Nội dung được dịch bởi AI, chỉ mang tính chất tham khảo
Giải pháp tĩnh đối xứng cầu trong một sửa đổi hồng ngoại không cục bộ của Thuyết Tương đối Tổng quát
Tóm tắt
Chúng tôi thảo luận về các giải pháp tĩnh đối xứng cầu trong một sửa đổi hồng ngoại không cục bộ gần đây được đề xuất cho phương trình Einstein, được gây ra bởi một hạng tử m²gμν□⁻¹ R, trong đó m là một độ đo khối lượng. Chúng tôi tìm thấy rằng, ngược lại với những gì xảy ra trong các lý thuyết trọng lực khối lượng thông thường, trong lý thuyết không cục bộ này không có sự gián đoạn vDVZ và các phi tuyến tính cổ điển không trở nên lớn dưới một bán kính Vainshtein mà về mặt tham số lớn hơn bán kính Schwarzschild rS. Ngược lại, trong phạm vi r ≪ m⁻¹, các sự điều chỉnh đối với metric do một cơ thể tĩnh trong GR tạo ra có dạng 1 + $$ \mathcal{O} $$ (m²r²) và ngày càng nhỏ lại khi giá trị của r trở nên nhỏ hơn. Các sửa đổi cho các giải pháp GR chỉ xuất hiện tại r ≳ m⁻¹. Đối với m = $$ \mathcal{O} $$ (H₀), như cần thiết để có những hậu quả vũ trụ học thú vị, lý thuyết không cục bộ do đó phục hồi tất cả các thành công của GR ở quy mô hệ mặt trời và phòng thí nghiệm.
Từ khóa
#nonlocal infrared modification #Einstein equations #static spherically symmetric solutions #General Relativity #Vainshtein radius #Schwarzschild radiusTài liệu tham khảo
M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [INSPIRE].
D.G. Boulware and S. Deser, Can gravitation have a finite range?, Phys. Rev. D 6 (1972) 3368 [INSPIRE].
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Ghost free Massive Gravity in the Stúckelberg language, Phys. Lett. B 711 (2012) 190 [arXiv:1107.3820] [INSPIRE].
S.F. Hassan and R.A. Rosen, Resolving the Ghost Problem in non-Linear Massive Gravity, Phys. Rev. Lett. 108 (2012) 041101 [arXiv:1106.3344] [INSPIRE].
S.F. Hassan, R.A. Rosen and A. Schmidt-May, Ghost-free Massive Gravity with a General Reference Metric, JHEP 02 (2012) 026 [arXiv:1109.3230] [INSPIRE].
S.F. Hassan and R.A. Rosen, Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity, JHEP 04 (2012) 123 [arXiv:1111.2070] [INSPIRE].
K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
C. de Rham, Massive Gravity, arXiv:1401.4173 [INSPIRE].
S. Dubovsky, T. Gregoire, A. Nicolis and R. Rattazzi, Null energy condition and superluminal propagation, JHEP 03 (2006) 025 [hep-th/0512260] [INSPIRE].
A. Nicolis, R. Rattazzi and E. Trincherini, Energy’s and amplitudes’ positivity, JHEP 05 (2010) 095 [Erratum ibid. 1111 (2011) 128] [arXiv:0912.4258] [INSPIRE].
A. Gruzinov, All Fierz-Paulian massive gravity theories have ghosts or superluminal modes, arXiv:1106.3972 [INSPIRE].
C. de Rham, G. Gabadadze and A.J. Tolley, Comments on (super)luminality, arXiv:1107.0710 [INSPIRE].
S. Deser and A. Waldron, Acausality of Massive Gravity, Phys. Rev. Lett. 110 (2013) 111101 [arXiv:1212.5835] [INSPIRE].
L. Berezhiani, G. Chkareuli and G. Gabadadze, Restricted Galileons, Phys. Rev. D 88 (2013) 124020 [arXiv:1302.0549] [INSPIRE].
K. Izumi and Y.C. Ong, An analysis of characteristics in nonlinear massive gravity, Class. Quant. Grav. 30 (2013) 184008 [arXiv:1304.0211] [INSPIRE].
L. Berezhiani, G. Chkareuli, C. de Rham, G. Gabadadze and A.J. Tolley, Mixed Galileons and Spherically Symmetric Solutions, Class. Quant. Grav. 30 (2013) 184003 [arXiv:1305.0271] [INSPIRE].
K. Koyama, G. Niz and G. Tasinato, Effective theory for the Vainshtein mechanism from the Horndeski action, Phys. Rev. D 88 (2013) 021502 [arXiv:1305.0279] [INSPIRE].
A.E. Gumrukcuoglu, C. Lin and S. Mukohyama, Open FRW universes and self-acceleration from nonlinear massive gravity, JCAP 11 (2011) 030 [arXiv:1109.3845] [INSPIRE].
