
1452:
1394:
1300:
1280:
1254:
1224:
1167:
1145:
1087:
1027:
967:
923:
903:
883:
830:
803:
764:
678:
642:
521:
501:
451:
420:
374:
301:
267:
235:
158:
138:
111:
2149:
2110:
2017:
1979:
1911:
1761:
1741:
1717:
1697:
1674:
1587:
1552:
1550:{\displaystyle n_{i}}
1525:
1502:
1453:
1395:
1301:
1281:
1255:
1253:{\displaystyle t_{0}}
1225:
1168:
1146:
1088:
1028:
968:
924:
904:
902:{\displaystyle \rho }
884:
831:
829:{\displaystyle p_{i}}
804:
765:
679:
643:
522:
502:
452:
421:
375:
302:
268:
236:
159:
139:
112:
110:{\displaystyle \eta }
2184:Cosmological horizon
2125:
2036:
1990:
1924:
1802:
1750:
1730:
1706:
1686:
1599:
1561:
1534:
1514:
1465:
1407:
1313:
1290:
1264:
1237:
1177:
1157:
1099:
1043:
979:
937:
913:
893:
843:
813:
786:
690:
655:
534:
511:
469:
434:
392:
311:
285:
266:{\displaystyle a(t)}
248:
171:
148:
128:
101:
48:cosmic light horizon
36:cosmological horizon
18:Cosmic light horizon
2496:2013JCAP...02..015M
2430:2012JCAP...12..035M
2328:2004PASA...21...97D
2189:Observable universe
2162:and approximates a
2160:thermal equilibrium
2154:) should be out of
1279:{\displaystyle z=0}
909:and total pressure
809:, partial pressure
597:
386:age of the universe
300:{\displaystyle t=0}
194:
72:age of the universe
68:observable universe
64:terrestrial horizon
60:age of the universe
2571:Physical cosmology
2144:
2105:
2030:across the sky of
2012:
1974:
1906:
1756:
1736:
1712:
1692:
1669:
1582:
1547:
1520:
1497:
1448:
1390:
1296:
1276:
1250:
1220:
1163:
1141:
1083:
1023:
963:
933:Hubble function
919:
899:
879:
826:
799:
760:
674:
638:
583:
517:
497:
447:
416:
370:
297:
263:
231:
180:
154:
134:
107:
80:cosmological model
2384:978-981-279-142-9
2278:978-0-521-82951-9
2251:978-0-521-57598-0
2224:978-0-521-66148-5
2103:
2068:
2010:
1999:
1972:
1957:
1934:
1856:
1844:
1825:
1759:{\displaystyle z}
1739:{\displaystyle t}
1715:{\displaystyle 1}
1695:{\displaystyle c}
1627:
1573:
1523:{\displaystyle N}
1486:
1471:
1388:
1299:{\displaystyle 1}
1260:(or equivalently
1218:
1166:{\displaystyle z}
1123:
1081:
1011:
961:
956:
922:{\displaystyle p}
755:
744:
636:
520:{\displaystyle t}
463:comoving distance
414:
368:
229:
157:{\displaystyle t}
137:{\displaystyle c}
92:comoving distance
46:'s text), or the
34:(also called the
16:(Redirected from
2578:
2555:
2554:
2552:
2550:
2539:
2530:
2524:
2523:
2489:
2469:
2458:
2457:
2423:
2403:
2397:
2396:
2372:
2362:
2356:
2355:
2321:
2319:astro-ph/0310808
2297:
2291:
2290:
2262:
2256:
2255:
2235:
2229:
2228:
2208:
2172:cosmic inflation
2153:
2151:
2150:
2145:
2143:
2142:
2114:
2112:
2111:
2106:
2104:
2102:
2098:
2097:
2085:
2084:
2074:
2070:
2069:
2066:
2057:
2056:
2046:
2021:
2019:
2018:
2013:
2011:
2008:
2000:
1997:
1983:
1981:
