Agravity. (English) Zbl 1333.83050
Summary: We explore the possibility that the fundamental theory of nature does not contain any scale. This implies a renormalizable quantum gravity theory where the graviton kinetic term has 4 derivatives, and can be reinterpreted as gravity minus an anti-graviton. We compute the super-Planckian RGE of adimensional gravity coupled to a generic matter sector. The Planck scale and a flat space can arise dynamically at quantum level provided that a quartic scalar coupling and its \(\beta\) function vanish at the Planck scale. This is how the Higgs boson behaves for \(M_h\approx125\) GeV and \(M_t\approx171\) GeV. Within agravity, inflation is a generic phenomenon: the slow-roll parameters are given by the \(\beta\)-functions of the theory, and are small if couplings are perturbative. The predictions \(n_s\approx0.967\) and \(r\approx0.13\) arise if the inflaton is identified with the Higgs of gravity. Furthermore, quadratically divergent corrections to the Higgs mass vanish: a small weak scale is natural and can be generated by agravity quantum corrections.
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
References:
| [1] | K.G. Wilson, The Renormalization Group and Strong Interactions, Phys. Rev.D 3 (1971) 1818 [INSPIRE]. |
| [2] | K.G. Wilson, The Origins of lattice gauge theory, Nucl. Phys. Proc. Suppl.140 (2005) 3 [hep-lat/0412043] [INSPIRE]. · doi:10.1016/j.nuclphysbps.2004.11.271 |
| [3] | L. Giusti, A. Romanino and A. Strumia, Natural ranges of supersymmetric signals, Nucl. Phys.B 550 (1999) 3 [hep-ph/9811386] [INSPIRE]. · doi:10.1016/S0550-3213(99)00153-4 |
| [4] | R. Barbieri and A. Strumia, The ’LEP paradox’, hep-ph/0007265 [INSPIRE]. |
| [5] | A. Strumia, The Fine-tuning price of the early LHC, JHEP04 (2011) 073 [arXiv:1101.2195] [INSPIRE]. · doi:10.1007/JHEP04(2011)073 |
| [6] | A. Arvanitaki, M. Baryakhtar, X. Huang, K. van Tilburg and G. Villadoro, The Last Vestiges of Naturalness, JHEP03 (2014) 022 [arXiv:1309.3568] [INSPIRE]. · doi:10.1007/JHEP03(2014)022 |
| [7] | A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett.B 91 (1980) 99 [INSPIRE]. · Zbl 1371.83222 · doi:10.1016/0370-2693(80)90670-X |
| [8] | R. Fakir and W.G. Unruh, Improvement on cosmological chaotic inflation through nonminimal coupling, Phys. Rev.D 41 (1990) 1783 [INSPIRE]. |
| [9] | D.I. Kaiser, Primordial spectral indices from generalized Einstein theories, Phys. Rev.D 52 (1995) 4295 [astro-ph/9408044] [INSPIRE]. |
| [10] | S. Tsujikawa and B. Gumjudpai, Density perturbations in generalized Einstein scenarios and constraints on nonminimal couplings from the Cosmic Microwave Background, Phys. Rev.D 69 (2004) 123523 [astro-ph/0402185] [INSPIRE]. |
| [11] | F.L. Bezrukov and M. Shaposhnikov, The Standard Model Higgs boson as the inflaton, Phys. Lett.B 659 (2008) 703 [arXiv:0710.3755] [INSPIRE]. · doi:10.1016/j.physletb.2007.11.072 |