A.E. Gumrukcuoglu, C. Lin and S. Mukohyama, Cosmological perturbations of self-accelerating universe in nonlinear massive gravity, JCAP 03 (2012) 006 [arXiv:1111.4107] [INSPIRE].
K. Koyama, G. Niz and G. Tasinato, The Self-Accelerating Universe with Vectors in Massive Gravity, JHEP 12 (2011) 065 [arXiv:1110.2618] [INSPIRE].
G. D’Amico, C. de Rham, S. Dubovsky, G. Gabadadze, D. Pirtskhalava et al., Massive Cosmologies, Phys. Rev. D 84 (2011) 124046 [arXiv:1108.5231] [INSPIRE].
A. De Felice, A.E. Gümrükçüoǧlu, C. Lin and S. Mukohyama, Nonlinear stability of cosmological solutions in massive gravity, JCAP 05 (2013) 035 [arXiv:1303.4154] [INSPIRE].
M. Jaccard, M. Maggiore and E. Mitsou, Nonlocal theory of massive gravity, Phys. Rev. D 88 (2013) 044033 [arXiv:1305.3034] [INSPIRE].
M. Maggiore, Phantom dark energy from non-local infrared modifications of General Relativity, Phys. Rev. D 89 (2014) 043008 [arXiv:1307.3898] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos, G. Dvali and G. Gabadadze, Nonlocal modification of gravity and the cosmological constant problem, hep-th/0209227 [INSPIRE].
G. Dvali, Predictive Power of Strong Coupling in Theories with Large Distance Modified Gravity, New J. Phys. 8 (2006) 326 [hep-th/0610013] [INSPIRE].
G.R. Dvali and G. Gabadadze, Gravity on a brane in infinite volume extra space, Phys. Rev. D 63 (2001) 065007 [hep-th/0008054] [INSPIRE].
G. Dvali, G. Gabadadze and M. Shifman, Diluting cosmological constant in infinite volume extra dimensions, Phys. Rev. D 67 (2003) 044020 [hep-th/0202174] [INSPIRE].
M. Porrati, Fully covariant van Dam-Veltman-Zakharov discontinuity and absence thereof, Phys. Lett. B 534 (2002) 209 [hep-th/0203014] [INSPIRE].
S. Deser and R.P. Woodard, Nonlocal Cosmology, Phys. Rev. Lett. 99 (2007) 111301 [arXiv:0706.2151] [INSPIRE].
T. Koivisto, Dynamics of Nonlocal Cosmology, Phys. Rev. D 77 (2008) 123513 [arXiv:0803.3399] [INSPIRE].
T.S. Koivisto, Newtonian limit of nonlocal cosmology, Phys. Rev. D 78 (2008) 123505 [arXiv:0807.3778] [INSPIRE].
S. Capozziello, E. Elizalde, S. Nojiri and S.D. Odintsov, Accelerating cosmologies from non-local higher-derivative gravity, Phys. Lett. B 671 (2009) 193 [arXiv:0809.1535] [INSPIRE].
E. Elizalde, E.O. Pozdeeva and S.Y. Vernov, de Sitter Universe in Non-local Gravity, Phys. Rev. D 85 (2012) 044002 [arXiv:1110.5806] [INSPIRE].
Y.-l. Zhang and M. Sasaki, Screening of cosmological constant in non-local cosmology, Int. J. Mod. Phys. D 21 (2012) 1250006 [arXiv:1108.2112] [INSPIRE].
E. Elizalde, E.O. Pozdeeva and S.Y. Vernov, Reconstruction Procedure in Nonlocal Models, Class. Quant. Grav. 30 (2013) 035002 [arXiv:1209.5957] [INSPIRE].
S. Park and S. Dodelson, Structure formation in a nonlocally modified gravity model, Phys. Rev. D 87 (2013) 024003 [arXiv:1209.0836] [INSPIRE].
K. Bamba, S. Nojiri, S.D. Odintsov and M. Sasaki, Screening of cosmological constant for de Sitter Universe in non-local gravity, phantom-divide crossing and finite-time future singularities, Gen. Rel. Grav. 44 (2012) 1321 [arXiv:1104.2692] [INSPIRE].
S. Deser and R.P. Woodard, Observational Viability and Stability of Nonlocal Cosmology, JCAP 11 (2013) 036 [arXiv:1307.6639] [INSPIRE].
P.G. Ferreira and A.L. Maroto, A few cosmological implications of tensor nonlocalities, Phys. Rev. D 88 (2013) 123502 [arXiv:1310.1238] [INSPIRE].
S. Dodelson and S. Park, Nonlocal Gravity and Structure in the Universe, arXiv:1310.4329 [INSPIRE].
R.P. Woodard, Nonlocal Models of Cosmic Acceleration, Found. Phys. 44 (2014) 213 [arXiv:1401.0254] [INSPIRE].
A.O. Barvinsky, Nonlocal action for long distance modifications of gravity theory, Phys. Lett. B 572 (2003) 109 [hep-th/0304229] [INSPIRE].
