390:
222:
2681:
is located where matter is distributed, and a separation of matter from gravitation only seems to appear after a collision or interaction has taken place. According to Ethan Siegel: "Adding dark matter makes this work, but non-local gravity would make differing before-and-after predictions that can't
925:
385:{\displaystyle R_{\alpha \beta }=\partial _{\gamma }\Gamma _{\alpha \beta }^{\gamma }-\partial _{\beta }\Gamma _{\alpha \gamma }^{\gamma }+\Gamma _{\alpha \beta }^{\gamma }\Gamma _{\gamma \delta }^{\delta }-\Gamma _{\alpha \delta }^{\gamma }\Gamma _{\gamma \beta }^{\delta }.}
1597:
107:-like modification of the gravitational force due to a point source. Intuitively, this result can be described as follows: far from a source gravity is stronger than the Newtonian prediction, but at shorter distances, it is counteracted by a repulsive
2672:
states that the Bullet
Cluster still "proves dark matter exists, but not for the reason most physicists think". There he argues in favor of dark matter over non-local gravity theories, such as STVG/MOG. Observations show that in "undisturbed"
2330:
1737:
819:
487:
2506:
1398:
827:
2094:
2573:
2620:
On the scale of the Solar System, the theory predicts no deviation from the results of Newton and
Einstein. This is also true for star clusters containing no more than a few million solar masses.
1482:
3141:
1945:
3040:
2229:
2376:
1861:
1631:
580:
1900:
1444:
952:
637:
1471:
3176:
2913:
2860:
2603:
1023:
1078:
600:
2148:
1780:
1055:
996:
126:. On a smaller scale, in the Solar System, STVG predicts no observable deviation from general relativity. The theory may also offer an explanation for the origin of
2124:
1807:
2168:
976:
3478:
2756:
210:
2235:
2416:
2396:
2188:
1965:
1760:
1655:
550:
530:
510:
184:
3284:
57:
645:
406:
3206:
3782:
2424:
3455:
3710:
1947:
is determined and the following equation of motion is obtained in the spherically symmetric, static gravitational field of a point mass of mass
3761:
3269:
3787:
3412:
3254:
3169:
2701:
31:
3532:
3463:
1086:
920:{\displaystyle B_{\alpha \beta }=\partial _{\alpha }\phi _{\beta }-\partial _{\beta }\phi _{\alpha }=(\mathrm {d} \phi )_{\alpha \beta }}
3586:
3767:
3315:
3298:
3239:
3420:
3249:
2696:
3162:
1973:
3221:
2512:
35:
3527:
3449:
1592:{\displaystyle S=\int {({\mathcal {L}}_{G}+{\mathcal {L}}_{\phi }+{\mathcal {L}}_{S}+{\mathcal {L}}_{M})}~\mathrm {d^{4}} x,}
3720:
3244:
3092:
2963:
Moffat, J. W.; Toth, V. T. (2007). "Modified
Gravity: Cosmology without dark matter or Einstein's cosmological constant".
3834:
3505:
397:
3399:
3389:
3264:
2691:
2638:
139:
3347:
1905:
3705:
3211:
2624:
2609:. These results form the basis of a series of calculations that are used to confront the theory with observation.
2196:
3499:
3494:
609:
3715:
3425:
3602:
3596:
2338:
1080:
are promoted to scalar fields by introducing associated kinetic and potential terms in the
Lagrangian density:
100:
3563:
2617:
STVG/MOG has been applied successfully to a range of astronomical, astrophysical, and cosmological phenomena.
3630:
53:
3431:
3341:
1812:
3547:
2987:
Moffat, J. W.; Toth, V. T. (2008). "Testing modified gravity with globular cluster velocity dispersions".
3839:
3679:
3658:
3651:
3591:
2989:
2806:
2656:
2645:
1646:
1605:
115:
3216:
555:
3746:
3665:
3644:
3637:
3512:
3367:
3325:
3111:
3059:
3008:
2932:
2879:
2825:
2775:
2127:
1866:
1406:
930:
615:
2804:
Brownstein, J. R.; Moffat, J. W. (2006). "Galaxy
Rotation Curves Without Non-Baryonic Dark Matter".
2707:
955:
3808:
3274:
3259:
3231:
3101:
3049:
2998:
2964:
2922:
2869:
2815:
2765:
2678:
1449:
2581:
3090:
Moffat, J. W.; Toth, V. T. (2009). "Fundamental parameter-free solutions in
Modified Gravity".
1001:
3792:
3700:
3444:
3372:
2649:
1060:
585:
61:
2909:"The Bullet Cluster 1E0657-558 evidence shows Modified Gravity in the absence of Dark Matter"
2133:
1765:
1031:
981:
3774:
3468:
3362:
3142:"The Bullet Cluster proves dark matter exists, but not for the reason most physicists think"
3119:
3067:
3016:
2940:
2887:
2833:
2783:
104:
88:
2325:{\displaystyle \alpha ={\frac {G_{\infty }-G_{N}}{G_{N}}}{\frac {M}{({\sqrt {M}}+E)^{2}}},}
2102:
1785:
3473:
3394:
3354:
3320:
2623:
The theory accounts for the rotation curves of spiral galaxies, correctly reproducing the
2153:
1863:
is its four-velocity. Assuming that the fifth-force charge is proportional to mass, i.e.,
1732:{\displaystyle {\mathcal {L}}_{\mathrm {TP} }=-m+\alpha \omega q_{5}\phi _{\mu }u^{\mu },}
1642:
961:
87:
Scalar–tensor–vector gravity theory, also known as MOdified
Gravity (MOG), is based on an
189:
3123:
3115:
3063:
3012:
2936:
2883:
2829:
2787:
2779:
3673:
2674:
2401:
2381:
2173:
1950:
1745:
535:
515:
495:
119:
145:
3828:
3610:
3279:
3072:
3035:
2945:
2908:
2892:
2855:
2733:
96:
2728:
3568:
3377:
3137:
2669:
998:
characterizes the strength of the coupling between the fifth force and matter, and
814:{\displaystyle {\mathcal {L}}_{\phi }=-{\frac {1}{4\pi }}\omega \left{\sqrt {-g}},}
606:
213:
92:
482:{\displaystyle {\mathcal {L}}_{G}=-{\frac {1}{16\pi G}}(R+2\Lambda ){\sqrt {-g}},}
3537:
123:
108:
2130:
of gravitation. Further study of the field equations allows a determination of
3751:
138:
STVG is formulated using the action principle. In the following discussion, a
3756:
3738:
3542:
3519:
2501:{\displaystyle D\simeq 25^{2}\cdot \,10M_{\odot }^{1/2}\mathrm {kpc} ^{-1},}
2659:
of the universe that is observed in the form of galaxy-galaxy correlations.