1980:
1975:
1973:
1970:
1959:
1958:
1955:
1946:
1945:
1936:
1935:
1932:
1915:
1913:
1912:
1907:
1902:
1901:
1889:
1888:
1879:
1878:
1857:
1854:
1846:
1845:
1842:
1827:
1826:
1823:
1814:
1813:
1765:
1763:
1762:
1757:
1745:
1743:
1742:
1737:
1721:
1719:
1718:
1713:
1701:
1699:
1698:
1693:
1678:
1676:
1675:
1670:
1641:
1640:
1628:
1626:
1618:
1617:
1616:
1603:
1591:
1589:
1588:
1583:
1575:
1574:
1566:
1556:
1554:
1553:
1548:
1546:
1545:
1529:
1527:
1526:
1521:
1506:
1504:
1503:
1498:
1487:
1484:
1482:
1481:
1472:
1469:
1457:
1455:
1454:
1449:
1444:
1443:
1419:
1418:
1399:
1397:
1396:
1391:
1389:
1387:
1386:
1385:
1384:
1358:
1357:
1342:
1340:
1339:
1305:
1303:
1302:
1297:
1285:
1283:
1282:
1277:
1259:
1257:
1256:
1251:
1249:
1248:
1229:
1227:
1226:
1221:
1219:
1217:
1203:
1202:
1193:
1172:
1170:
1169:
1164:
1150:
1148:
1147:
1142:
1140:
1139:
1124:
1122:
1121:
1109:
1092:
1090:
1089:
1084:
1082:
1080:
1079:
1070:
1069:
1060:
1055:
1054:
1032:
1030:
1029:
1024:
1022:
1021:
1012:
1010:
996:
991:
990:
972:
970:
969:
964:
962:
957:
949:
947:
928:
926:
925:
920:
908:
906:
905:
900:
888:
886:
885:
880:
878:
877:
868:
867:
855:
854:
835:
833:
832:
827:
825:
824:
808:
806:
805:
800:
798:
797:
769:
767:
766:
761:
756:
753:
745:
742:
734:
733:
715:
714:
702:
701:
683:
681:
680:
675:
673:
672:
647:
645:
644:
639:
637:
635:
631:
616:
615:
599:
596:
591:
558:
557:
526:
524:
523:
518:
506:
504:
503:
498:
487:
486:
456:
454:
453:
448:
446:
445:
425:
423:
422:
417:
415:
412:
410:
409:
379:
377:
376:
371:
369:
366:
364:
363:
345:
344:
329:
328:
306:
304:
303:
298:
272:
270:
269:
264:
240:
238:
237:
232:
230:
228:
224:
209:
208:
196:
193:
188:
163:
161:
160:
155:
143:
141:
140:
135:
116:
114:
113:
108:
40:comoving horizon
32:particle horizon
21:
2586:
2585:
2581:
2580:
2579:
2577:
2576:
2575:
2561:
2560:
2559:
2558:
2548:
2546:
2537:
2532:
2531:
2527:
2471:
2470:
2461:
2405:
2404:
2400:
2385:
2364:
2363:
2359:
2336:10.1071/AS03040
2299:
2298:
2294:
2279:
2264:
2263:
2259:
2252:
2237:
2236:
2232:
2225:
2210:
2209:
2202:
2197:
2180:
2134:
2123:
2122:
2115:
2089:
2076:
2075:
2061:
2048:
2047:
2034:
2033:
1988:
1987:
1984:
1950:
1937:
1927:
1922:
1921:
1916:
1893:
1880:
1867:
1837:
1818:
1805:
1800:
1799:
1782:
1780:Horizon problem
1776:
1774:Horizon problem
1748:
1747:
1728:
1727:
1704:
1703:
1684:
1683:
1632:
1619:
1608:
1604:
1597:
1596:
1559:
1558:
1537:
1532:
1531:
1530:is the largest
1512:
1511:
1473:
1463:
1462:
1435:
1410:
1405:
1404:
1376:
1371:
1346:
1331:
1311:
1310:
1288:
1287:
1262:
1261:
1240:
1235:
1234:
1204:
1194:
1175:
1174:
1155:
1154:
1131:
1113:
1097:
1096:
1071:
1061:
1046:
1041:
1040:
1013:
1000:
982:
977:
976:
935:
934:
911:
910:
891:
890:
869:
859:
846:
841:
840:
816:
811:
810:
789:
784:
783:
776:
725:
706:
693:
688:
687:
664:
653:
652:
624:
617:
608:
600:
549:
532:
531:
509:
508:
478:
467:
466:
437:
432:
431:
401:
390:
389:
355:
336:
320:
309:
308:
283:
282:
246:
245:
217:
210:
201:
197:
169:
168:
146:
145:
126:
125:
99:
98:
88:
28:
23:
22:
15:
12:
11:
5:
2584:
2582:
2574:
2573:
2563:
2562:
2557:
2556:
2525:
2459:
2398:
2383:
2357:
2292:
2277:
2257:
2250:
2230:
2223:
2199:
2198:
2196:
2193:
2192:
2191:
2186:
2179:
2176:
2156:causal contact
2141:
2137:
2133:
2130:
2101:
2096:
2092:
2088:
2083:
2079:
2073:
2064:
2060:
2055:
2051:
2044:
2041:
2032:
2006:
2003:
1995:
1968:
1965:
1962:
1953:
1949:
1944:
1940:
1930:
1920:
1905:
1900:
1896:
1892:
1887:
1883:
1877:
1874:
1870:
1866:
1863:
1860:
1852:
1849:
1840:
1836:
1833:
1830:
1821:
1817:
1812:
1808:
1798:
1778:Main article:
1775:
1772:
1755:
1735:
1711:
1691:
1680:
1679:
1668:
1665:
1662:
1659:
1656:
1653:
1650:
1647:
1644:
1639:
1635:
1631:
1625:
1622:
1615:
1611:
1607:
1581:
1578:
1572:
1569:
1544:
1540:
1519:
1508:
1507:
1496:
1493:
1490:
1480:
1476:
1447:
1442:
1438:
1434:
1431:
1428:
1425:
1422:
1417:
1413:
1401:
1400:
1383:
1379:
1374:
1370:
1367:
1364:
1361:
1356:
1353:
1349:
1345:
1338:
1334:
1330:
1327:
1324:
1321:
1318:
1295:
1275:
1272:
1269:
1247:
1243:
1231:
1230:
1216:
1213:
1210:
1207:
1201:
1197:
1191:
1188:
1185:
1182:
1162:
1151:
1138:
1134:
1130:
1127:
1120:
1116:
1112:
1107:
1104:
1093:
1078:
1074:
1068:
1064:
1058:
1053:
1049:
1033:
1020:
1016:
1009:
1006:
1003:
999:
994:
989:
985:
973:
960:
955:
952:
945:
942:
918:
898:
876:
872:
866:
862:
858:
853:
849:
838:state equation
823:
819:
796:
792:
775:
772:
771:
770:
759:
751:
748:
740:
737:
732:
728:
724:
721:
718:
713:
709:
705:
700:
696:
671:
667:
663:
660:
651:and for today
649:
648:
634:
630:
627:
623:
620:
614:
611:
607:
603:
595:
590:
586:
582:
579:
576:
573:
570:
567:
564:
561:
556:
552:
548:
545:
542:
539:
516:
496:
493:
490:
485:
481:
477:
474:
444:
440:
408:
404:
400:
397:
362:
358:
354:
351:
348:
343:
339:
335:
332:
327:
323:
319:
316:
296:
293:
290:
262:
259:
256:
253:
242:
241:
227:
223:
220:
216:
213:
207:
204:
200:
192:
187:
183:
179:
176:
153:
133:
123:speed of light
106:
96:conformal time
87:
84:
76:speed of light
44:Scott Dodelson
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2583:
2572:
2569:
2568:
2566:
2545:
2544:
2536:
2529:
2526:
2521:
2517:
2513:
2509:
2505:
2501:
2497:
2493:
2488:
2483:
2479:
2475:
2468:
2466:
2464:
2460:
2455:
2451:
2447:
2443:
2439:
2435:
2431:
2427:
2422:
2417:
2413:
2409:
2402:
2399:
2394:
2390:
2386:
2380:
2376:
2371:
2370:
2361:
2358:
2353:
2349:
2345:
2341:
2337:
2333:
2329:
2325:
2320:
2315:
2312:(1): 97–109.