A.O. Barvinsky, Dark energy and dark matter from nonlocal ghost-free gravity theory, Phys. Lett. B 710 (2012) 12 [arXiv:1107.1463] [INSPIRE].
A.O. Barvinsky, Serendipitous discoveries in nonlocal gravity theory, Phys. Rev. D 85 (2012) 104018 [arXiv:1112.4340] [INSPIRE].
S. Deser, Covariant Decomposition and the Gravitational Cauchy Problem, Ann. Inst. Henri Poincare 7 (1967) 149.
J.J. York, Covariant decompositions of symmetric tensors in the theory of gravitation, Ann. Inst. Henri Poincare 21 (1974) 319.
S. Foffa, M. Maggiore and E. Mitsou, Apparent ghosts and spurious degrees of freedom in non-local theories, Phys. Lett. B 733 (2014) 76 [arXiv:1311.3421] [INSPIRE].
S. Foffa, M. Maggiore and E. Mitsou, Cosmological dynamics and dark energy from non-local infrared modifications of gravity, arXiv:1311.3435 [INSPIRE].
Y. Dirian, S. Foffa, N. Khosravi, M. Kunz and M. Maggiore, Cosmological perturbations and structure formation in nonlocal infrared modifications of general relativity, JCAP 06 (2014) 033 [arXiv:1403.6068] [INSPIRE].
R.D. Jordan, Effective Field Equations for Expectation Values, Phys. Rev. D 33 (1986) 444 [INSPIRE].
E. Calzetta and B.L. Hu, Closed Time Path Functional Formalism in Curved Space-Time: Application to Cosmological Back Reaction Problems, Phys. Rev. D 35 (1987) 495 [INSPIRE].
M.E. Soussa and R.P. Woodard, A Nonlocal metric formulation of MOND, Class. Quant. Grav. 20 (2003) 2737 [astro-ph/0302030] [INSPIRE].
N.C. Tsamis and R.P. Woodard, A Caveat on Building Nonlocal Models of Cosmology, arXiv:1405.4470 [INSPIRE].
M. Maggiore and M. Mancarella, Non-local gravity and dark energy, Phys. Rev. D 90 (2014) 023005 [arXiv:1402.0448] [INSPIRE].
M. Chevallier and D. Polarski, Accelerating universes with scaling dark matter, Int. J. Mod. Phys. D 10 (2001) 213 [gr-qc/0009008] [INSPIRE].
E.V. Linder, Exploring the expansion history of the universe, Phys. Rev. Lett. 90 (2003) 091301 [astro-ph/0208512] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].
A.I. Vainshtein, To the problem of nonvanishing gravitation mass, Phys. Lett. B 39 (1972) 393 [INSPIRE].
C. Deffayet, G.R. Dvali, G. Gabadadze and A.I. Vainshtein, Nonperturbative continuity in graviton mass versus perturbative discontinuity, Phys. Rev. D 65 (2002) 044026 [hep-th/0106001] [INSPIRE].
N. Arkani-Hamed, H. Georgi and M.D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys. 305 (2003) 96 [hep-th/0210184] [INSPIRE].
K. Koyama, G. Niz and G. Tasinato, Analytic solutions in non-linear massive gravity, Phys. Rev. Lett. 107 (2011) 131101 [arXiv:1103.4708] [INSPIRE].
K. Koyama, G. Niz and G. Tasinato, Strong interactions and exact solutions in non-linear massive gravity, Phys. Rev. D 84 (2011) 064033 [arXiv:1104.2143] [INSPIRE].
N.A. Koshelev, Comments on scalar-tensor representation of nonlocally corrected gravity, Grav. Cosmol. 15 (2009) 220 [arXiv:0809.4927] [INSPIRE].
T.S. Koivisto, Cosmology of modified (but second order) gravity, AIP Conf. Proc. 1206 (2010) 79 [arXiv:0910.4097] [INSPIRE].
S.M. Carroll, Lecture notes on general relativity, gr-qc/9712019 [INSPIRE].
M. Jaccard, M. Maggiore and E. Mitsou, Bardeen variables and hidden gauge symmetries in linearized massive gravity, Phys. Rev. D 87 (2013) 044017 [arXiv:1211.1562] [INSPIRE].
S. Deser, J. Trubatch and S. Trubatch, The Massive Spin-Two Field, Can. J. Phys. 44 (1966) 1715 [INSPIRE].
L. Alberte, A.H. Chamseddine and V. Mukhanov, Massive Gravity: Resolving the Puzzles, JHEP 12 (2010) 023 [arXiv:1008.5132] [INSPIRE].
T. Biswas, E. Gerwick, T. Koivisto and A. Mazumdar, Towards singularity and ghost free theories of gravity, Phys. Rev. Lett. 108 (2012) 031101 [arXiv:1110.5249] [INSPIRE].
T. Biswas, T. Koivisto and A. Mazumdar, Nonlocal theories of gravity: the flat space propagator, arXiv:1302.0532 [INSPIRE].