×

Large-\(N\) random matrix gravity and the double hierarchy problem. (English) Zbl 1485.83050

Summary: Why are the cosmological constant, electroweak and Planck scales so different? This “double hierarchy” problem, where \(\Lambda \ll M^2_{EW} \ll M^2_p\), is one of the most pressing in fundamental physics. We show that in a theory of \(N\) randomly coupled massive gravitons at the electroweak scale, these scales are linked precisely by such a double hierarchy for large \(N\), with intriguing cosmological consequences. Surprisingly, in all the physical scales, only one massless graviton emerges which is also, effectively, the only one that is coupled to matter, giving rise to standard Einstein gravity, with \(M_p^2 G_{\mu\nu} = T_{\mu\nu}\) at large \(N\). In addition there is a tower of massive gravitons, the lightest of which can drive late-time acceleration. In this scenario, the observed empirical relation \(\Lambda M_p^2 \sim M_{EW}^4\) as well as the double hierarchy, arise naturally since \(\Lambda \sim M^2_{EW}/\sqrt{N}\) and \(M^2_p \sim \sqrt{N}M_{EW}^2\).

MSC:

83C56 Dark matter and dark energy
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
15B52 Random matrices (algebraic aspects)
81V10 Electromagnetic interaction; quantum electrodynamics
81V15 Weak interaction in quantum theory
83F05 Relativistic cosmology
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] E.P. Wigner, Characteristic Vectors of Bordered Matrices With Infinite Dimensions, Annals Math.62 (1955) 548. · Zbl 0067.08403 · doi:10.2307/1970079
[2] Dyson, F. J., Statistical theory of the energy levels of complex systems. I, J. Math. Phys., 3, 140-156 (1962) · Zbl 0105.41604 · doi:10.1063/1.1703773
[3] Dyson, Freeman J., A Brownian-Motion Model for the Eigenvalues of a Random Matrix, J. Math. Phys., 3, 1191-1198 (1962) · Zbl 0111.32703 · doi:10.1063/1.1703862
[4] F.J. Dyson, The threefold way. Algebraic structure of symmetry groups and ensembles in quantum mechanics, J. Math. Phys.3 (1962) 1199. · Zbl 0134.45703 · doi:10.1063/1.1703863
[5] F.J. Dyson and M.L. Mehta, Statistical theory of the energy levels of complex systems. IV.J. Math. Phys.4 (1963) 701. · Zbl 0133.45201 · doi:10.1063/1.1704008
[6] M.L. Mehta and F.J. Dyson, Statistical theory of the energy levels of complex systems. V.J. Math. Phys.4 (1963) 713. · Zbl 0133.45202 · doi:10.1063/1.1704009
[7] Dyson, Freeman J., Correlations between the eigenvalues of a random matrix, Commun. Math. Phys., 19, 235-250 (1970) · Zbl 0221.62019 · doi:10.1007/BF01646824
[8] Dyson, F. J., Fredholm Determinants and Inverse Scattering Problems, Commun. Math. Phys., 47, 171-183 (1976) · Zbl 0323.33008 · doi:10.1007/BF01608375
[9] Bohigas, O.; Giannoni, M. J.; Schmit, C., Characterization of chaotic quantum spectra and universality of level fluctuation laws, Phys. Rev. Lett., 52, 1-4 (1984) · Zbl 1119.81326 · doi:10.1103/PhysRevLett.52.1
[10] Brezin, E.; Kazakov, V. A., Exactly Solvable Field Theories of Closed Strings, Phys. Lett. B, 236, 144-150 (1990) · doi:10.1016/0370-2693(90)90818-Q
[11] Gross, David J.; Migdal, Alexander A.; Brezin, E.; Wadia, S. R., Nonperturbative Two-Dimensional Quantum Gravity, Phys. Rev. Lett., 64, 127 (1990) · Zbl 1050.81610 · doi:10.1103/PhysRevLett.64.127
[12] Douglas, Michael R.; Shenker, Stephen H.; Brezin, E.; Wadia, S. R., Strings in Less Than One-Dimension, Nucl. Phys. B, 335, 635 (1990) · doi:10.1016/0550-3213(90)90522-F
[13] Kontsevich, M., Intersection theory on the moduli space of curves and the matrix Airy function, Commun. Math. Phys., 147, 1-23 (1992) · Zbl 0756.35081 · doi:10.1007/BF02099526
[14] L. Arnold, On Asymptotic Disribution of Eigenvalues of Random Matrices, J. Math. Anal. Appl.20 (1967) 262. · Zbl 0246.60029 · doi:10.1016/0022-247x(67)90089-3
[15] L.A. Pastur, On the spectrum of random matrices, Theor. Math.10 (1972) 67. · doi:10.1007/bf01035768
[16] Z. Füredi and J. Komlós, The eigenvalues of random symmetric matrices, Combinatorica1 (1981) 233. · Zbl 0494.15010 · doi:10.1007/bf02579329
[17] Sachdev, Subir; Ye, Jinwu, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett., 70, 3339 (1993) · doi:10.1103/PhysRevLett.70.3339
[18] A. Kitaev, A simple model of quantum holography (part 1), talk at KITP, April 7, 2015 [http://online.kitp.ucsb.edu/online/entangled15/kitaev/].