| [12] | F. Bezrukov, A. Magnin, M. Shaposhnikov and S. Sibiryakov, Higgs inflation: consistency and generalisations, JHEP01 (2011) 016 [arXiv:1008.5157] [INSPIRE]. · Zbl 1214.83051 · doi:10.1007/JHEP01(2011)016 |
| [13] | C.P. Burgess, H.M. Lee and M. Trott, Power-counting and the Validity of the Classical Approximation During Inflation, JHEP09 (2009) 103 [arXiv:0902.4465] [INSPIRE]. · doi:10.1088/1126-6708/2009/09/103 |
| [14] | J.L.F. Barbon and J.R. Espinosa, On the Naturalness of Higgs Inflation, Phys. Rev.D 79 (2009) 081302 [arXiv:0903.0355] [INSPIRE]. |
| [15] | A. Linde, Inflationary Cosmology after Planck 2013, arXiv:1402.0526 [INSPIRE]. · Zbl 1326.83008 |
| [16] | C.P. Burgess, S.P. Patil and M. Trott, On the Predictiveness of Single-Field Inflationary Models, arXiv:1402.1476 [INSPIRE]. |
| [17] | G.F. Giudice and H.M. Lee, Starobinsky-like inflation from induced gravity, arXiv:1402.2129 [INSPIRE]. · Zbl 1370.83117 |
| [18] | T. Prokopec and J. Weenink, Naturalness in Higgs inflation in a frame independent formalism, arXiv:1403.3219 [INSPIRE]. |
| [19] | J. Joergensen, F. Sannino and O. Svendsen, BICEP2 hints towards Quantum Corrections for Non-Minimally Coupled Inflationary Theories, arXiv:1403.3289 [INSPIRE]. |
| [20] | Planck collaboration, P.A.R. Ade et al., Planck 2013 results. XXII. Constraints on inflation, arXiv:1303.5082 [INSPIRE]. |
| [21] | F. Englert, C. Truffin and R. Gastmans, Conformal Invariance in Quantum Gravity, Nucl. Phys.B 117 (1976) 407 [INSPIRE]. · doi:10.1016/0550-3213(76)90406-5 |
| [22] | C. Wetterich, <Emphasis Type=”Italic“>Cosmology and the Fate of Dilatation Symmetry,” Nucl. Phys.B 302 (1988) 668 [INSPIRE] · doi:10.1016/0550-3213(88)90193-9 |
| [23] | W. Bardeen, On Naturalness in the Standard Model, FERMILAB-CONF-95-391-T · JFM 63.1407.05 |
| [24] | C.T. Hill, Conjecture on the physical implications of the scale anomaly, hep-th/0510177 [INSPIRE]. |
| [25] | R. Hempfling, The Next-to-minimal Coleman-Weinberg model, Phys. Lett.B 379 (1996) 153 [hep-ph/9604278] [INSPIRE]. · doi:10.1016/0370-2693(96)00446-7 |
| [26] | K.A. Meissner and H. Nicolai, Conformal Symmetry and the Standard Model, Phys. Lett.B 648 (2007) 312 [hep-th/0612165] [INSPIRE]. · Zbl 1248.81274 · doi:10.1016/j.physletb.2007.03.023 |
| [27] | J.P. Fatelo, J.M. Gerard, T. Hambye and J. Weyers, Symmetry breaking induced by top loops, Phys. Rev. Lett.74 (1995) 492 [INSPIRE]. · doi:10.1103/PhysRevLett.74.492 |
| [28] | T. Hambye, Symmetry breaking induced by top quark loops from a model without scalar mass, Phys. Lett.B 371 (1996) 87 [hep-ph/9510266] [INSPIRE]. · doi:10.1016/0370-2693(95)01570-1 |
| [29] | W.-F. Chang, J.N. Ng and J.M.S. Wu, Shadow Higgs from a scale-invariant hidden U(1)(s) model, Phys. Rev.D 75 (2007) 115016 [hep-ph/0701254] [INSPIRE]. |
| [30] | R. Foot, A. Kobakhidze and R.R. Volkas, Electroweak Higgs as a pseudo-Goldstone boson of broken scale invariance, Phys. Lett.B 655 (2007) 156 [arXiv:0704.1165] [INSPIRE]. · doi:10.1016/j.physletb.2007.06.084 |
