MILGROM’S LAW AND Λ’S SHADOW: HOW MASSIVE GRAVITY CONNECTS GALACTIC AND COSMIC DYNAMICS

다국어 초록 (Multilingual Abstract)

Massive gravity provides a natural solution for the dark energy problem of cosmology and is also a candidate for resolving the dark matter problem. I demonstrate that, assuming reasonable scaling relations, massive gravity can provide for Milgrom’s law of gravity (or “modified Newtonian dynamics”) which is known to remove the need for particle dark matter from galactic dynamics. Milgrom’s law comes with a characteristic acceleration, Milgrom’s constant, which is observationally constrained to a0 ≈ 1.1×10−10ms−2. In the derivation presented here, this constant arises naturally from the cosmologically required mass of gravitons like a0 ∝ c√ ∝ cH0√3 , with , H0, and being the cosmological constant, the Hubble constant, and the third cosmological parameter, respectively. My derivation suggests that massive gravity could be the mechanism behind both, dark matter and dark energy.

참고문헌 (Reference)

1 Vainshtein, A. I, "To the Problem of Non-Vanishing Gravitation Mass" 39 : 393-, 1972

2 Hinterbichler, K, "Theoretical Aspects of Massive Gravity" 84 : 671-, 2012

3 Trippe, S, "The “Graviton Picture”: a Bohr Model for Gravitation on Galactic Scales?" 93 : 213-, 2015

4 Trippe, S, "The ‘Missing Mass Problem’ in Astronomy and the Need for a Modified Law of Gravity" 69 : 173-, 2014

5 Sanders, R. H, "The Universal Faber–Jackson Relation" 407 : 1128-, 2010

6 Avilez-Lopez, A., "The Parameterized Post-Newtonian-Vainshteinian Formalism"

7 Cardone, V. F., "The Modified Newtonian Dynamics Fundamental Plane" 412 : 2617-, 2011

8 McGaugh, S. S, "The Mass Discrepancy–Acceleration Relation: Disk Mass and the Dark Matter Distribution" 609 : 652-, 2004

9 Kroupa, P, "The Dark Matter Crisis: Falsification of the Current Standard Model of Cosmology" 29 : 395-, 2012

10 Bahcall, N. A., "The Cosmic Triangle: Revealing the State of the Universe" 284 : 1481-, 1999

11 McGaugh, S. S, "The Baryonic Tully–Fisher Relation of Galaxies with Extended Rotation Curves and the Stellar Mass of Rotating Galaxies" 632 : 859-, 2005

12 Chae, K. -H., "Testing Modified Newtonian Dynamics through Statistics of Velocity Dispersion Profiles in the Inner Regions of Elliptical Galaxies"

13 Gentile, G., "THINGS about MOND" 527 : A76-, 2011

14 Milgrom, M., "Rings and Shells of “Dark Matter” as MOND Artifacts" 678 : 131-, 2008

15 Ade, P. A. R., "Planck 2013 Results. XVI. Cosmological Parameters" 571 : A16-, 2013

16 De Felice, A., "On the Cosmology of Massive Gravity" 30 : 184004-, 2013

17 Fierz, M., "On Relativistic Wave Equations for Arbitrary Spin in an Electromagnetic Field" 173 : 211-, 1939

18 MYUNG-HYUN RHEE, "ON THE PHYSICAL BASIS OF THE TULLY-FISHER RELATION" 한국천문학회 37 (37): 15-39, 2004

19 McGaugh, S. S, "Novel Test of Modified Newtonian Dynamics with Gas Rich Galaxies" 106 : 121303-, 2011

20 Famaey, B., "Modified Newtonian Dynamics (MOND): Observational Phenomenology and Relativistic Extensions" 15 : 10-, 2012

21 Clifton, T., "Modified Gravity and Cosmology" 513 : 1-, 2012

22 de Rham, C, "Massive Gravity" 17 : 7-, 2014

23 Milgrom, M, "MOND Theory" 93 : 107-, 2015

24 MYUNG-HYUN RHEE, "MASS-TO-LIGHT RATIO AND THE TULLY-FISHER RELATION" 한국천문학회 37 (37): 91-118, 2004

25 Baker, T., "Linking Tests of Gravity on All Scales: From the Strong-Field Regime to Cosmology" 802 : 63-, 2015

26 Milgrom, M, "Isothermal Spheres in the Modified Dynamics" 287 : 571-, 1984

27 Walker, M. G., "Is the Universe Simpler than CDM?" 55 : 198-, 2014

28 Griffiths, D., "Introduction to Elementary Particles" Wiley-VCH 2008

29 Xu, D., "How Well Can Dark-Matter Substructures Account for the Observed Radio Flux-Ratio Anomalies?" 447 : 3189-, 2015

30 van Putten, M. H. P. M, "Galaxy Rotation Curves in de Sitter Space"

31 Kroupa, P, "Galaxies as Simple Dynamical Systems:Observational Data Disfavor Dark Matter and Stochastic Star Formation" 93 : 169-, 2015

32 Wu, X., "Galactic Rotation Curves, the Baryon-to-Dark-Halo-Mass Relation and Space-Time Scale Invariance" 446 : 330-, 2015

33 Tasinato, G., "Exact Solutions in Massive Gravity" 30 : 184002-, 2013

34 Milgrom, M, "Dynamics Predictions Agree with Observations of the Hi Kinematics in Faint Dwarf Galaxies Contrary to the Conclusions of Lo, Sargent, and Young" 429 : 540-, 1994

35 Volkov, M. S, "Cosmological Solutions with Massive Gravitons in the Bigravity Theory, J. High Energy Phys" 35-, 2012

36 Cardone, V. F., "Constraining Massive Gravity with Recent Cosmological Data" 85 : 124005-, 2012

37 Sascha Trippe, "CAN MASSIVE GRAVITY EXPLAIN THE MASS DISCREPANCY--ACCELERATION RELATION OF DISK GALAXIES?" 한국천문학회 46 (46): 133-140, 2013

38 McGaugh, S. S, "Balance of Dark and Luminous Mass in Rotating Galaxies" 95 : 171302-, 2005

39 Babichev, E., "An Introduction to the Vainshtein Mechanism, Class" 30 : 184001-, 2013

40 van Putten, M. H. P. M., "Accelerated Expansion from Cosmological Holography" 450 : L48-, 2015

41 Sascha Trippe, "A SIMPLIFIED TREATMENT OF GRAVITATIONAL INTERACTION ON GALACTIC SCALES" 한국천문학회 46 (46): 41-47, 2013

42 Lee, J., "A New Dynamical Mass Estimate for the Virgo Cluster Using the Radial Velocity Profile of the Filament Galaxies"

43 Milgrom, M, "A Modification of the Newtonian Dynamics:Implications for Galaxy Systems" 270 : 384-, 1983

44 Milgrom, M, "A Modification of the Newtonian Dynamics:Implications for Galaxies" 270 : 371-, 1983

45 Milgrom, M, "A Modification of the Newtonian Dynamics as a Possible Alternative to the Hidden Mass Hypothesis" 270 : 365-, 1983

46 Sanders, R. H., "A Faber–Jackson Relation for Clusters of Galaxies: Implications for Modified Dynamics" 284 : L31-, 1994

47 Sascha Trippe, "A DERIVATION OF MODIFIED NEWTONIAN DYNAMICS" 한국천문학회 46 (46): 93-96, 2013