759:
89:
2377:
772:
25:
817:
917:(FLRW). The Milne solution can be obtained from the more generic FLRW model by demanding that the energy density, pressure and cosmological constant all equal zero and the spatial curvature is negative. From these assumptions and the Friedmann equations it follows that the scale factor must depend on time coordinate linearly.
1277:
Milne proposed that the universe's density changes in time because of an initial outward explosion of matter. Milne's model assumes an inhomogeneous density function which is
Lorentz Invariant (around the event t=x=y=z=0). When rendered graphically Milne's density distribution shows a
1036:
160:
1123:
1173:
1203:
1255:
2080:
914:
859:
530:
1208:
The empty space that the Milne model describes can be identified with the inside of a light cone of an event in
Minkowski space by a change of coordinates.
803:
1282:
pattern with outer edges moving outward at the speed of light. Every inertial body perceives itself to be at the center of the explosion of matter (see
926:
182:
2404:
920:
Setting the spatial curvature and speed of light to unity the metric for a Milne universe can be expressed with hyperspherical coordinates as:
95:
1047:
387:
2127:
2362:
740:
2151:
1897:
550:
392:
1261:
to Milne's model implies that a full general relativistic treatment using Milne's assumptions would result in a linearly increasing
796:
505:
1933:
1887:
418:
252:
2399:
2071:
1471:
1438:
1406:
1332:
457:
1555:
789:
1808:
1523:
1493:
169:
2179:
1813:
1530:
A thorough historical and theoretical study of the
British Tradition in Cosmology, and one long celebration of Milne.
195:
64:
1219:. As he initially described it, the model has no expansion of space, so all of the redshift (except that caused by
2133:
758:
475:
88:
1846:
1349:
382:
1949:
2380:
2122:
2027:
1957:
469:
177:
2090:
515:
2409:
1944:
1298:
535:
1134:
1985:
1719:
1704:
776:
267:
187:
2272:
1714:
1667:
875:
680:
228:
46:
35:
2302:
1928:
1609:
480:
292:
2414:
2327:
1877:
1637:
1548:
715:
705:
555:
372:
2056:
1978:
1598:
1589:
890:
700:
434:
1227:
associated with the hypothetical "explosion". However, the mathematical equivalence of the zero
2282:
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2051:
2009:
1683:
1647:
1287:
1266:
867:
670:
655:
500:
262:
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2287:
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1831:
1234:
645:
213:
1375:
42:
2192:
2118:
1962:
1564:
1371:
1224:
465:
8:
2267:
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2252:
2084:
2033:
1851:
1836:
1662:
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1318:
1283:
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1220:
898:
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2014:
1995:
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1604:
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1433:(1st ed.). Cambridge, UK ; New York: Cambridge University Press. p. 27.
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1216:
1212:
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367:
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80:
2342:
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1402:
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894:
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829:
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315:
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2237:
2184:
2161:
1739:
1511:
1379:
665:
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2307:
1383:
1182:-corrected radial component for negatively curved space that varies between 0 and
685:
2322:
2297:
2222:
2217:
2100:
2061:
2023:
1967:
1841:
1777:
1497:
1428:
1322:
879:
720:
695:
580:
575:
439:
320:
282:
2105:
1286:), and sees the local universe as homogeneous and isotropic in the sense of the
490:
2347:
2019:
2003:
1999:
1902:
1872:
1729:
1632:
1505:
1228:
1031:{\displaystyle ds^{2}=dt^{2}-t^{2}(d\chi ^{2}+\sinh ^{2}{\chi }d\Omega ^{2})\ }
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1507:
Non-Standard
Relativity: a Philosopher's Handbook of Heresies in Physics
2352:
1918:
1762:
1757:
833:
735:
297:
223:
155:{\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}
1118:{\displaystyle d\Omega ^{2}=d\theta ^{2}+\sin ^{2}\theta d\phi ^{2}\ }
1749:
1179:
306:
1462:
Misner, Charles W.; Thorne, Kip S.; Wheeler, John
Archibald (1971).
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1642:
1366:
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485:
325:
885:
Since it features both zero energy density and maximally negative
858:
in 1935. It is mathematically equivalent to a special case of the
1297:, the universe's density must be negligible in comparison to the
1972:
1533:
1399:
Spacetime and geometry: an introduction to general relativity
816:
1401:(1st ed.). San Francisco: Addison Wesley. p. 341.
