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Bimetric gravity

Bimetric gravity or bigravity refers to two different classes of theories. The first class of theories relies on modified mathematical theories of gravity (or gravitation) in which two metric tensors are used instead of one.[1][2] The second metric may be introduced at high energies, with the implication that the speed of light could be energy-dependent, enabling models with a variable speed of light.

If the two metrics are dynamical and interact, a first possibility implies two graviton modes, one massive and one massless; such bimetric theories are then closely related to massive gravity.[3] Several bimetric theories with massive gravitons exist, such as those attributed to Nathan Rosen (1909–1995)[4][5][6] or Mordehai Milgrom with relativistic extensions of Modified Newtonian Dynamics (MOND).[7] More recently, developments in massive gravity have also led to new consistent theories of bimetric gravity.[8] Though none has been shown to account for physical observations more accurately or more consistently than the theory of general relativity, Rosen's theory has been shown to be inconsistent with observations of the Hulse–Taylor binary pulsar.[5] Some of these theories lead to cosmic acceleration at late times and are therefore alternatives to dark energy.[9][10] Bimetric gravity is also at odds with measurements of gravitational waves emitted by the neutron-star merger GW170817.[11]

On the contrary, the second class of bimetric gravity theories does not rely on massive gravitons and does not modify Newton's law, but instead describes the universe as a manifold having two coupled Riemannian metrics, where matter populating the two sectors interact through gravitation (and antigravitation if the topology and the Newtonian approximation considered introduce negative mass and negative energy states in cosmology as an alternative to dark matter and dark energy). Some of these cosmological models also use a variable speed of light in the high energy density state of the radiation-dominated era of the universe, challenging the inflation hypothesis.[12][13][14][15][16]

  1. ^ Rosen, Nathan (1940), "General Relativity and Flat Space. I", Phys. Rev., 57 (2): 147–150, Bibcode:1940PhRv...57..147R, doi:10.1103/PhysRev.57.147
  2. ^ Rosen, Nathan (1940), "General Relativity and Flat Space. II", Phys. Rev., 57 (2): 150, Bibcode:1940PhRv...57..150R, doi:10.1103/PhysRev.57.150
  3. ^ Hassan, S.F.; Rosen, Rachel A. (2012). "Bimetric Gravity from Ghost-free Massive Gravity". JHEP. 1202 (2): 126. arXiv:1109.3515. Bibcode:2012JHEP...02..126H. doi:10.1007/JHEP02(2012)126. S2CID 118427524.
  4. ^ Rosen, Nathan (1973), "A bi-metric Theory of Gravitation", Gen. Rel. Grav., 4 (6): 435–447, Bibcode:1973GReGr...4..435R, doi:10.1007/BF01215403, S2CID 189831561
  5. ^ a b Cite error: The named reference NR was invoked but never defined (see the help page).
  6. ^ Cite error: The named reference Tech was invoked but never defined (see the help page).
  7. ^ Milgrom, M. (2009). "Bimetric MOND gravity". Phys. Rev. D. 80 (12): 123536. arXiv:0912.0790. Bibcode:2009PhRvD..80l3536M. doi:10.1103/PhysRevD.80.123536. S2CID 119229428.
  8. ^ Zyga, Lisa (21 September 2017). "Gravitational waves may oscillate, just like neutrinos". Phys.org. Omicron Technology Limited.
  9. ^ Akrami, Yashar; Koivisto, Tomi S.; Sandstad, Marit (2013). "Accelerated expansion from ghost-free bigravity: a statistical analysis with improved generality". JHEP. 1303 (3): 099. arXiv:1209.0457. Bibcode:2013JHEP...03..099A. doi:10.1007/JHEP03(2013)099. S2CID 54533200.
  10. ^ Akrami, Yashar; Hassan, S.F.; Könnig, Frank; Schmidt-May, Angnis; Solomon, Adam R. (2015). "Bimetric gravity is cosmologically viable". Physics Letters B. 748: 37–44. arXiv:1503.07521. Bibcode:2015PhLB..748...37A. doi:10.1016/j.physletb.2015.06.062. S2CID 118371127.
  11. ^ Baker T, Bellini E, Ferreira PG, Lagos M, Noller J, Sawicki I (December 2017). "Strong Constraints on Cosmological Gravity from GW170817 and GRB 170817A". Physical Review Letters. 119 (25): 251301. arXiv:1710.06394. Bibcode:2017PhRvL.119y1301B. doi:10.1103/PhysRevLett.119.251301. PMID 29303333. S2CID 36160359.
  12. ^ Henry-Couannier, F. (30 April 2005). "Discrete symmetries and general relativity, the dark side of gravity". International Journal of Modern Physics A. 20 (11): 2341–2345. arXiv:gr-qc/0410055. Bibcode:2005IJMPA..20.2341H. doi:10.1142/S0217751X05024602. S2CID 5063.
  13. ^ Hossenfelder, S. (15 August 2008). "A Bi-Metric Theory with Exchange Symmetry". Physical Review D. 78 (4): 044015. arXiv:0807.2838. Bibcode:2008PhRvD..78d4015H. doi:10.1103/PhysRevD.78.044015. S2CID 119152509.
  14. ^ Hossenfelder, Sabine (June 2009). Antigravitation. 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions. Boston: American Institute of Physics. arXiv:0909.3456. doi:10.1063/1.3327545.
  15. ^ Petit, J.-P.; d'Agostini, G. (10 November 2014). "Cosmological bimetric model with interacting positive and negative masses and two different speeds of light, in agreement with the observed acceleration of the Universe" (PDF). Modern Physics Letters A. 29 (34): 1450182. Bibcode:2014MPLA...2950182P. doi:10.1142/S021773231450182X.
  16. ^ O'Dowd, Matt (7 February 2019). "Sound Waves from the Beginning of Time". PBS Space Time. PBS. 16 minutes in. Retrieved 8 February 2019. An alternate model that how negative mass might behave: in so-called 'bimetric gravity' you can have positive and negative masses, but each is described by its own set of Einstein field equations. That's kinda like having 'parallel spacetimes', one with positive and one with negative masses, which can still interact gravitationally. In these models, like masses attract and opposite masses repel… and you don't get the crazy 'runaway motion' that occurs if you put both positive and negative masses in the same spacetime. So no perpetual motion machines… It can also be used to explain dark energy and dark matter.

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