| [31] | R. Foot, A. Kobakhidze, K. McDonald and R. Volkas, Neutrino mass in radiatively-broken scale-invariant models, Phys. Rev.D 76 (2007) 075014 [arXiv:0706.1829] [INSPIRE]. |
| [32] | R. Foot, A. Kobakhidze, K.L. McDonald and R.R. Volkas, A Solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory, Phys. Rev.D 77 (2008) 035006 [arXiv:0709.2750] [INSPIRE]. |
| [33] | S. Iso, N. Okada and Y. Orikasa, The minimal B-L model naturally realized at TeV scale, Phys. Rev.D 80 (2009) 115007 [arXiv:0909.0128] [INSPIRE]. |
| [34] | T. Hur and P. Ko, Scale invariant extension of the standard model with strongly interacting hidden sector, Phys. Rev. Lett.106 (2011) 141802 [arXiv:1103.2571] [INSPIRE]. · doi:10.1103/PhysRevLett.106.141802 |
| [35] | L. Alexander-Nunneley and A. Pilaftsis, The Minimal Scale Invariant Extension of the Standard Model, JHEP09 (2010) 021 [arXiv:1006.5916] [INSPIRE]. · Zbl 1291.81410 · doi:10.1007/JHEP09(2010)021 |
| [36] | S. Iso and Y. Orikasa, TeV Scale B-L model with a flat Higgs potential at the Planck scale - in view of the hierarchy problem -, PTEP2013 (2013) 023B08 [arXiv:1210.2848] [INSPIRE]. |
| [37] | C. Englert, J. Jaeckel, V.V. Khoze and M. Spannowsky, Emergence of the Electroweak Scale through the Higgs Portal, JHEP04 (2013) 060 [arXiv:1301.4224] [INSPIRE]. · doi:10.1007/JHEP04(2013)060 |
| [38] | E.J. Chun, S. Jung and H.M. Lee, Radiative generation of the Higgs potential, Phys. Lett.B 725 (2013) 158 [arXiv:1304.5815] [INSPIRE]. · Zbl 1331.81359 · doi:10.1016/j.physletb.2013.06.055 |
| [39] | M. Heikinheimo, A. Racioppi, M. Raidal, C. Spethmann and K. Tuominen, Physical Naturalness and Dynamical Breaking of Classical Scale Invariance, Mod. Phys. Lett.A 29 (2014) 1450077 [arXiv:1304.7006] [INSPIRE]. · Zbl 1291.81455 · doi:10.1142/S0217732314500771 |
| [40] | T. Henz, J.M. Pawlowski, A. Rodigast and C. Wetterich, Dilaton Quantum Gravity, Phys. Lett.B 727 (2013) 298 [arXiv:1304.7743] [INSPIRE]. · Zbl 1331.81216 · doi:10.1016/j.physletb.2013.10.015 |
| [41] | T. Hambye and A. Strumia, Dynamical generation of the weak and Dark Matter scale, Phys. Rev.D 88 (2013) 055022 [arXiv:1306.2329] [INSPIRE]. |
| [42] | C.D. Carone and R. Ramos, Classical scale-invariance, the electroweak scale and vector dark matter, Phys. Rev.D 88 (2013) 055020 [arXiv:1307.8428] [INSPIRE]. |
| [43] | V.V. Khoze, Inflation and Dark Matter in the Higgs Portal of Classically Scale Invariant Standard Model, JHEP11 (2013) 215 [arXiv:1308.6338] [INSPIRE]. · doi:10.1007/JHEP11(2013)215 |
| [44] | I. Quiros, Scale invariance and broken electroweak symmetry may coexist together, arXiv:1312.1018 [INSPIRE]. |
| [45] | I. Quiros, Scale invariant theory of gravity and the standard model of particles, arXiv:1401.2643 [INSPIRE]. |