2311:
2307:
2303:
2296:
2293:
2288:
2284:
2280:
2274:
2270:
2269:
2261:
2258:
2253:
2247:
2243:
2242:
2234:
2231:
2226:
2220:
2216:
2215:
2207:
2205:
2201:
2194:
2190:
2187:
2185:
2182:
2181:
2177:
2175:
2173:
2169:
2165:
2161:
2157:
2139:
2135:
2131:
2128:
2120:
2094:
2090:
2081:
2077:
2062:
2053:
2049:
2042:
2039:
2031:
2029:
2025:
2004:
2001:
1993:
1966:
1963:
1951:
1942:
1938:
1928:
1919:
1898:
1894:
1885:
1881:
1875:
1872:
1868:
1864:
1861:
1858:
1850:
1847:
1838:
1834:
1831:
1819:
1810:
1806:
1797:
1795:
1791:
1790:recombination
1787:
1781:
1773:
1771:
1769:
1768:event horizon
1753:
1733:
1725:
1724:natural units
1709:
1689:
1666:
1663:
1657:
1651:
1645:
1637:
1633:
1629:
1623:
1620:
1613:
1609:
1605:
1595:
1594:
1593:
1579:
1576:
1570:
1567:
1542:
1538:
1517:
1494:
1491:
1488:
1478:
1474:
1461:
1460:
1459:
1440:
1436:
1432:
1429:
1423:
1420:
1415:
1411:
1381:
1377:
1368:
1365:
1362:
1354:
1351:
1343:
1336:
1332:
1328:
1322:
1316:
1309:
1308:
1307:
1293:
1273:
1270:
1267:
1245:
1241:
1211:
1205:
1199:
1195:
1189:
1186:
1183:
1180:
1160:
1153:The redshift
1152:
1136:
1128:
1125:
1118:
1114:
1110:
1105:
1094:
1076:
1072:
1066:
1062:
1056:
1051:
1038:
1034:
1018:
1014:
1007:
1004:
1001:
997:
992:
987:
983:
974:
958:
953:
950:
943:
940:
932:
931:
930:
916:
896:
874:
870:
864:
860:
856:
851:
847:
839:
821:
817:
794:
790:
781:
773:
757:
749:
746:
738:
735:
730:
726:
722:
719:
711:
707:
698:
694:
686:
685:
684:
669:
665:
661:
658:
628:
625:
618:
612:
609:
605:
601:
593:
588:
584:
577:
571:
568:
562:
554:
550:
543:
537:
530:
529:
528:
514:
494:
491:
483:
479:
472:
464:
458:
442:
438:
429:
406:
402:
398:
395:
387:
383:
360:
356:
352:
349:
346:
341:
337:
333:
325:
321:
314:
294:
291:
288:
280:
276:
257:
251:
221:
218:
211:
205:
202:
198:
190:
185:
181:
177:
174:
167:
166:
165:
151:
131:
124:
120:
104:
97:
93:
85:
83:
81:
77:
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
33:
19:
2547:. Retrieved
2541:
2528:
2477:
2473:
2411:
2407:
2401:
2368:
2360:
2309:
2305:
2295:
2267:
2260:
2240:
2233:
2213:
2119:angular size
2116:
2028:great circle
1985:
1917:
1783:
1681:
1509:
1402:
1232:
1036:
777:
650:
527:is given by
459:
381:
275:scale factor
243:
164:is given by
121:, times the
95:
90:In terms of
89:
47:
39:
35:
31:
29:
2414:(12): 035.
2549:5 November
2480:(2): 015.
2195:References
74:times the
2520:119614479
2512:1475-7516
2487:1302.2186
2454:119704554
2446:1475-7516
2421:1302.1609
2393:191658608
2344:1323-3580
2164:blackbody
2140:∘
2132:∼
2129:θ
2009: Gpc
2002:≪
1998: Mpc
1971: kpc
1873:−
1865:×
1855: Mpc
1839:η
1792:when the
1571:˙
1437:ω
1348:Ω
1344:∑
1133:Ω
1129:∑
1115:ρ
1111:ρ
1103:Ω
1073:ρ
1063:ρ
1048:Ω
1005:π
984:ρ
954:˙
897:ρ
871:ρ
861:ω
791:ρ
743: Gpc
727:η
585:∫
439:η
399:×
353:×
338:η
315:η
182:∫
175:η
105:η
52:particles
2565:Category
2352:13068122
2287:61757089
2178:See also
1786:Big Bang
629:′
613:′
222:′
206:′
119:Big Bang
56:observer
2492:Bibcode
2476:. 015.
