Linearization the New Model of Mimetic Bi-Gravity

Document Type : Original Scientific Paper

Authors

1 ‎Department of Physics‎, ‎University of Kashan,‎ ‎Kashan‎, ‎I‎. ‎R‎. ‎Iran

2 ‎Department of Physics, Isfahan University of Technology, ‎Isfahan‎, ‎I‎. ‎R‎. ‎Iran

10.22052/mir.2025.256035.1493

Abstract

‎This paper presents a novel integration of mimetic gravity and massive bi-gravity theories‎. ‎Despite the success of general relativity (GR)‎, ‎explaining cosmic phenomena requires additional elements like dark matter and dark energy‎. ‎Mimetic gravity extends GR's degrees of freedom while respecting conformal symmetry‎, ‎and bi-gravity introduces an additional metric field for massive gravity‎. We redefine the action for combining these theories and linearize it around a flat spacetime solution‎. ‎Our analysis highlights the dynamical behavior and stability of the combined model‎, ‎offering insights for further theoretical and empirical investigations‎. ‎This work contributes to bridging GR with quantum field theories and exploring new directions in gravitational research‎.

Keywords

Main Subjects


[1] L. Sebastiani, S. Vagnozzi and R. Myrzakulov, Mimetic gravity: A review of recent developments and applications to cosmology and astrophysics, Adv. High Energy Phys. 2017 (2017) #3156915, https://doi.org/10.1155/2017/3156915.
[2] A. Rida Khalifeh, N. Bellomo, J. Luis Bernal and R. Jimenez, Can dark matter be geometry? A case study with mimetic dark matter, Phys. Dark Universe. 30 (2020) #100646, https://doi.org/10.1016/j.dark.2020.100646.
[3] G. Jiang, Dark and Luminous Matter in Galaxies and Large Scale Structure, Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1213378610, 2008.
[4] P. Jirou-sek, On Extended Mimetic Gravity, Charles University in Prague, Faculty of Mathematics and Physics, Prague, 2016.
[5] M. Bañados and P. G. Ferreira, Eddington’s theory of gravity and its progeny, Phys. Rev. Lett. 105 (2010) #011101, https://doi.org/10.1103/PhysRevLett.105.011101.
[6] L. Mirzagholi and A. Vikman, Imperfect dark matter, J. Cosmol. Astropart. Phys. 2015 (2015) #028, https://doi.org/10.1088/1475-7516/2015/06/028.
[7] H. Firouzjahi, M. A. Gorji, S. A. Hosseini Mansoori, A. Karami and T. Rostami, Two-field disformal transformation and mimetic cosmology, J. Cosmol. Astropart. Phys. 2018 (2018) #046, https://doi.org/10.1088/1475-7516/2018/11/046
[8] A. H. Chamseddine and V. Mukhanov, Mimetic dark matter, J. High Energ. Phys. 2013 (2013) #135, https://doi.org/10.1007/JHEP11(2013)135.
[9] S. Nojiri and S. D. Odintsov, Mimetic F(R) gravity: Inflation, dark energy and bounce, Mod. Phys. Lett. 29 (2014) #1450211, https://doi.org/10.1142/S0217732314502113.
[10] Z. Haghani, M. Shiravand and S. Shahidi, Energy conditions in mimetic-f(R) gravity, Int. J. Mod. Phys. D. 27 (2018) #1850049, https://doi.org/10.1142/S0218271818500499.
[11] D. Momeni, A. Altaibayeva and R. Myrzakulov, New modified mimetic gravity, Int. J. Geom. Methods Mod. Phys. 11 (2014) #1450091, https://doi.org/10.1142/S0219887814500911.
[12] M. Carrera and D. Giulini, Classical Analysis of the van Dam-Veltman Discontinuity, arXiv:gr-qc/0107058v1 16 Jul 2001.
[13] E. Babichev and C. Deffayet, An introduction to the Vainshtein mechanism, Class. Quantum Grav. 30 (2013) #184001.
[14] C. de Rham, G. Gabadadze and A. J. Tolley, Resummation of massive gravity, Phys. Rev. Lett. 106 (2011) #231101.
[15] M. F. Paulos and A. J. Tolley, Massive gravity theories and limits of ghost-free bigravity models, J. High Energ. Phys. 2012 (2012) 1-18, https://doi.org/10.1007/JHEP09(2012)002.
[16] S. F. Hassan and R. A. Rosen, Resolving the ghost problem in non-linear massive gravity, Phys. Rev. Lett. 108 (2012) #041101, https://doi.org/10.1103/PhysRevLett.108.041101.
[17] Y. Yamashita, A. De Felice and T. Tanaka, Appearance of boulware-deser ghost in bigravity with doubly coupled matter, Int. J. Mod. Phys. D. 23 (2014) #1443003, https://doi.org/10.1142/S0218271814430032.
[18] P. Wolfgang and F. Markus, Üelektromagnetischen feld,ber relativistische feldgleichungen von teilchen mit beliebigem spin im, Helvetica Physica Acta 12 (1939) 297-300.
[19] M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 173 (1939) 211-232.
[20] K. Hinterbichler, Theoretical aspects of massive gravity, Rev. Mod. Phys. 84 (2012) 671-710, https://doi.org/10.1103/RevModPhys.84.671.
[21] G. Cusin, R. Durrer, P. Guarato and M. Motta, A general mass term for bigravity, arXiv:1512.02131v3 [astro-ph.CO] 2016.