| [46] | C.T. Hill, Is the Higgs Boson Associated with Coleman-Weinberg Dynamical Symmetry Breaking?, Phys. Rev.D 89 (2014) 073003 [arXiv:1401.4185] [INSPIRE]. |
| [47] | M. Farina, D. Pappadopulo and A. Strumia, A modified naturalness principle and its experimental tests, JHEP08 (2013) 022 [arXiv:1303.7244] [INSPIRE]. |
| [48] | K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev.D 16 (1977) 953 [INSPIRE]. |
| [49] | G. Magnano, M. Ferraris and M. Francaviglia, Nonlinear gravitational Lagrangians, Gen. Rel. Grav.19 (1987) 465. · Zbl 0626.53064 · doi:10.1007/BF00760651 |
| [50] | G. Magnano, M. Ferraris and M. Francaviglia, Legendre transformation and dynamical structure of higher derivative gravity, Class. Quant. Grav.7 (1990) 557 [INSPIRE]. · Zbl 0697.53065 · doi:10.1088/0264-9381/7/4/007 |
| [51] | A. Jakubiec and J. Kijowski, On Theories of Gravitation With Nonlinear Lagrangians, Phys. Rev.D 37 (1988) 1406 [INSPIRE]. |
| [52] | J.C. Alonso, J.F. Barbero G., J. Julve and A. Tiemblo, Particle contents of higher derivative gravity, Class. Quant. Grav.11 (1994) 865 [INSPIRE]. · Zbl 0797.53072 |
| [53] | A. Hindawi, B.A. Ovrut and D. Waldram, Consistent spin two coupling and quadratic gravitation, Phys. Rev.D 53 (1996) 5583 [hep-th/9509142] [INSPIRE]. |
| [54] | M. Ostrogradski, Memoires sur les equations differentielles relatives au probleme des isoperimetres, Mem. Ac. St. PetersbourgVI (1850) 385. |
| [55] | A.V. Smilga, Ghost-free higher-derivative theory, Phys. Lett.B 632 (2006) 433 [hep-th/0503213] [INSPIRE]. · Zbl 1247.81550 · doi:10.1016/j.physletb.2005.10.014 |
| [56] | A. Mostafazadeh, A Hamiltonian Formulation of the Pais-Uhlenbeck Oscillator that Yields a Stable and Unitary Quantum System, Phys. Lett.A 375 (2010) 93 [arXiv:1008.4678] [INSPIRE]. · Zbl 1241.70023 · doi:10.1016/j.physleta.2010.10.050 |
| [57] | M. Pavsic, Stable Self-Interacting Pais-Uhlenbeck Oscillator, Mod. Phys. Lett.A 28 (2013) 1350165 [arXiv:1302.5257] [INSPIRE]. · Zbl 1279.83032 · doi:10.1142/S0217732313501654 |
| [58] | A. Pais and G.E. Uhlenbeck, On Field theories with nonlocalized action, Phys. Rev.79 (1950) 145 [INSPIRE]. · Zbl 0040.13203 · doi:10.1103/PhysRev.79.145 |
| [59] | T.D. Lee and G.C. Wick, Negative Metric and the Unitarity of the S Matrix, Nucl. Phys.B 9 (1969) 209 [INSPIRE]. · Zbl 0165.58203 · doi:10.1016/0550-3213(69)90098-4 |
| [60] | T.D. Lee and G.C. Wick, Unitarity in the N θθ Sector of Soluble Model With Indefinite Metric, Nucl. Phys.B 10 (1969) 1 [INSPIRE]. · doi:10.1016/0550-3213(69)90275-2 |
| [61] | T.D. Lee and G.C. Wick, Finite Theory of Quantum Electrodynamics, Phys. Rev.D 2 (1970) 1033 [INSPIRE]. · Zbl 1227.81252 |
| [62] | N. Nakanishi, Lorentz noninvariance of the complex-ghost relativistic field theory, Phys. Rev.D 3 (1971) 811 [INSPIRE]. |
| [63] | T.D. Lee and G.C. Wick, Questions of Lorentz Invariance in Field Theories With Indefinite Metric, Phys. Rev.D 3 (1971) 1046 [INSPIRE]. |