2426:Bibcode
2324:Bibcode
413: s
367: s
277:of the
273:is the
244:where
58:in the
2518:
2510:
2452:
2444:
2391:
2381:
2350:
2342:
2285:
2275:
2248:
2221:
1682:where
1592:) is:
1510:where
428:photon
38:, the
2538:(PDF)
2516:S2CID
2482:arXiv
2450:S2CID
2416:arXiv
2348:S2CID
2314:arXiv
2551:2015
2508:ISSN
2478:2013
2442:ISSN
2412:2012
2389:OCLC
2379:ISBN
2340:ISSN
2283:OCLC
2273:ISBN
2246:ISBN
2219:ISBN
2117:(an
2005:14.4
1577:>
1492:>
1035:The
836:and
780:FLRW
750:46.9
739:14.4
396:4.35
384:the
350:1.48
42:(in
30:The
2500:doi
2434:doi
2377:–.
2332:doi
2136:1.7
2121:of
2067:CMB
1994:284
1967:261
1956:CMB
1933:CMB
1862:8.9
1851:284
1843:CMB
1824:CMB
382:not
2567::
2540:.
2514:.
2506:.
2498:.
2490:.
2462:^
2448:.
2440:.
2432:.
2424:.
2410:.
2387:.
2375:70
2346:.
2338:.
2330:.
2322:.
2310:21
2308:.
2304:.
2281:.
2203:^
2174:.
1869:10
1770:.
407:17
403:10
361:18
357:10
82:.
2553:.
2522:.
2502::
2494::
2484::
2456:.
2436::
2428::
2418::
2395:.
2354:.
2334::
2326::
2316::
2289:.
2254:.
2227:.
2100:)
2095:0
2091:t
2087:(
2082:p
2078:H
2072:)
2063:t
2059:(
2054:p
2050:H
2043:=
2040:f
1964:=
1961:)
1952:t
1948:(
1943:p
1939:H
1929:a
1904:)
1899:0
1895:t
1891:(
1886:p
1882:H
1876:3
1859:=
1848:=
1835:c
1832:=
1829:)
1820:t
1816:(
1811:p
1807:H
1754:z
1734:t
1722:(
1710:1
1690:c
1667:c
1664:+
1661:)
1658:z
1655:(
1652:H
1649:)
1646:z
1643:(
1638:p
1634:H
1630:=
1624:t
1621:d
1614:p
1610:H
1606:d
1580:0
1568:a
1543:i
1539:n
1518:N
1495:2
1489:N
1479:p
1475:H
1446:)
1441:i
1433:+
1430:1
1427:(
1424:3
1421:=
1416:i
1412:n
1382:i
1378:n
1373:)
1369:z
1366:+
1363:1
1360:(
1355:0
1352:i
1337:0
1333:H
1329:=
1326:)
1323:z
1320:(
1317:H
1294:1
1274:0
1271:=
1268:z
1246:0
1242:t
1215:)
1212:t
1209:(
1206:a
1200:0
1196:a
1190:=
1187:z
1184:+
1181:1
1161:z
1137:i
1126:=
1119:c
1106:=
1077:c
1067:i
1057:=
1052:i
1037:i
1019:2
1015:H
1008:G
1002:8
998:3
993:=
988:c
959:a
951:a
944:=
941:H
917:p
875:i
865:i
857:=
852:i
848:p
822:i
818:p
795:i
758:.
747:=
736:=
731:0
723:c
720:=
717:)
712:0
708:t
704:(
699:p
695:H
670:0
666:t
662:=
659:t
633:)
626:t
622:(
619:a
610:t
606:d
602:c
594:t
589:0
581:)
578:t
575:(
572:a
569:=
566:)
563:t
560:(
555:p
551:H
547:)
544:t
541:(
538:a
515:t
495:1
492:=
489:)
484:0
480:t
476:(
473:a
443:0
347:=
342:0
334:=
331:)
326:0
322:t
318:(
295:0
292:=
289:t
261:)
258:t
255:(
252:a
226:)
219:t
215:(
212:a
203:t
199:d
191:t
186:0
178:=
152:t
132:c
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.