3154:
17:
3813:
3623:
3616:
2927:
2874:
2820:
3185:
1473:
are the self-interaction potentials associated with the scalar fields.
127:
49:
2770:
2378:
is determined from cosmological observations, while for the constants
2630:
STVG is in good agreement with the mass profiles of galaxy clusters.
118:, the mass profiles of galaxy clusters, gravitational lensing in the
2633:
STVG can also account for key cosmological observations, including:
1393:{\displaystyle {\mathcal {L}}_{S}=-{\frac {1}{G}}\left{\sqrt {-g}},}
3020:
2837:
3405:
3106:
3054:
3003:
2969:
3158:
2606:
2754:
Moffat, J. W. (2006). "Scalar–Tensor–Vector
Gravity Theory".
1649:. First a test particle Lagrangian is postulated in the form
1662:
1645:
of STVG can be developed from the action integral using the
1612:
1553:
1536:
1519:
1502:
1093:
652:
413:
2089:{\displaystyle {\ddot {r}}=-{\frac {G_{N}M}{r^{2}}}\left,}
3041:
Monthly
Notices of the Royal Astronomical Society Letters
2568:{\displaystyle E\simeq 50^{2}\cdot \,10M_{\odot }^{1/2},}
1782:
is a factor representing the nonlinearity of the theory,
2856:"Galaxy Cluster Masses Without Non-Baryonic Dark Matter"
95:, while elevating the three constants of the theory to
2682:
both match up, simultaneously, with what we observe."
64:. The theory is also often referred to by the acronym
2584:
2515:
2427:
2404:
2384:
2341:
2238:
2199:
2176:
2156:
2136:
2105:
1976:
1953:
1908:
1869:
1815:
1788:
1768:
1748:
1658:
1608:
1485:
1452:
1409:
1089:
1063:
1034:
1004:
984:
964:
933:
830:
648:
618:
588:
558:
538:
518:
498:
409:
225:
192:
148:
122:, and cosmological observations without the need for
212:, and we are using the following definition for the
3801:
3733:
3691:
3577:
3556:
3487:
3334:
3308:
3297:
3230:
3199:
3192:
2418:galaxy rotation curves yield the following values:
27:
Modified theory of gravity developed by John Moffat
2597:
2567:
2500:
2410:
2390:
2370:
2324:
2223:
2182:
2162:
2142:
2118:
2088:
1959:
1939:
1894:
1855:
1801:
1774:
1754:
1731:
1625:
1591:
1465:
1438:
1392:
1072:
1049:
1017:
990:
970:
946:
919:
813:
631:
594:
574:
544:
524:
504:
481:
384:
204:
178:
2914:Monthly Notices of the Royal Astronomical Society
2861:Monthly Notices of the Royal Astronomical Society
2849:
2847:
1940:{\displaystyle \kappa ={\sqrt {G_{N}/\omega }}}
1809:is the test particle's fifth-force charge, and
3479:Degenerate Higher-Order Scalar-Tensor theories
2757:Journal of Cosmology and Astroparticle Physics
3170:
3085:
3083:
2982:
2980:
2958:
2956:
2799:
2797:
1637:Spherically symmetric, static vacuum solution
8:
3036:"Modified gravity and the origin of inertia"
2224:{\displaystyle \mu ={\frac {D}{\sqrt {M}}},}
2729:"Gravity theory dispenses with dark matter"
1633:is the ordinary matter Lagrangian density.
186:will be used; the speed of light is set to
114:STVG has been used successfully to explain
58:Perimeter Institute for Theoretical Physics
3305:
3196:
3177:
3163:
3155:
3105:
3071:
3053:
3002:
2968:
2944:
2926:
2907:Brownstein, J. R.; Moffat, J. W. (2007).
2891:
2873:
2854:Brownstein, J. R.; Moffat, J. W. (2006).