1953:
1466:(1st ed.). San Francisco: W. H. Freeman. p. 721.
1500:- a detailed non-technical introduction to the Milne model
1301:
at all times for which the Milne model is taken to apply.
913:
The Milne universe is a special case of a more general
1237:
1188:
1137:
1050:
929:
98:
45:. Please help to ensure that disputed statements are
1461:
1249:
1197:
1167:
1117:
1030:
154:
1350:"Planck 2018 results VI. Cosmological parameters"
2391:
893:. Cosmologists actually observe the universe's
1549:
797:
1503:
1491:Milne Cosmology: Why I Keep Talking About It
1360:. Astronomy & Astrophysics Journal: A6.
1347:
1324:Relativity, Gravitation and World-structure
1272:
820:Milne's model follows the description from
1556:
1542:
1211:Milne developed this model independent of
804:
790:
1422:
1420:
1418:
1365:
915:FriedmannâLemaĂźtreâRobertsonâWalker model
65:Learn how and when to remove this message
1426:
901:and its curvature to be consistent with
815:
41:Relevant discussion may be found on the
1396:
1348:Planck Collaboration (September 2020).
889:, the Milne model is inconsistent with
2392:
1455:
1415:
2405:Exact solutions in general relativity
1537:
1390:
1317:
870:. The Milne model is also similar to
1168:{\displaystyle \chi =\sinh ^{-1}{r}}
836:along with "elsewhere" in spacetime.
18:
2128:TolmanâOppenheimerâVolkoff equation
2081:FriedmannâLemaĂźtreâRobertsonâWalker
1269:is uniquely zero for such a model.
1128:is the metric for a two-sphere and
13:
1192:
1055:
1013:
115:
14:
2426:
1898:HamiltonâJacobiâEinstein equation
1430:Physical foundations of cosmology
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771:
770:
757:
87:
23:
1293:In order to be consistent with
908:
1705:Massâenergy equivalence (E=mc)
1563:
1341:
1311:
1022:
972:
1:
1504:True Wegener, Mogens (2021).
1484:
2400:Obsolete theories in physics
1354:Astronomy & Astrophysics
1278:three-dimensional spherical
7:
1720:Relativistic Doppler effect
1384:10.1051/0004-6361/201833910
874:in that both are simple re-
832:containing past and future
268:Gravitational time dilation
10:
2431:
2191:In computational physics:
1715:Relativity of simultaneity
388:MathissonâPapapetrouâDixon
229:Pseudo-Riemannian manifold
2373:
2205:
2070:
2042:
2028:LenseâThirring precession
1911:
1860:
1822:
1801:
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1676:
1618:
1610:Doubly special relativity
1582:
1571:
1516:10.1515/9783110813531-031
1496:12 September 2006 at the
891:cosmological observations
1888:Post-Newtonian formalism
1878:Einstein field equations
1814:Mathematical formulation
1638:Hyperbolic orthogonality
1427:Mukhanov, V. F. (2005).
1304:
1273:Milne's density function
1198:{\displaystyle +\infty }
393:HamiltonâJacobiâEinstein
373:Einstein field equations
196:Mathematical formulation
1599:Galilean transformation
1590:Principle of relativity
1376:2020A&A...641A...6P
1265:for all time since the
1250:{\displaystyle \rho =0}
1684:Lorentz transformation
1397:Carroll, Sean (2004).
1288:cosmological principle
1267:deceleration parameter
1251:
1215:but with awareness of
1199:
1169:
1119:
1032:
897:to be consistent with
868:cosmological principle
837:
263:Gravitational redshift
156:
2152:WeylâLewisâPapapetrou
1893:Raychaudhuri equation
1832:Equivalence principle
1252:
1200:
1170:
1120:
1033:
862:in the limit of zero
819:
551:WeylâLewisâPapapetrou
506:KerrâNewmanâde Sitter
326:EinsteinâRosen bridge
258:Gravitational lensing
214:Equivalence principle
157:
2193:Numerical relativity
2034:pulsar timing arrays
1319:Milne, Edward Arthur
1235:
1225:recessional velocity
1223:) is explained by a
1186:
1135:
1048:
927:
846:special-relativistic
481:EinsteinâRosen waves
207:Fundamental concepts
96:
34:factual accuracy is
2410:Minkowski spacetime
2085:Friedmann equations
1979:HulseâTaylor binary
1941:Gravitational waves
1837:Riemannian geometry
1663:Proper acceleration
1648:Maxwell's equations
1594:Galilean relativity
1510:. Books on Demand.
