Hamiltonian cosmology of bigravity

D. Boulware and S. Deser, “Can gravitation have a finite range?,” Phys. Rev. D 6, 3368–3382 (1972).

C. de Rham and G. Gabadadze, “Generalization of the Fierz-Pauli action,” Phys. Rev. D 82, 044020 (2010).

C. de Rham, G. Gabadadze, and A. J. Tolley, “Resummation of massive gravity,” Phys. Rev. Lett. 106, 231101 (2011).

S. F. Hassan and R. A. Rosen, “Bimetric gravity from ghost-free massive gravity,” JHEP 02, 126 (2012).

S. F. Hassan and R. A. Rosen, “Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity,” JHEP 04, 123 (2012).

V. O. Soloviev, “Hamiltonian approach in relativistic theory of gravitation and in general relativity,” Sov. J. Part. Nucl. 19, 482–497 (1988).

M. Ryan, “Hamiltonian cosmology”, in Lecture Notes in Physics, Vol. 13, Ed. by J. Ehlers, K. Hepp, and H. A. Weidenmueller (Springer-Verlag, Berlin-Heidelberg-New York, 1972).

D. Comelli, M. Crisostomi, K. Koyama, L. Pilo, and G. Tasinato, “Cosmology of bigravity with doubly coupled matter,” JCAP 04, 026 (2015).

A. E. Gumrukcuoglu, L. Heisenberg, Sh. Mukohyama, and N. Tanahashi, “Cosmology in bimetric theory with an effective composite coupling to matter,” JCAP 04, 008 (2015).

Ya. Akrami, S. F. Hassan, F. Könnig, A. Schmidt-May, and A. R. Solomon, “Bimetric gravity is cosmologically viable,” Phys. Lett. B 748, 37–44 (2015).

V. O. Soloviev and M. V. Chichikina, “Bigravity in the Kuchar’s Hamiltonian formalism: The general case,” Theor. Math. Phys. 176, 1163–1175 (2013).

V. O. Soloviev and M. V. Tchichikina, “Bigravity in the Kuchar’s Hamiltonian formalism: The special case,” Phys. Rev. D 88, 084026 (2013).

D. Comelli, F. Nesti, and L. Pilo, “Weak massive gravity,” Phys. Rev. D 87, 124021 (2013); “Massive gravity: A general analysis,” JHEP 07, 161 (2013).

V. O. Soloviev, “Bigravity in tetrad Hamiltonian formalism,” Theor. Math. Phys. 182, 294–307 (2015).

V. O. Soloviev, “Bigravity in tetrad Hamiltonian formalism and matter couplings,” ArXiv:1410.0048 (2014).

J. Kluson, “Hamiltonian formalism of bimetric gravity In vierbein formulation,” Eur. Phys. J. 74, 2985 (2014).

A. Golovnev, “On the Hamiltonian analysis of nonlinear massive gravity,” Phys. Lett. B 707, 404–408 (2012).

S. Deser, M. Sandora, A. Waldron, G. Zahariade, “Covariant constraints for generic massive gravity and analysis of its characteristics,” Phys. Rev. D 90, 104043 (2014).

K. Kuchar, “Geometry of hyperspace, I,” J. Math. Phys. 17, 777–791 (1976).

K. Kuchar, “Kinematics of tensor fields in hyperspace, II,” J. Math. Phys. 17, 792–800 (1976).

K. Kuchar, “Dynamics of tensor fields in hyperspace, III,” J. Math. Phys. 17, 801–820 (1976).

K. Kuchar, “Geometrodynamics with tensor sources, IV,” J. Math. Phys. 18, 1589–1597 (1977).

P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University, New York, 1964).

D. Fairlie and A. Leznov, “General solutions of the Monge-Ampère equation in -dimensional space,” J. Geom. Phys. 16, 385–390 (1995).

S. Deser and C. J. Isham, Phys. Rev. D 14, 2505 (1976).

J. E. Nelson and C. Teitelboim, Ann. Phys. 116, 86 (1978)

M. Henneaux, Gen. Rel. Grav. 9, 1031 (1978).

S. Alexandrov, K. Krasnov, and S. Speziale, “Chiral description of ghost-free massive gravity,” JHEP 1306, 068 (2013).

S. Alexandrov, “Canonical structure of tetrad bimetric gravity,” Gen. Rel. Grav. 46, 1639 (2014).

Yu. Sakakihara and J. Soda, “Primordial gravitational waves in bimetric gravity,” JCAP 09, 015 (2015).

Yu. Sakakihara and T. Tanaka, “Primordial fluctuations from inflation in dRGT bimetric theory of gravity,” ArXiv:1605.05790 (2016).