2819:
2769:
2589:
2583:
2552:
2548:
2543:
2535:
2526:
2514:
2486:
2475:
2464:
2460:
2455:
2447:
2438:
2426:
2403:
2383:
2371:{\displaystyle G_{\infty }\simeq 20G_{N}}
2362:
2346:
2340:
2310:
2293:
2284:
2276:
2265:
2252:
2245:
2237:
2206:
2198:
2175:
2170:for a point gravitational source of mass
2155:
2135:
2110:
2104:
2066:
2016:
2002:
1995:
1978:
1977:
1975:
1952:
1927:
1921:
1915:
1907:
1874:
1868:
1842:
1836:
1820:
1814:
1793:
1787:
1767:
1747:
1720:
1710:
1700:
1668:
1667:
1661:
1660:
1657:
1617:
1611:
1610:
1607:
1576:
1571:
1558:
1552:
1551:
1541:
1535:
1534:
1524:
1518:
1517:
1507:
1501:
1500:
1495:
1484:
1457:
1451:
1427:
1414:
1408:
1377:
1357:
1342:
1322:
1315:
1304:
1284:
1277:
1260:
1247:
1232:
1218:
1205:
1198:
1187:
1173:
1160:
1153:
1139:
1125:
1110:
1098:
1092:
1091:
1088:
1062:
1033:
1009:
1003:
983:
963:
938:
932:
908:
896:
884:
874:
861:
851:
835:
829:
798:
778:
765:
755:
745:
731:
719:
706:
692:
669:
657:
651:
650:
647:
623:
617:
587:
563:
557:
537:
517:
497:
466:
430:
418:
412:
411:
408:
373:
365:
355:
347:
334:
326:
316:
308:
295:
287:
277:
264:
256:
246:
230:
224:
191:
147:
1476:The STVG action integral takes the form
552:is the determinant of the metric tensor
3783:Gravitational interaction of antimatter
2719:
2646:accelerating expansion of the universe
3788:Physics in the medieval Islamic world
3711:(2+1)-dimensional topological gravity
3207:Newton's law of universal gravitation
1856:{\displaystyle u^{\mu }=dx^{\mu }/ds}
7:
3533:Asymptotic safety in quantum gravity
3034:Moffat, J. W.; Toth, V. T. (2009).
1028:The three constants of the theory,
3285:Gibbons–Hawking–York boundary term
2482:
2479:
2476:
2347:
2253:
1672:
1669:
1626:{\displaystyle {\mathcal {L}}_{M}}
1573:
1257:
1244:
1215:
1202:
1170:
1157:
897:
871:
848:
589:
512:is the trace of the Ricci tensor,
460:
362:
344:
323:
305:
284:
274:
253:
243:
91:and postulates the existence of a
25:
3400:Modified Newtonian dynamics, MOND
3316:Classical theories of gravitation
2697:Nonsymmetric gravitational theory
1025:is a self-interaction potential.
978:is the mass of the vector field,
575:{\displaystyle g_{\alpha \beta }}
3073:10.1111/j.1745-3933.2009.00633.x
2946:10.1111/j.1365-2966.2007.12275.x
2893:10.1111/j.1365-2966.2006.09996.x
3222:History of gravitational theory
1895:{\displaystyle q_{5}=\kappa m,}
1439:{\displaystyle V_{G},V_{\mu },}
947:{\displaystyle \phi _{\alpha }}
632:{\displaystyle \phi _{\alpha }}
532:is the gravitational constant,
36:Bi-scalar tensor vector gravity
3528:Causal dynamical triangulation
3217:Poisson's equation for gravity
2307:
2290:
2059:
2044:
1564:
1496:
1369:
1363:
1334:
1328:
1296:
1290:
905:
893:
790:
784:
602:is the cosmological constant.
463:
448:
173:
149:
1:
3124:10.1088/0264-9381/26/8/085002
3093:Classical and Quantum Gravity
2788:10.1088/1475-7516/2006/03/004
2727:McKee, M. (25 January 2006).
2702:Tensor–vector–scalar gravity
2677:the reconstructed mass from
2668:A 2017 article on Forbes by
612:for the STVG covector field
42:Scalar–tensor–vector gravity
32:Tensor–vector–scalar gravity
3390:Infinite derivative gravity
2692:Modified Newtonian dynamics
2639:cosmic microwave background
2613:Agreement with observations
1762:is the test particle mass,
1466:{\displaystyle V_{\omega }}
398:Einstein–Hilbert Lagrangian
3856:
3578:Unified-field-theoric and
2637:The acoustic peaks in the
2598:{\displaystyle M_{\odot }}
48:) is a modified theory of
29:
3721:Jackiw–Teitelboim gravity
3500:Canonical quantum gravity
3495:Euclidean quantum gravity
1018:{\displaystyle V_{\phi }}
927:is the field strength of
111:due to the vector field.
3597:Superfluid vacuum theory
3421:Nonsymmetric gravitation
3270:Post-Newtonian formalism
1073:{\displaystyle \omega ,}
595:{\displaystyle \Lambda }
101:weak-field approximation
30:Not to be confused with
3762:Mechanical explanations
3631:Heterotic string theory
3587:Noncommutative geometry
3506:Wheeler–DeWitt equation
3232:General relativity (GR)
3212:Gauss's law for gravity
3186:Theories of gravitation
2143:{\displaystyle \alpha }
1775:{\displaystyle \alpha }
1050:{\displaystyle G,\mu ,}
991:{\displaystyle \omega }
3603:Logarithmic BEC vacuum
3548:Rainbow gravity theory
3426:Scalar–tensor theories
3200:Newtonian gravity (NG)
2664:Problems and criticism
2648:that is apparent from
2599:
2569:
2502:
2412:
2392:
2372:
2326:
2225:
2184:
2164:
2144:
2120:
2090:
1961:
1941:
1896:
1857:
1803:
1776:
1756:
1733:
1627:
1593:
1467:
1440:
1394:
1074:
1051:
1019:
992:
972:
948:
921:
815:
633:
596:
576:
546:
526:
506:
483:
386:
206:
180:
116:galaxy rotation curves
56:, a researcher at the
3680:Twistor string theory
3659:Type II string theory
3652:Bosonic string theory
3592:Semiclassical gravity
3557:Unified-field-theoric
3342:Poincaré gauge theory
2990:Astrophysical Journal
2807:Astrophysical Journal
2679:gravitational lensing
2657:matter power spectrum
2600:
2570:
2503:
2413:
2393:
2373:
2327:
2226:
2185:
2165:
2145:
2121:
2119:{\displaystyle G_{N}}
2091:
1962:
1942:
1897:
1858:
1804:
1802:{\displaystyle q_{5}}
1777:
1757:
1734:
1647:variational principle
1628:
1594:
1468:
1441:
1395:
1075:
1052:
1020:
993:
973:
949:
922:
816:
634:
597:
577:
547:
527:
507:
484:
387:
207:
181:
3747:Aristotelian physics
3716:Gauss–Bonnet gravity
3666:Little string theory
3645:Type 0 string theory
3638:Type I string theory
3513:Loop quantum gravity
3440:Scalar–tensor–vector
3413:Tensor–vector–scalar
3368:Gauge theory gravity
3326:Theory of everything
2582:
2513:
2425:
2402:
2382:
2339:
2236:
2197:
2174:
2163:{\displaystyle \mu }
2154:
2134:
2103:
1974:
1951:
1906:
1867:
1813:
1786:
1766:
1746:
1656:
1606:
1483:
1450:
1407:
1087:
1061:
1032:
1002:
982:
971:{\displaystyle \mu }
962:
931:
828:
646:
616:
586:
556:
536:
516:
496:
407:
223:
190:
146:
134:Mathematical details
3835:Theories of gravity
3564:Kaluza–Klein theory
3140:(9 November 2017).