| [64] | S.W. Hawking and T. Hertog, Living with ghosts, Phys. Rev.D 65 (2002) 103515 [hep-th/0107088] [INSPIRE]. |
| [65] | C.M. Bender and P.D. Mannheim, No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model, Phys. Rev. Lett.100 (2008) 110402 [arXiv:0706.0207] [INSPIRE]. · doi:10.1103/PhysRevLett.100.110402 |
| [66] | R.E. Cutkosky, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, A non-analytic S matrix, Nucl. Phys.B 12 (1969) 281 [INSPIRE]. · doi:10.1016/0550-3213(69)90169-2 |
| [67] | N. Nakanishi, Remarks on the complex-ghost relativistic field theory, Phys. Rev.D 3 (1971) 3235 [INSPIRE]. |
| [68] | D.G. Boulware, G.T. Horowitz and A. Strominger, Zero Energy Theorem for Scale Invariant Gravity, Phys. Rev. Lett.50 (1983) 1726 [INSPIRE]. · doi:10.1103/PhysRevLett.50.1726 |
| [69] | E.S. Fradkin and A.A. Tseytlin, Conformal supergravity, Phys. Rept.119 (1985) 233 [INSPIRE]. · doi:10.1016/0370-1573(85)90138-3 |
| [70] | R.P. Woodard, Avoiding dark energy with 1/r modifications of gravity, Lect. Notes Phys.720 (2007) 403 [astro-ph/0601672] [INSPIRE]. · doi:10.1007/978-3-540-71013-4_14 |
| [71] | A.V. Smilga, Comments on the dynamics of the Pais-Uhlenbeck oscillator, SIGMA5 (2009) 017 [arXiv:0808.0139] [INSPIRE]. · Zbl 1208.81094 |
| [72] | J. Maldacena, Einstein Gravity from Conformal Gravity, arXiv:1105.5632 [INSPIRE]. · Zbl 1258.83002 |
| [73] | G. ’t Hooft, A class of elementary particle models without any adjustable real parameters, Found. Phys.41 (2011) 1829 [arXiv:1104.4543] [INSPIRE]. · Zbl 1245.81304 · doi:10.1007/s10701-011-9586-8 |
| [74] | M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 1. Wave Function Renormalization, Nucl. Phys.B 222 (1983) 83 [INSPIRE]. · doi:10.1016/0550-3213(83)90610-7 |
| [75] | M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 2. Yukawa Couplings, Nucl. Phys.B 236 (1984) 221 [INSPIRE]. · doi:10.1016/0550-3213(84)90533-9 |
| [76] | M.E. Machacek and M.T. Vaughn, Two Loop Renormalization Group Equations in a General Quantum Field Theory. 3. Scalar Quartic Couplings, Nucl. Phys.B 249 (1985) 70 [INSPIRE]. · doi:10.1016/0550-3213(85)90040-9 |
| [77] | R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun.64 (1991) 345 [INSPIRE]. · doi:10.1016/0010-4655(91)90130-D |
| [78] | T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun.140 (2001) 418 [hep-ph/0012260] [INSPIRE]. · Zbl 0994.81082 · doi:10.1016/S0010-4655(01)00290-9 |
| [79] | R.P. Woodard, The Vierbein Is Irrelevant in Perturbation Theory, Phys. Lett.B 148 (1984) 440 [INSPIRE]. · doi:10.1016/0370-2693(84)90734-2 |
| [80] | R. Contino, L. Pilo, R. Rattazzi and A. Strumia, Graviton loops and brane observables, JHEP06 (2001) 005 [hep-ph/0103104] [INSPIRE]. · doi:10.1088/1126-6708/2001/06/005 |
| [81] | G. Narain and R. Anishetty, Running Couplings in Quantum Theory of Gravity Coupled with Gauge Fields, JHEP10 (2013) 203 [arXiv:1309.0473] [INSPIRE]. · Zbl 1342.83109 · doi:10.1007/JHEP10(2013)203 |