D. D. Holm, “Hamiltonian formalism for General-Relativistic adiabatic fluids,” Physica D 17, 1 (1985).

V. O. Soloviev, “Boundary values as Hamiltonian variables, III: Ideal fluid with free surface,” J. Math. Phys. 43, 3655 (2002).

M. S. Volkov, “Cosmological solutions with massive gravitons in the bigravity theory,” JHEP 01, 035 (2012).

M. von Strauss, A. Schmidt-May, J. Enander, E. Mörtsell, and S. F. Hassan, “Cosmological solutions in bimetric gravity and their observational tests,” JCAP 03, 042 (2012).

D. Comelli, M. Crisostomi, F. Nesti, and L. Pilo, “FRW cosmology in ghost free massive gravity,” JHEP 03, 067 (2012).

Ya. Akrami, T. S. Koivisto, and M. Sandstad, “Accelerated expansion from ghost-free bigravity: A statistical analysis with improved generality,” JHEP 03, 099 (2013).

K. Aoki and K. Maeda, “Cosmology in ghost-free bigravity theory with twin matter fluids: The origin of “dark matter”, ArXiv:1312.7040 (2013).

K. Aoki and K. Maeda, “Dark matter in ghost-free bigravity theory: From a galaxy scale to the universe,” ArXiv:1409.0202 (2014).

G. D’Amico, C. de Rham, S. Dubovsky, G. Gabadadze, D. Pirtskhalava, and A. J. Tolley, “Massive cosmologies,” Phys. Rev. D 84, 124046 (2011).

A. E. Gumrukcuoglu, C. Lin, and Sh. Mukohyama, “Open FRW universes and self-acceleration from nonlinear massive gravity,” JCAP 11, 030 (2011).

Ya. Akrami, T. S. Koivisto, D. F. Mota, and M. Sandstad, “Bimetric gravity doubly coupled to matter: Theory and cosmological implications,” JCAP 10, 046 (2013).

Ya. Akrami, T. S. Koivisto, and A. R. Solomon, “The nature of spacetime in bigravity: Two metrics or none?, ”Gen. Rel. Grav. 47, 1838 (2015).

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, 1443003 (2014).

C. de Rham, L. Heisenberg, and R. H. Ribeiro, “On couplings to matter in massive bi-gravity,” Class. Quantum Grav. 32, 035022 (2015).

C. de Rham, L. Heisenberg, and R. H. Ribeiro, “Ghosts and matter couplings in massive gravity, bigravity and multigravity,” Phys. Rev. D 90, 124042 (2014).

J. Nöller and S. Melville, “The coupling to matter in massive, bi- and multi-gravity,” JCAP 01, 023 (2016).

L. Heisenberg, “Quantum corrections in massive bigravity and new effective composite metrics,” Class. Quant. Grav. 32, 105011 (2015).

K. Hinterbichler and R. A. Rosen, “A note on ghostfree matter couplings in massive gravity and multi-gravity,” Phys. Rev. D 92, 024030 (2015).

C. de Rham and A. J. Tolley, “Vielbein to the Rescue?,” Phys. Rev. D 92, 024024 (2015).

J. Enander, A. R. Solomon, Ya. Akrami, and E. Mörtsell, “Cosmic expansion histories in massive bigravity with symmetric matter coupling,” JCAP 01, 006 (2015).

M. Lagos and J. Nöller, “New massive bigravity cosmologies with double matter coupling,” JCAP 01, 023 (2016).

A. R. Solomon, J. Enander, Ya. Akrami, T. S. Koivisto, F. Könnig, and E. Mörtsell, “Cosmological viability of massive gravity with generalized matter coupling,” JCAP 04, 027 (2015).

S. S. Gershtein, A. A. Logunov, and M. A. Mestvirishvili, “Upper limit on the graviton mass,” Dokl. Phys. 43 (5), 293–296 (1998).

A. A. Logunov, Relativistic Theory of Gravity (Nauka, Moscow, 2015) [in Russian].

L. Heisenberg and A. Refregier, “Cosmology in massive gravity with effective composite metric,” ArXiv:1604.07306 (2016).

L. Heisenberg and A. Refregier, “Cosmology in doubly coupled massive gravity: Constraints from SNIa, BAO and CMB,” ArXiv:1604.07680 (2016).

F. Könnig, H. Nersisyan, Ya. Akrami, L. Amendola, and M. Zumalacárregui, “A spectre is haunting the cosmos: Quantum stability of massive gravity with ghosts,” ArXiv:1605.08757 (2016).