3116:2009CQGra..26h5002M
3064:2009MNRAS.395L..25M
3013:2008ApJ...680.1158M
2937:2007MNRAS.382...29B
2884:2006MNRAS.367..527B
2830:2006ApJ...636..721B
2780:2006JCAP...03..004M
2708:Reinventing Gravity
2605:is the mass of the
2561:
2473:
956:exterior derivative
378:
360:
339:
321:
300:
269:
205:{\displaystyle c=1}
3809:Gravitational wave
3692:Generalisations /
3580:quantum-mechanical
3488:Quantum-mechanical
3301:general relativity
3275:Linearized gravity
2595:
2565:
2539:
2498:
2451:
2408:
2388:
2368:
2322:
2221:
2180:
2160:
2140:
2116:
2086:
1957:
1937:
1892:
1853:
1799:
1772:
1752:
1729:
1623:
1589:
1463:
1436:
1390:
1070:
1047:
1015:
988:
968:
944:
917:
811:
629:
592:
572:
542:
522:
502:
479:
396:We begin with the
382:
361:
343:
322:
304:
283:
252:
202:
176:
103:, STVG produces a
3822:
3821:
3793:Theory of impetus
3729:
3728:
3701:Liouville gravity
3445:Conformal gravity
3373:Composite gravity
3363:Bimetric theories
3293:
3292:
2650:type Ia supernova
2411:{\displaystyle E}
2391:{\displaystyle D}
2317:
2298:
2282:
2216:
2215:
2183:{\displaystyle M}
2128:Newton's constant
2022:
1986:
1960:{\displaystyle M}
1935:
1755:{\displaystyle m}
1570:
1385:
1348:
1310:
1238:
1193:
1133:
1118:
806:
739:
700:
682:
605:We introduce the
545:{\displaystyle g}
525:{\displaystyle G}
505:{\displaystyle R}
474:
446:
62:Waterloo, Ontario
16:(Redirected from
3847:
3777:
3775:Entropic gravity
3770:
3694:extensions of GR
3682:
3668:
3661:
3654:
3647:
3640:
3633:
3626:
3619:
3605:
3522:
3515:
3508:
3469:Geometrodynamics
3458:
3434:
3415:
3408:
3357:
3350:
3306:
3197:
3179:
3172:
3165:
3156:
3150:
3149:
3134:
3128:
3127:
3109:
3087:
3078:
3077:
3075:
3057:
3031:
3025:
3024:
3006:
2997:(2): 1158–1161.