[19] A. Kitaev, A simple model of quantum holography (part 2), talk at KITP, May 27, 2015 [http://online.kitp.ucsb.edu/online/entangled15/kitaev2/].
[20] Maldacena, Juan; Stanford, Douglas, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev. D, 94 (2016) · doi:10.1103/PhysRevD.94.106002
[21] Khosravi, Nima, Ensemble Average Theory of Gravity, Phys. Rev. D, 94 (2016) · doi:10.1103/PhysRevD.94.124035
[22] Khosravi, Nima, Über-gravity and the cosmological constant problem, Phys. Dark Univ., 21, 21-26 (2018) · doi:10.1016/j.dark.2018.05.003
[23] Arkani-Hamed, Nima; Cohen, Timothy; D’Agnolo, Raffaele Tito; Hook, Anson; Kim, Hyung Do; Pinner, David, Solving the Hierarchy Problem at Reheating with a Large Number of Degrees of Freedom, Phys. Rev. Lett., 117 (2016) · doi:10.1103/PhysRevLett.117.251801
[24] Dvali, Gia, Black Holes and Large N Species Solution to the Hierarchy Problem, Fortsch. Phys., 58, 528-536 (2010) · Zbl 1196.81258 · doi:10.1002/prop.201000009
[25] Dvali, Gia; Redi, Michele, Phenomenology of 10^32 Dark Sectors, Phys. Rev. D, 80 (2009) · doi:10.1103/PhysRevD.80.055001
[26] Hook, Anson, Solving the Hierarchy Problem Discretely, Phys. Rev. Lett., 120 (2018) · doi:10.1103/PhysRevLett.120.261802
[27] de Rham, Claudia; Gabadadze, Gregory; Tolley, Andrew J., Resummation of Massive Gravity, Phys. Rev. Lett., 106 (2011) · Zbl 1306.83062 · doi:10.1103/PhysRevLett.106.231101
[28] Arkani-Hamed, Nima; Georgi, Howard; Schwartz, Matthew D., Effective field theory for massive gravitons and gravity in theory space, Annals Phys., 305, 96-118 (2003) · Zbl 1022.81035 · doi:10.1016/S0003-4916(03)00068-X
[29] Khosravi, Nima; Rahmanpour, Nafiseh; Sepangi, Hamid Reza; Shahidi, Shahab, Multi-Metric Gravity via Massive Gravity, Phys. Rev. D, 85 (2012) · doi:10.1103/PhysRevD.85.024049
[30] Alberte, Lasma; de Rham, Claudia; Momeni, Arshia; Rumbutis, Justinas; Tolley, Andrew J., EFT of Interacting Spin-2 Fields, JHEP, 01, 131 (2020) · Zbl 1434.81063 · doi:10.1007/JHEP01(2020)131
[31] Gumrukcuoglu, A. Emir; Lin, Chunshan; Mukohyama, Shinji, Open FRW universes and self-acceleration from nonlinear massive gravity, JCAP, 11 (2011) · doi:10.1088/1475-7516/2011/11/030
[32] Comelli, D.; Crisostomi, M.; Nesti, F.; Pilo, L., FRW Cosmology in Ghost Free Massive Gravity, JHEP, 03, 067 (2012) · Zbl 1309.83030 · doi:10.1007/JHEP03(2012)067
[33] Volkov, Mikhail S., Cosmological solutions with massive gravitons in the bigravity theory, JHEP, 01, 035 (2012) · Zbl 1306.83031 · doi:10.1007/JHEP01(2012)035
[34] von Strauss, Mikael; Schmidt-May, Angnis; Enander, Jonas; Mortsell, Edvard; Hassan, S. F., Cosmological Solutions in Bimetric Gravity and their Observational Tests, JCAP, 03 (2012) · doi:10.1088/1475-7516/2012/03/042