P. Brax, A.-Ch. Davis, and J. Nöller, “Dark energy and doubly coupled bigravity,” ArXiv:1606.05590 (2016).

X. Gao and L. Heisenberg, “Doubly coupled matter fields in massive bigravity,” ArXiv:1606.06141 (2016).

C. M. Will, Theory and Experiment in Gravitational Physics (Cambridge University Press, 1994).

C. M. Will, “The confrontation between General Relativity and experiment,” Living Rev. Relativity 17, 4–117 (2014).

J. Murata and S. Tanaka, “A review of short-range gravity experiments in the LHC era,” Class. Quant. Grav. 32, 033001–033032 (2015).

T. Baker, D. Psaltis, and C. Skordis, “Linking tests of gravity on all scales: From the strong-field regime to cosmology,” Astrophys. J. 802 (63), 1–19 (2015).

B. P. Abbott et al. (LIGO Scientific Collab. and Virgo Collab.), “GW150914: First results from the search for binary black hole coalescence with Advanced LIGO,” Phys. Rev. D 93, 122003 (2016).

B. P. Abbott et al. (LIGO Scientific Collab. and Virgo Collab.), “Observing gravitational-wave transient GW150914 with minimal assumptions,” Phys. Rev. D 93, 122004 (2016).

S. Capozziello and V. Faraoni, Beyond Einstein gravity: A survey of gravitational theories for cosmology and astrophysics: Fundamental Theories of Physics, Book 170 (Springer, 2011).

T. Clifton, P. G. Ferreira, A. Padilla, and C. Skordis, “Modified gravity and cosmology,” Phys. Rep. 513 (1), 1–189 (2012).

M. Sami and R. Myrzakulov, “Late time cosmic acceleration: ABCD of dark energy and modified theories of gravity,” ArXiv:1309.4188 (2013).

A. Joyce, B. Jain, J. Khoury, and M. Trodden, “Beyond the cosmological Standard Model,” Phys. Rep. 568, 1–98 (2014).

P. Bull et al., “Beyond CDM: Problems, solutions and the road ahead,” Phys. Dark Universe 12, 56–99 (2016), ArXiv:1512.05356 (2015).

K. Koyama, “Cosmological tests of modified gravity,” Rep. Prog. Phys. 79 (4), 046902 (2016).

V. A. Rubakov and P. G. Tinjakov, “Infrared-modified gravities and massive gravitons,” Phys. Usp. 51, 759–792 (2008).

D. Blas, “Aspects of infrared modifications of gravity,” ArXiv:0809.3744 (2008).

M. V. Bebronne, “Theoretical and phenomenological aspects of theories with massive gravitons,” ArXiv:0910.4066 (2009).

K. Hinterbichler, “Theoretical aspects of massive gravity,” Rev. Mod. Phys. 84, 671–710 (2012).

C. de Rham, “Massive gravity,” Living Rev. Relat. 17, 7 (2014).

A. Schmidt-May and M. von Strauss, “Recent developments in bimetric theory,” ArXiv:1512.00021 (2015).

C. de Rham, J. T. Deskins, A. J. Tolley, and S.-Y. Zhou, “Graviton mass bounds,” ArXiv:1606.08462 (2106).

A. Solomon, “Cosmology beyond Einstein,” ArXiv:1508.06859 (2015).

A. I. Vainshtein, “To the problem of non-vanishing gravitation mass,” Phys. Lett. B 39, 393–394 (1972).

S. Deser, “Massive to gauge field reduction and gravitational wave zone information,” ArXiv:1604.04015 (2016).

A. F. Zakharov, P. Jovanovic, D. Borka, and V. Borka Jovanovic, “Constraining the range of Yukawa gravity interaction from S2 star orbits II: Bounds on graviton mass,” ArXiv:1605.00913 (2016).

A. F. Ali and S. Das, “Stringent theoretical and experimental bounds on graviton mass,” ArXiv:1605.05928 (2016).

K. Aoki and Sh. Mukohyama, “Bigravitons as dark matter and gravitational waves,” ArXiv:1604.06704 (2016).

E. Babichev, L. Marzola, M. Raidal, A. Schmidt-May, F. Urban, H. Veermae, and M. von Strauss, “Gravitational origin of dark matter,” ArXiv:1604.08564 (2016).

L. Blanchet and L. Heisenberg, “Dark matter via massive bi-gravity,” Phys. Rev. D 91, 103518 (2015).

L. Blanchet and L. Heisenberg, “Dipolar dark matter,” ArXiv:1505.05146 (2015).

L. Bernard, L. Blanchet, and L. Heisenberg, “Bimetric gravity and dark matter,” ArXiv:1507.02802 (2015).