2984:
2975:
2974:
2972:
2960:
2951:
2950:
2948:
2930:
2928:astro-ph/0702146
2904:
2898:
2897:
2895:
2877:
2875:astro-ph/0507222
2851:
2842:
2841:
2823:
2821:astro-ph/0506370
2801:
2792:
2791:
2773:
2751:
2745:
2744:
2742:
2741:
2724:
2625:Tully–Fisher law
2604:
2602:
2601:
2596:
2594:
2593:
2574:
2572:
2571:
2566:
2560:
2556:
2547:
2531:
2530:
2507:
2505:
2504:
2499:
2494:
2493:
2485:
2472:
2468:
2459:
2443:
2442:
2417:
2415:
2414:
2409:
2397:
2395:
2394:
2389:
2377:
2375:
2374:
2369:
2367:
2366:
2351:
2350:
2331:
2329:
2328:
2323:
2318:
2316:
2315:
2314:
2299:
2294:
2285:
2283:
2281:
2280:
2271:
2270:
2269:
2257:
2256:
2246:
2230:
2228:
2227:
2222:
2217:
2211:
2207:
2189:
2187:
2186:
2181:
2169:
2167:
2166:
2161:
2149:
2147:
2146:
2141:
2125:
2123:
2122:
2117:
2115:
2114:
2095:
2093:
2092:
2087:
2082:
2078:
2077:
2076:
2023:
2021:
2020:
2011:
2007:
2006:
1996:
1988:
1987:
1979:
1966:
1964:
1963:
1958:
1946:
1944:
1943:
1938:
1936:
1931:
1926:
1925:
1916:
1901:
1899:
1898:
1893:
1879:
1878:
1862:
1860:
1859:
1854:
1846:
1841:
1840:
1825:
1824:
1808:
1806:
1805:
1800:
1798:
1797:
1781:
1779:
1778:
1773:
1761:
1759:
1758:
1753:
1738:
1736:
1735:
1730:
1725:
1724:
1715:
1714:
1705:
1704:
1677:
1676:
1675:
1666:
1665:
1632:
1630:
1629:
1624:
1622:
1621:
1616:
1615:
1598:
1596:
1595:
1590:
1582:
1581:
1580:
1568:
1567:
1563:
1562:
1557:
1556:
1546:
1545:
1540:
1539:
1529:
1528:
1523:
1522:
1512:
1511:
1506:
1505:
1472:
1470:
1469:
1464:
1462:
1461:
1445:
1443:
1442:
1437:
1432:
1431:
1419:
1418:
1399:
1397:
1396:
1391:
1386:
1378:
1376:
1372:
1362:
1361:
1349:
1347:
1346:
1337:
1327:
1326:
1316:
1311:
1309:
1308:
1299:
1289:
1288:
1278:
1273:
1269:
1265:
1264:
1252:
1251:
1239:
1237:
1236:
1227:
1223:
1222:
1210:
1209:
1199:
1194:
1192:
1191:
1182:
1178:
1177:
1165:
1164:
1154:
1147:
1146:
1134:
1126:
1119:
1111:
1103:
1102:
1097:
1096:
1079:
1077:
1076:
1071:
1056:
1054:
1053:
1048:
1024:
1022:
1021:
1016:
1014:
1013:
997:
995:
994:
989:
977:
975:
974:
969:
953:
951:
950:
945:
943:
942:
926:
924:
923:
918:
916:
915:
900:
889:
888:
879:
878:
866:
865:
856:
855:
843:
842:
820:
818:
817:
812:
807:
799:
797:
793:
783:
782:
770:
769:
760:
759:
750:
749:
740:
732:
727:
726:
714:
713:
701:
693:
683:
681:
670:
662:
661:
656:
655:
638:
636:
635:
630:
628:
627:
601:
599:
598:
593:
581:
579:
578:
573:
571:
570:
551:
549:
548:
543:
531:
529:
528:
523:
511:
509:
508:
503:
488:
486:
485:
480:
475:
467:
447:
445:
431:
423:
422:
417:
416:
391:
389:
388:
383:
377:
372:
359:
354:
338:
333:
320:
315:
299:
294:
282:
281:
268:
263:
251:
250:
238:
237:
211:
209:
208:
203:
185:
183:
182:
179:{\displaystyle }
177:
89:action principle
21:
3855:
3854:
3850:
3849:
3848:
3846:
3845:
3844:
3825:
3824:
3823:
3818:
3797:
3773:
3766:
3737:
3735:
3725:
3706:Lovelock theory
3693:
3687:
3678:
3664:
3657:
3650:
3643:
3636:
3629:
3622:
3615:
3601:
3579:
3573:
3552:
3518:
3511:
3504:
3483:
3474:Induced gravity
3454:
3450:Scalar theories
3430:
3411:
3404:
3395:Massive gravity
3355:Teleparallelism
3353:
3348:Einstein–Cartan
3346:
3330:
3321:Quantum gravity
3300:
3299:Alternatives to
3289:
3255:Exact solutions
3226:
3188:
3183:
3153:
3136:
3135:
3131:
3089:
3088:
3081:
3033:
3032:
3028:
2986:
2985:
2978:
2962:
2961:
2954:
2906:
2905:
2901:
2853:
2852:
2845:
2803:
2802:
2795:
2753:
2752:
2748:
2739:
2737:
2726:
2725:
2721:
2717:
2688:
2675:galaxy clusters
2666:
2615:
2585:
2580:
2579:
2522:
2511:
2510:
2474:
2434:
2423:
2422:
2400:
2399:
2380:
2379:
2358:
2342:
2337:
2336:
2306:
2289:
2272:
2261:
2248:
2247:
2234:
2233:
2195:
2194:
2172:
2171:
2152:
2151:
2132:
2131:
2106:
2101:
2100:
2062:
2028:
2024:
2012:
1998:
1997:
1972:
1971:
1949:
1948:
1917:
1904:
1903:
1870:
1865:
1864:
1832:
1816:
1811:
1810:
1789:
1784:
1783:
1764:
1763:
1744:
1743:
1716:
1706:
1696:
1659:
1654:
1653:
1643:field equations
1639:
1609:
1604:
1603:
1572:
1550:
1533:
1516:
1499:
1481:
1480:
1453:
1448:
1447:
1423:
1410:
1405:
1404:
1353:
1338:
1318:
1317:
1300:
1280:
1279:
1256:
1243:
1228:
1214:
1201:
1200:
1183:
1169:
1156:
1155:
1152:
1148:
1135:
1124:
1120:
1090:
1085:
1084:
1059:
1058:
1030:
1029:
1005:
1000:
999:
980:
979:
960:
959:
934:
929:
928:
904:
880:
870:
857:
847:
831:
826:
825:
774:
761:
751:
741:
715:
702:
691:
687:
674:
649:
644:
643:
619:
614:
613:
584:
583:
559:
554:
553:
534:
533:
514:
513:
494:
493:
435:
410:
405:
404:
395:
273:
242:
226:
221:
220:
188:
187:
144:
143:
136:
85:
39:
28:
23:
22:
15:
12:
11:
5:
3853:
3851:
3843:
3842:
3837:
3827:
3826:
3820:
3819:
3817:
3816:
3811:
3805:
3803:
3802:Related topics
3799:
3798:
3796:
3795:
3790:
3785:
3780:
3779:
3778:
3771:
3759:
3754:
3749:
3743:
3741:
3731:
3730:
3727:
3726:
3724:
3723:
3718:
3713:
3708:
3703:
3697:
3695:
3689:
3688:
3686:
3685:
3684:
3683:
3674:Twistor theory
3671:
3670:
3669:
3662:
3655:
3648:
3641:
3634:
3627:
3620:
3608:
3607:
3606:
3594:
3589:
3583:
3581:
3575:
3574:
3572:
3571:
3566:
3560:
3558:
3554:
3553:
3551:
3550:
3545:
3540:
3535:
3530:
3525:
3524:
3523:
3516:
3509:
3497:
3491:
3489:
3485:
3484:
3482:
3481:
3476:
3471:
3466:
3461:
3460:
3459:
3447:
3442:
3437:
3436:
3435:
3423:
3418:
3417:
3416:
3409:
3397:
3392:
3387:
3375:
3370:
3365:
3360:
3359:
3358:
3351:
3338:
3336:
3332:
3331:
3329:
3328:
3323:
3318:
3312:
3310:
3303:
3295:
3294:
3291:
3290:
3288:
3287:
3282:
3277:
3272:
3267:
3262:
3257:
3252:
3247:
3242:
3236:
3234:
3228:
3227:
3225:
3224:
3219:
3214:
3209:
3203:
3201:
3194:
3190:
3189:
3184:
3182:
3181:
3174:
3167:
3159:
3152:
3151:
3129:
3079:
3026:
3021:10.1086/587926
2976:
2952:
2899:
2868:(2): 527–540.