[35] Burgess, C. P.; Allen, R. E.; Nanopoulos, Dimitri V.; Pope, C. N., Towards a natural theory of dark energy: Supersymmetric large extra dimensions, AIP Conf. Proc., 743, 417-449 (2004) · doi:10.1063/1.1848343
[36] Burgess, C. P., Supersymmetric large extra dimensions and the cosmological constant: An Update, Annals Phys., 313, 283-401 (2004) · Zbl 1054.83028 · doi:10.1016/j.aop.2004.04.012
[37] Babichev, Eugeny; Marzola, Luca; Raidal, Martti; Schmidt-May, Angnis; Urban, Federico; Veermäe, Hardi, Bigravitational origin of dark matter, Phys. Rev. D, 94 (2016) · doi:10.1103/PhysRevD.94.084055
[38] Babichev, Eugeny; Marzola, Luca; Raidal, Martti; Schmidt-May, Angnis; Urban, Federico; Veermäe, Hardi, Heavy spin-2 Dark Matter, JCAP, 09 (2016) · doi:10.1088/1475-7516/2016/09/016
[39] González Albornoz, N. L.; Schmidt-May, Angnis; von Strauss, Mikael, Dark matter scenarios with multiple spin-2 fields, JCAP, 01 (2018) · Zbl 1527.83140 · doi:10.1088/1475-7516/2018/01/014
[40] Aoki, Katsuki; Mukohyama, Shinji, Massive gravitons as dark matter and gravitational waves, Phys. Rev. D, 94 (2016) · doi:10.1103/PhysRevD.94.024001
[41] Marsh, David J. E., Axion Cosmology, Phys. Rept., 643, 1-79 (2016) · doi:10.1016/j.physrep.2016.06.005
[42] Duffy, Leanne D.; van Bibber, Karl, Axions as Dark Matter Particles, New J. Phys., 11 (2009) · doi:10.1088/1367-2630/11/10/105008
[43] Hinterbichler, Kurt; Rosen, Rachel A., Interacting Spin-2 Fields, JHEP, 07, 047 (2012) · Zbl 1397.83153 · doi:10.1007/JHEP07(2012)047
[44] Noller, Johannes; Scargill, James H. C.; Ferreira, Pedro G., Interacting spin-2 fields in the Stückelberg picture, JCAP, 02 (2014) · Zbl 1333.83170 · doi:10.1088/1475-7516/2014/02/007
[45] Scargill, James H. C.; Noller, Johannes; Ferreira, Pedro G., Cycles of interactions in multi-gravity theories, JHEP, 12, 160 (2014) · Zbl 1333.83170 · doi:10.1007/JHEP12(2014)160
[46] Hassan, S. F.; Rosen, Rachel A., Resolving the Ghost Problem in non-Linear Massive Gravity, Phys. Rev. Lett., 108 (2012) · Zbl 1348.83065 · doi:10.1103/PhysRevLett.108.041101
[47] Niedermann, Florian; Padilla, Antonio; Saffin, Paul M., Higher Order Clockwork Gravity, Phys. Rev. D, 98 (2018) · doi:10.1103/PhysRevD.98.104014
[48] Kaplan, David E.; Rattazzi, Riccardo, Large field excursions and approximate discrete symmetries from a clockwork axion, Phys. Rev. D, 93 (2016) · doi:10.1103/PhysRevD.93.085007
[49] Choi, Kiwoon; Im, Sang Hui, Realizing the relaxion from multiple axions and its UV completion with high scale supersymmetry, JHEP, 01, 149 (2016) · Zbl 1388.81796 · doi:10.1007/JHEP01(2016)149
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.