| [82] | M. Shaposhnikov and C. Wetterich, Asymptotic safety of gravity and the Higgs boson mass, Phys. Lett.B 683 (2010) 196 [arXiv:0912.0208] [INSPIRE]. · doi:10.1016/j.physletb.2009.12.022 |
| [83] | E. Elizalde, S.D. Odintsov and A. Romeo, Renormalization group properties of higher derivative quantum gravity with matter in (4-epsilon)-dimensions, Nucl. Phys.B 462 (1996) 315 [hep-th/9502131] [INSPIRE]. · Zbl 1004.81522 · doi:10.1016/0550-3213(95)00674-5 |
| [84] | I.L. Buchbinder, D.D. Odintsov and I.L. Shapiro, Effective Action in Quantum Gravity, IOP (1992). |
| [85] | E.V. Gorbar and I.L. Shapiro, Renormalization group and decoupling in curved space. 2. The Standard model and beyond, JHEP06 (2003) 004 [hep-ph/0303124] [INSPIRE]. · doi:10.1088/1126-6708/2003/06/004 |
| [86] | Y. Yoon and Y. Yoon, Asymptotic conformal invariance of SU(2) and standard models in curved space-time, Int. J. Mod. Phys.A 12 (1997) 2903 [hep-th/9612001] [INSPIRE]. · doi:10.1142/S0217751X97001602 |
| [87] | I.G. Avramidi, Covariant methods for the calculation of the effective action in quantum field theory and investigation of higher derivative quantum gravity, hep-th/9510140 [INSPIRE]. |
| [88] | E.S. Fradkin and A.A. Tseytlin, Renormalizable asymptotically free quantum theory of gravity, Nucl. Phys.B 201 (1982) 469 [INSPIRE]. · doi:10.1016/0550-3213(82)90444-8 |
| [89] | G ‘t Hooft and M. Veltman, One loop divergencies in the theory of gravitation, Annal. IHPA 20 (1974) 69. · Zbl 1422.83019 |
| [90] | S. Deser and P. van Nieuwenhuizen, One Loop Divergences of Quantized Einstein-Maxwell Fields, Phys. Rev.D 10 (1974) 401. |
| [91] | S. Deser and P. van Nieuwenhuizen, Nonrenormalizability of the Quantized Dirac-Einstein System, Phys. Rev.D 10 (1974) 411. |
| [92] | A.D. Sakharov, Vacuum quantum fluctuations in curved space and the theory of gravitation, Sov. Phys. Dokl.12 (1968) 1040 [INSPIRE]. |
| [93] | D. Buttazzo et al., Investigating the near-criticality of the Higgs boson, JHEP12 (2013) 089 [arXiv:1307.3536] [INSPIRE]. · doi:10.1007/JHEP12(2013)089 |
| [94] | D.H. Lyth, What would we learn by detecting a gravitational wave signal in the cosmic microwave background anisotropy?, Phys. Rev. Lett.78 (1997) 1861 [hep-ph/9606387] [INSPIRE]. · doi:10.1103/PhysRevLett.78.1861 |
| [95] | M. Sher, The Renormalization Group and Inflationary Potentials, Phys. Lett.B 135 (1984) 52 [INSPIRE]. · doi:10.1016/0370-2693(84)90452-0 |
| [96] | A. Arvanitaki and S. Dimopoulos, private communication. |
| [97] | M.M. Anber, J.F. Donoghue and M. El-Houssieny, Running couplings and operator mixing in the gravitational corrections to coupling constants, Phys. Rev.D 83 (2011) 124003 [arXiv:1011.3229] [INSPIRE]. |
| [98] | L. Randall, Composite axion models and Planck scale physics, Phys. Lett.B 284 (1992) 77 [INSPIRE]. · doi:10.1016/0370-2693(92)91928-3 |
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.