1327:. Clarendon Press.
1284:observable universe
1221:peculiar velocities
856:Edward Arthur Milne
826:observable universe
435:KaluzaâKlein theory
321:Minkowski spacetime
273:Gravitational waves
2134:ReissnerâNordström
2052:BransâDicke theory
1883:Linearized gravity
1710:Length contraction
1628:Frame of reference
1605:Special relativity
1295:general relativity
1247:
1217:special relativity
1213:general relativity
1195:
1165:
1115:
1028:
838:
822:special relativity
764:Physics portal
536:OppenheimerâSnyder
476:ReissnerâNordström
368:Linearized gravity
316:Spacetime diagrams
219:Special relativity
152:
81:General relativity
16:Cosmological model
2387:
2386:
2201:
2200:
2180:OzsvĂĄthâSchĂŒcking
1786:
1785:
1768:Minkowski diagram
1725:Thomas precession
1668:Relativistic mass
1473:978-0-7167-0334-1
1440:978-0-521-56398-7
1408:978-0-8053-8732-2
1334:978-0-598-42415-0
1257:) version of the
1114:
1027:
895:density parameter
887:spatial curvature
876:parameterizations
866:and it obeys the
830:spacetime diagram
814:
813:
447:
446:
333:
332:
75:
74:
67:
2422:
2379:
2378:
2162:van Stockum dust
1934:Two-body problem
1852:Mach's principle
1799:
1798:
1740:Terrell rotation
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1338:
1315:
1299:critical density
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546:van Stockum dust
531:RobertsonâWalker
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47:reliably sourced
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2415:1935 in science
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2197:
2101:BKL singularity
2091:LemaĂźtreâTolman
2066:
2062:Quantum gravity
2044:
2038:
2024:geodetic effect
1998:(together with
1968:LISA Pathfinder
1907:
1856:
1842:Penrose diagram
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1778:Minkowski space
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1498:Wayback Machine
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427:Advanced theory
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2140:Axisymmetric:
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2000:Einstein cross
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2216:
2214:
2211:
2210:
2208:
2204:
2194:
2190:
2189:
2186:
2183:
2181:
2178:
2176:
2172:
2171:
2168:
2165:
2163:
2160:
2158:
2155:
2153:
2150:
2147:
2143:
2139:
2138:
2135:
2132:
2129:
2126:
2124:
2120:
2119:Schwarzschild
2116:
2115:
2112:
2109:
2107:
2104:
2102:
2099:
2097:
2094:
2092:
2089:
2086:
2082:
2078:
2077:
2075:
2073:
2069:
2063:
2060:
2058:
2055:
2053:
2050:
2049:
2047:
2041:
2035:
2032:
2029:
2025:
2021:
2018:
2016:
2015:Shapiro delay
2013:
2011:
2008:
2005:
2001:
1997:
1994:
1991:
1987:
1984:
1983:
1980:
1977:
1974:
1971:
1969:
1966:
1964:
1961:
1959:
1958:collaboration
1955:
1951:
1948:
1946:
1942:
1939:
1938:
1935:
1932:
1930:
1927:
1925:
1924:Event horizon
1922:
1920:
1917:
1916:
1914:
1910:
1904:
1901:
1899:
1896:
1894:
1891:
1889:
1886:
1884:
1881:
1879:
1876:
1874:
1871:
1869:
1868:ADM formalism
1866:
1865:
1863:
1859:
1853:
1850:
1848:
1845:
1843:
1840:
1838:
1835:
1833:
1830:
1829:
1827:
1821:
1815:
1812:
1810:
1807:
1806:
1804:
1800:
1797:
1795:
1789:
1779:
1776:
1774:
1773:Biquaternions
1771:
1769:
1766:
1764:
1761:
1759:
1756:
1755:
1753:
1751:
1747:
1741:
1738:
1736:
1733:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1711:
1708:
1706:
1703:
1701:
1700:Time dilation
1698:
1697:
1695:
1691:
1685:
1682:
1681:
1679:
1675:
1669:
1666:
1664:
1661:
1659:
1656:
1654:
1653:Proper length
1651:
1649:
1646:
1644:
1641:
1639:
1636:
1634:
1631:
1629:
1626:
1625:
1623:
1617:
1611:
1608:
1606:
1603:
1600:
1597:
1595:
1591:
1588:
1587:
1585:
1581:
1578:
1576:
1570:
1566:
1559:
1554:
1552:
1547:
1545:
1540:
1539:
1536:
1527:
1521:
1517:
1513:
1509:
1508:
1502:
1499:
1495:
1492:
1489:
1488:
1475:
1469:
1465:
1458:
1450:
1446:
1442:
1436:
1432:
1431:
1423:
1421:
1419:
1410:
1404:
1400:
1393:
1385:
1381:
1377:
1373:
1368:
1363:
1359:
1355:
1351:
1344:
1336:
1330:
1326:
1325:
1320:
1314:
1310:
1302:
1300:
1296:
1291:
1289:
1285:
1281:
1280:Lobachevskian
1270:
1268:
1264:
1260:
1244:
1241:
1238:
1230:
1226:
1222:
1218:
1214:
1209:
1206:
1189:
1181:
1161:
1157:
1152:
1149:
1145:
1141:
1138:
1131:
1130:
1129:
1107:
1103:
1099:
1096:
1093:
1088:
1084:
1080:
1075:
1071:
1067:
1064:
1059:
1051:
1044:
1043:
1042:
1017:
1009:
1005:
1001:
996:
992:
988:
983:
979:
975:
967:
963:
959:
954:
950:
946:
943:
938:
934:
930:
923:
922:
921:
918:
916:
906:
904:
900:
896:
892:
888:
883:
881:
877:
873:
872:Rindler space
869:
865:
861:
857:
853:
850:
847:
843:
835:
831:
827:
823:
818:
807:
802:
800:
795:
793:
788:
787:
785:
784:
778:
768:
765:
760:
754:
753:
752:
751:
744:
743:
739:
737:
734:
732:
729:
727:
724:
722:
719:
717:
714:
712:
709:
707:
704:
702:
699:
697:
694:
692:
689:
687:
684:
682:
681:Chandrasekhar
679:
677:
674:
672:
669:
667:
664:
662:
659:
657:
654:
652:
649:
647:
644:
642:
639:
637:
634:
632:
629:
627:
624:
622:
619:
617:
614:
612:
609:
607:
604:
602:
599:
597:
596:Schwarzschild
594:
592:
589:
587:
584:
582:
579:
577:
574:
573:
565:
564:
557:
556:HartleâThorne
554:
552:
549:
547:
544:
542:
539:
537:
534:
532:
529:
527:
524:
522:
519:
517:
514:
512:
509:
507:
504:
502:
499:
497:
494:
492:
489:
487:
484:
482:
479:
477:
474:
471:
467:
466:Schwarzschild
464:
463:
459:
453:
452:
441:
438:
436:
433:
432:
431:
430:
426:
425:
420:
417:
415:
412:
410:
407:
406:
405:
404:
400:
399:
394:
391:
389:
386:
384:
381:
379:
376:
374:
371:
369:
366:
365:
364:
363:
359:
358:
348:
345:
344:
339:
338:
327:
324:
322:
319:
317:
314:
313:
312:
311:
308:
305:
304:
299:
296:
294:
291:
289:
288:Event horizon
286:
284:
281:
279:
276:
274:
271:
269:
266:
264:
261:
259:
256:
254:
251:
250:
249:
248:
238:
237:
230:
227:
225:
222:
220:
217:
215:
212:
211:
203:
202:
197:
194:
189:
186:
184:
181:
179:
176:
175:
173:
171:
168:
167:
166:
165:
147:
144:
140:
135:
131:
126:
123:
119:
112:
107:
104:
100:
90:
86:
85:
82:
79:
78:
69:
66:
58:
48:
44:
38:
37:
30:
21:
20:
2363:
2110:
2057:KaluzaâKlein
1809:Introduction
1735:Twin paradox
1506:
1463:
1457:
1429:
1398:
1392:
1357:
1353:
1343:
1323:
1313:
1292:
1276:
1263:scale factor
1210:
1207:
1177:
1127:
1040:
919:
912:
909:Milne metric
884:
854:proposed by
849:cosmological
841:
839:
741:
701:Raychaudhuri
525:
170:Introduction
61:
52:
33:
2146:KerrâNewman
2117:Spherical:
1986:Other tests
1929:Singularity
1861:Formulation
1823:Fundamental
1677:Formulation
1658:Proper time
1619:Fundamental
1464:Gravitation
1259:FLRW metric
842:Milne model
834:light cones
716:van Stockum
646:Oppenheimer
501:KerrâNewman
293:Singularity
2394:Categories
2298:Zel'dovich
2206:Scientists
2185:Alcubierre
1992:of Mercury
1990:precession
1919:Black hole
1802:Background
1794:relativity
1763:World line
1758:Light cone
1583:Background
1575:relativity
1565:Relativity
1485:References
1367:1807.06209
860:FLRW model
569:Scientists
401:Formalisms
349:Formalisms
298:Black hole
224:World line
2268:Robertson
2253:Friedmann
2248:Eddington
2238:de Sitter
2072:Solutions
1950:detectors
1945:astronomy
1912:Phenomena
1847:Geodesics
1750:Spacetime
1693:Phenomena
1239:ρ
1193:∞
1180:curvature
1158:
1150:−
1139:χ
1104:ϕ
1097:θ
1094:
1072:θ
1056:Ω
1014:Ω
1006:χ
1002:
980:χ
960:−
661:Robertson
626:Friedmann
621:Eddington
611:Nordström
601:de Sitter
458:Solutions
383:Geodesics
378:Friedmann
360:Equations
346:Equations
307:Spacetime
242:Phenomena
148:ν
145:μ
136:κ
127:ν
124:μ
116:Λ
108:ν
105:μ
43:talk page
2381:Category
2258:LemaĂźtre
2223:Einstein
2213:Poincaré
2173:Others:
2157:TaubâNUT
2123:interior
2045:theories
2043:Advanced
2010:redshift
1825:concepts
1643:Rapidity
1621:concepts
1494:Archived
1449:61440784
1321:(1935).
903:flatness
878:of flat
777:Category
641:LemaĂźtre
606:Reissner
591:Poincaré
576:Einstein
521:TaubâNUT
486:Wormhole
470:interior
183:Timeline
55:May 2018
36:disputed
2323:Hawking
2318:Penrose
2303:Novikov
2283:Wheeler
2228:Hilbert
2218:Lorentz
2175:pp-wave
1996:lensing
1792:General
1573:Special
1372:Bibcode
1178:is the
696:Hawking
691:Penrose
666:Bardeen
656:Wheeler
586:Hilbert
581:Lorentz
541:pp-wave
178:History
2364:others
2353:Thorne
2343:Misner
2328:Taylor
2313:Geroch
2308:Ehlers
2278:Zwicky
2096:Kasner
1522:
1470:
1447:
1437:
1405:
1331:
1113:
1041:where
1026:
844:was a
824:of an
775:
742:others
736:Thorne
726:Newman
706:Taylor
686:Ehlers
671:Walker
636:Zwicky
511:Kasner
2358:Weiss
2338:Bondi
2333:Hulse
2263:Milne
2167:discs
2111:Milne
2106:Gödel
1963:Virgo
1362:arXiv
1305:Notes
899:unity
852:model
711:Hulse
651:Gödel
631:Milne
526:Milne
491:Gödel
188:Tests
2293:Kerr
2243:Weyl
2142:Kerr
2002:and
1956:and
1954:LIGO
1520:ISBN
1468:ISBN
1445:OCLC
1435:ISBN
1403:ISBN
1329:ISBN
1146:sinh
993:sinh
840:The
721:Taub
676:Kerr
616:Weyl
496:Kerr
414:BSSN
2348:Yau
1973:GEO
1512:doi
1380:doi
1358:641
1085:sin
828:'s
731:Yau
409:ADM
2396::
2022:/
1988::
1943::
1518:.
1443:.
1417:^
1378:.
1370:.
1356:.
1352:.
1290:.
1205:.
905:.
882:.
2148:)
2144:(
2130:)
2121:(
2087:)
2083:(
2030:)
2026:(
2006:)
1975:)
1952:(
1601:)
1592:(
1557:e
1550:t
1543:v
1528:.
1514::
1476:.
1451:.
1411:.
1386:.
1382::
1374::
1364::
1337:.
1245:0
1242:=
1231:(
1190:+
1162:r
1153:1
1142:=
1108:2
1100:d
1089:2
1081:+
1076:2
1068:d
1065:=
1060:2
1052:d
1023:)
1018:2
1010:d
997:2
989:+
984:2
976:d
973:(
968:2
964:t
955:2
951:t
947:d
944:=
939:2
935:s
931:d
805:e
798:t
791:v
472:)
468:(
141:T
132:=
120:g
113:+
101:G
68:)
62:(
57:)
53:(
49:.
39:.
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