2843:
2838:10.1086/498208
2814:(2): 721–741.
2793:
2746:
2718:
2716:
2713:
2712:
2711:
2704:
2699:
2694:
2687:
2684:
2665:
2662:
2661:
2660:
2653:
2642:
2614:
2611:
2592:
2588:
2576:
2575:
2564:
2559:
2555:
2551:
2546:
2542:
2538:
2534:
2529:
2525:
2521:
2518:
2508:
2497:
2492:
2489:
2484:
2481:
2478:
2471:
2467:
2463:
2458:
2454:
2450:
2446:
2441:
2437:
2433:
2430:
2407:
2387:
2365:
2361:
2357:
2354:
2349:
2345:
2333:
2332:
2321:
2313:
2309:
2305:
2302:
2297:
2292:
2288:
2279:
2275:
2268:
2264:
2260:
2255:
2251:
2244:
2241:
2231:
2220:
2214:
2210:
2205:
2202:
2179:
2159:
2139:
2113:
2109:
2097:
2096:
2085:
2081:
2075:
2072:
2069:
2065:
2061:
2058:
2055:
2052:
2049:
2046:
2043:
2040:
2037:
2034:
2031:
2027:
2019:
2015:
2010:
2005:
2001:
1994:
1991:
1985:
1982:
1956:
1934:
1930:
1924:
1920:
1914:
1911:
1891:
1888:
1885:
1882:
1877:
1873:
1852:
1849:
1845:
1839:
1835:
1831:
1828:
1823:
1819:
1796:
1792:
1771:
1751:
1740:
1739:
1728:
1723:
1719:
1713:
1709:
1703:
1699:
1695:
1692:
1689:
1686:
1683:
1680:
1674:
1671:
1664:
1638:
1635:
1620:
1614:
1600:
1599:
1588:
1585:
1579:
1575:
1566:
1561:
1555:
1549:
1544:
1538:
1532:
1527:
1521:
1515:
1510:
1504:
1498:
1494:
1491:
1488:
1460:
1456:
1435:
1430:
1426:
1422:
1417:
1413:
1401:
1400:
1389:
1384:
1381:
1375:
1371:
1368:
1365:
1360:
1356:
1352:
1345:
1341:
1336:
1333:
1330:
1325:
1321:
1314:
1307:
1303:
1298:
1295:
1292:
1287:
1283:
1276:
1272:
1268:
1263:
1259:
1255:
1250:
1246:
1242:
1235:
1231:
1226:
1221:
1217:
1213:
1208:
1204:
1197:
1190:
1186:
1181:
1176:
1172:
1168:
1163:
1159:
1151:
1145:
1142:
1138:
1132:
1129:
1123:
1117:
1114:
1109:
1106:
1101:
1095:
1069:
1066:
1046:
1043:
1040:
1037:
1012:
1008:
987:
967:
954:(given by the
941:
937:
914:
911:
907:
903:
899:
895:
892:
887:
883:
877:
873:
869:
864:
860:
854:
850:
846:
841:
838:
834:
822:
821:
810:
805:
802:
796:
792:
789:
786:
781:
777:
773:
768:
764:
758:
754:
748:
744:
738:
735:
730:
725:
722:
718:
712:
709:
705:
699:
696:
690:
686:
680:
677:
673:
668:
665:
660:
654:
626:
622:
591:
569:
566:
562:
541:
521:
501:
490:
489:
478:
473:
470:
465:
462:
459:
456:
453:
450:
444:
441:
438:
434:
429:
426:
421:
415:
393:
392:
381:
376:
371:
368:
364:
358:
353:
350:
346:
342:
337:
332:
329:
325:
319:
314:
311:
307:
303:
298:
293:
290:
286:
280:
276:
272:
267:
262:
259:
255:
249:
245:
241:
236:
233:
229:
201:
198:
195:
175:
172:
169:
166:
163:
160:
157:
154:
151:
135:
132:
120:Bullet Cluster
84:
81:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3852:
3841:
3838:
3836:
3833:
3832:
3830:
3815:
3812:
3810:
3807:
3806:
3804:
3800:
3794:
3791:
3789:
3786:
3784:
3781:
3776:
3772:
3769:
3768:Fatio–Le Sage
3765:
3764:
3763:
3760:
3758:
3755:
3753:
3750:
3748:
3745:
3744:
3742:
3740:
3734:Pre-Newtonian
3732:
3722:
3719:
3717:
3714:
3712:
3709:
3707:
3704:
3702:
3699:
3698:
3696:
3690:
3681:
3677:
3676:
3675:
3672:
3667:
3663:
3660:
3656:
3653:
3649:
3646:
3642:
3639:
3635:
3632:
3628:
3625:
3621:
3618:
3614:
3613:
3612:
3611:String theory
3609:
3604:
3600:
3599:
3598:
3595:
3593:
3590:
3588:
3585:
3584:
3582:
3576:
3570:
3567:
3565:
3562:
3561:
3559:
3555:
3549:
3546:
3544:
3541:
3539:
3536:
3534:
3531:
3529:
3526:
3521:
3517:
3514:
3510:
3507:
3503:
3502:
3501:
3498:
3496:
3493:
3492:
3490:
3486:
3480:
3477:
3475:
3472:
3470:
3467:
3465:
3462:
3457:
3453:
3452:
3451:
3448:
3446:
3443:
3441:
3438:
3433:
3429:
3428:
3427:
3424:
3422:
3419:
3414:
3410:
3407:
3403:
3402:
3401:
3398:
3396:
3393:
3391:
3388:
3386:
3384:
3380:
3376:
3374:
3371:
3369:
3366:
3364:
3361:
3356:
3352:
3349:
3345:
3344:
3343:
3340:
3339:
3337:
3333:
3327:
3324:
3322:
3319:
3317:
3314:
3313:
3311:
3307:
3304:
3302:
3296:
3286:
3283:
3281:
3280:ADM formalism
3278:
3276:
3273:
3271:
3268:
3266:
3263:
3261:
3258:
3256:
3253:
3251:
3248:
3246:
3243:
3241:
3238:
3237:
3235:
3233:
3229:
3223:
3220:
3218:
3215:
3213:
3210:
3208:
3205:
3204:
3202:
3198:
3195:
3191:
3187:
3180:
3175:
3173:
3168:
3166:
3161:
3160:
3157:
3147:
3143:
3139:
3138:Siegel, Ethan
3133:
3130:
3125:
3121:
3117:
3113:
3108:
3103:
3100:(8): 085002.
3099:
3095:
3094:
3086:
3084:
3080:
3074:
3069:
3065:
3061:
3056:
3051:
3047:
3043:
3042:
3037:
3030:
3027:
3022:
3018:
3014:
3010:
3005:
3000:
2996:
2992:
2991:
2983:
2981:
2977:
2971:
2966:
2959:
2957:
2953:
2947:
2942:
2938:
2934:
2929:
2924:
2920:
2916:
2915:
2910:
2903:
2900:
2894:
2889:
2885:
2881:
2876:
2871:
2867:
2863:
2862:
2857:
2850:
2848:
2844:
2839:
2835:
2831:
2827:
2822:
2817:
2813:
2809:
2808:
2800:
2798:
2794:
2789:
2785:
2781:
2777:
2772:
2771:gr-qc/0506021
2767:
2763:
2759:
2758:
2750:
2747:
2736:
2735:
2734:New Scientist
2730:
2723:
2720:
2714:
2710:
2709:
2705:
2703:
2700:
2698:
2695:
2693:
2690:
2689:
2685:
2683:
2680:
2676:
2671:
2663:
2658:
2654:
2652:observations;
2651:
2647:
2643:
2640:
2636:
2635:
2634:
2631:
2628:
2626:
2621:
2618:
2612:
2610:
2608:
2590:
2586:
2562:
2557:
2553:
2549:
2544:
2540:
2536:
2532:
2527:
2523:
2519:
2516:
2509:
2495:
2490:
2487:
2469:
2465:
2461:
2456:
2452:
2448:
2444:
2439:
2435:
2431:
2428:
2421:
2420:
2419:
2405:
2385:
2363:
2359:
2355:
2352:
2343:
2319:
2311:
2303:
2300:
2295:
2286:
2277:
2273:
2266:
2262:
2258:
2249:
2242:
2239:
2232:
2218:
2212:
2208:
2203:
2200:
2193:
2192:
2191:
2177:
2157:
2137:
2129:
2111:
2107:
2083:
2079:
2073:
2070:
2067:
2063:
2056:
2053:
2050:
2047:
2041:
2038:
2035:
2032:
2029:
2025:
2017:
2013:
2008:
2003:
1999:
1992:
1989:
1983:
1980:
1970:
1969:
1968:
1954:
1932:
1928:
1922:
1918:
1912:
1909:
1902:the value of
1889:
1886:
1883:
1880:
1875:
1871:
1850:
1847:
1843:
1837:
1833:
1829:
1826:
1821:
1817:
1794:
1790:
1769:
1749:
1726:
1721:
1717:
1711:
1707:
1701:
1697:
1693:
1690:
1687:
1684:
1681:
1678:
1652:
1651:
1650:
1648:
1644:
1636:
1634:
1618:
1586:
1583:
1577:
1559:
1547:
1542:
1530:
1525:
1513:
1508:
1492:
1489:
1486:
1479:
1478:
1477:
1474:
1458:
1454:
1433:
1428:
1424:
1420:
1415:
1411:
1387:
1382:
1379:
1373:
1366:
1358:
1354:
1350:
1343:
1339:
1331:
1323:
1319:
1312:
1305:
1301:
1293:
1285:
1281:
1274:
1270:
1266:
1261:
1253:
1248:
1240:
1233:
1229:
1224:
1219:
1211:
1206:
1195:
1188:
1184:
1179:
1174:
1166:
1161:
1149:
1143:
1140:
1136:
1130:
1127:
1121:
1115:
1112:
1107:
1104:
1099:
1083:
1082:
1081:
1067:
1064:
1044:
1041:
1038:
1035:
1026:
1010:
1006:
985:
965:
957:
939:
935:
912:
909:
901:
890:
885:
881:
875:
867:
862:
858:
852:
844:
839:
836:
832:
808:
803:
800:
794:
787:
779:
775:
771:
766:
762:
756:
752:
746:
742:
736:
733:
728:
723:
720:
716:
710:
707:
703:
697:
694:
688:
684:
678:
675:
671:
666:
663:
658:
642:
641:
640:
624:
620:
611:
608:
607:Maxwell-Proca
603:
567:
564:
560:
539:
519:
499:
476:
471:
468:
457:
454:
451:
442:
439:
436:
432:
427:
424:
419:
403:
402:
401:
399:
379:
374:
369:
366:
356:
351:
348:
340:
335:
330:
327:
317:
312:
309:
301:
296:
291:
288:
278:
270:
265:
260:
257:
247:
239:
234:
231:
227:
219:
218:
217:
215:
199:
196:
193:
170:
167:
164:
161:
158:
155:
152:
142:signature of
141:
133:
131:
129:
125:
121:
117:
112:
110:
106:
102:
98:
97:scalar fields
94:
90:
82:
80:
78:
76:
72:
67:
63:
59:
55:
52:developed by
51:
47:
43:
37:
33:
19:
3840:Astrophysics
3736:theories and
3569:Supergravity
3439:
3382:
3378:
3240:Introduction
3145:
3132:
3097:
3091:
3045:
3039:
3029:
2994:
2988:
2921:(1): 29–47.
2918:
2912:
2902:
2865:
2859:
2811:
2805:
2761:
2755:
2749:
2738:. Retrieved
2732:
2722:
2706:
2670:Ethan Siegel
2667:
2632:
2629:
2622:
2619:
2616:
2577:
2334:
2190:in the form
2098:
1741:
1640:
1601:
1475:
1402:
1027:
823:
604:
491:
394:
214:Ricci tensor
137:
113:
93:vector field
86:
74:
70:
69:
65:
45:
41:
40:
3538:Causal sets
3432:Brans–Dicke
3250:Mathematics
124:dark matter
109:fifth force
54:John Moffat
3829:Categories
3752:CGHS model
3739:toy models
3048:(1): L25.
2740:2008-07-26
2715:References
2641:radiation;
610:Lagrangian
18:MOG theory
3757:RST model
3543:DGP model
3520:Spin foam
3464:Whitehead
3456:Nordström
3385:) gravity
3335:Classical
3309:Paradigms
3260:Resources
3107:0712.1796
3055:0710.3415
3004:0708.1935
2970:0710.0364
2591:⊙
2545:⊙
2533:⋅
2520:≃
2488:−
2457:⊙
2445:⋅
2432:≃
2353:≃
2348:∞
2259:−
2254:∞
2240:α
2201:μ
2158:μ
2138:α
2071:μ
2068:−
2054:μ
2042:α
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2036:α
1993:−
1984:¨
1933:ω
1910:κ
1884:κ
1838:μ
1822:μ
1770:α
1722:μ
1712:μ
1708:ϕ
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1526:ϕ
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1459:ω
1429:μ
1380:−
1367:ω
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1332:μ
1324:μ
1267:ω
1262:β
1258:∂
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1225:μ
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1065:ω
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940:α
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910:α
902:ϕ
886:α
882:ϕ
876:β
872:∂
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853:α
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840:β
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801:−
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780:ϕ
767:α
763:ϕ
757:α
753:ϕ
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729:−
724:β
721:α
711:β
708:α
685:ω
679:π
667:−
659:ϕ
625:α
621:ϕ
590:Λ
568:β
565:α
469:−
461:Λ
440:π
428:−
375:δ
370:β
367:γ
363:Γ
357:γ
352:δ
349:α
345:Γ
341:−
336:δ
331:δ
328:γ
324:Γ
318:γ
313:β
310:α
306:Γ
297:γ
292:γ
289:α
285:Γ
279:β
275:∂
271:−
266:γ
261:β
258:α
254:Γ
248:γ
244:∂
235:β
232:α
171:−
165:−
159:−
99:. In the
3814:Graviton
3624:F-theory
3617:M-theory
3193:Standard
2764:(3): 4.
2686:See also
582:, while
83:Overview
3245:History
3112:Bibcode
3060:Bibcode
3009:Bibcode
2933:Bibcode
2880:Bibcode
2826:Bibcode
2776:Bibcode
128:inertia
73:dified
50:gravity
3146:Forbes
2578:where
2335:where
2099:where
1742:where
1602:where
1569:
1403:where
824:where
492:where
140:metric
105:Yukawa
77:ravity
3406:AQUAL
3265:Tests
3102:arXiv
3050:arXiv
2999:arXiv
2965:arXiv
2923:arXiv
2870:arXiv
2816:arXiv
2766:arXiv
2762:2006
2655:The
2644:The
2398:and
2150:and
1641:The
1446:and
1057:and
958:),
46:STVG
3120:doi
3068:doi
3046:395
3017:doi
2995:680
2941:doi
2919:382
2888:doi
2866:367
2834:doi
2812:636
2784:doi
2607:Sun
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66:MOG
60:in
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3144:.
3118:.
3110:.
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2301:+
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2291:(
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