Propagating gravitons vs. ‘dark matter’ in asymptotically safe quantum gravity

A bstractWithin the Asymptotic Safety scenario, we discuss whether Quantum Einstein Gravity (QEG) can give rise to a semi-classical regime of propagating physical gravitons (gravitational waves) governed by an effective theory which complies with the standard rules of local quantum field theory. According to earlier investigations based on single-metric truncations there is a tension between this requirement and the condition of Asymptotic Safety since the former (latter) requires a positive (negative) anomalous dimension of Newton’s constant. We show that the problem disappears using the bi-metric renormalization group flows that became available recently: they admit an asymptotically safe UV limit and, at the same time, a genuine semi-classical regime with a positive anomalous dimension. This brings the gravitons of QEG on a par with arbitrary (standard model, etc.) particles which exist as asymptotic states. We also argue that metric perturbations on almost Planckian scales might not be propagating, and we propose an interpretation as a form of ‘dark matter’.

[1]  A. Maas Describing gauge bosons at zero and finite temperature , 2011 .

[2]  O. Zanusso,et al.  Asymptotic safety in Einstein gravity and scalar-fermion matter. , 2010, Physical review letters.

[3]  C. Wetterich The average action for scalar fields near phase transitions , 1993 .

[4]  Adriano Contillo,et al.  Renormalization group flow of Hořava-Lifshitz gravity at low energies , 2013 .

[5]  Frank Saueressig,et al.  ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY , 2009, 0901.2984.

[6]  Martin Reuter,et al.  Running gauge coupling in asymptotically safe quantum gravity , 2009, 0910.4938.

[7]  Martin Reuter,et al.  QED coupled to QEG , 2011, 1101.6007.

[8]  M. Reuter,et al.  Effective Lagrangians in Quantum Electrodynamics , 1985 .

[9]  中西 襄,et al.  Covariant operator formalism of gauge theories and quantum gravity , 1990 .

[10]  Carlo Pagani,et al.  Consistent closure of renormalization group flow equations in quantum gravity , 2013, 1304.4777.

[11]  J. Pawlowski,et al.  Confinement from correlation functions , 2013, 1301.4163.

[12]  Martin Reuter,et al.  Effective Potential of the Conformal Factor: Gravitational Average Action and Dynamical Triangulations , 2008, 0806.3907.

[13]  C. Wetterich,et al.  Exact evolution equation for the effective potential , 1993, 1710.05815.

[14]  Astrid Eichhorn,et al.  Ghost anomalous dimension in asymptotically safe quantum gravity , 2010, 1001.5033.

[15]  Donoghue,et al.  Leading quantum correction to the Newtonian potential. , 1993, Physical review letters.

[16]  F. Saueressig,et al.  A Class of nonlocal truncations in quantum Einstein gravity and its renormalization group behavior , 2002 .

[17]  Frank Saueressig,et al.  Quantum Einstein gravity , 2012, 1202.2274.

[18]  Frank Saueressig,et al.  Matter Induced Bimetric Actions for Gravity , 2010, 1003.5129.

[19]  Jan M. Pawlowski,et al.  The phase diagram of quantum gravity from diffeomorphism-invariant RG-flows , 2012, 1203.4207.

[20]  L. Kruglyak,et al.  Non-newtonian forces and the invisible mass problem , 1987 .

[21]  Martin Reuter,et al.  Conformal sector of quantum Einstein gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance , 2008, 0804.1475.

[22]  F. Hehl,et al.  Formal framework for a nonlocal generalization of Einstein’s theory of gravitation , 2009, 0902.0560.

[23]  Frank Saueressig,et al.  Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity , 2007, 0708.1317.

[24]  Martin Reuter,et al.  Nonperturbative evolution equation for quantum gravity , 1998 .

[25]  L. Zambelli,et al.  Gravitational corrections to Yukawa systems , 2009, 0904.0938.

[26]  Martin Reuter,et al.  A minimal length from the cutoff modes in asymptotically safe quantum gravity , 2006 .

[27]  Quantum gravitational corrections to the nonrelativistic scattering potential of two masses , 2003 .

[28]  Andreas Nink,et al.  On the physical mechanism underlying asymptotic safety , 2012, 1208.0031.

[29]  C. Wetterich,et al.  Average action for the Higgs model with abelian gauge symmetry , 1993 .

[30]  Martin Reuter,et al.  Einstein–Cartan gravity, Asymptotic Safety, and the running Immirzi parameter , 2013, 1301.5135.

[31]  Juergen A. Dietz,et al.  Asymptotic safety in the f(R) approximation , 2012, 1211.0955.

[32]  J. E. Tohline Stabilizing a Cold Disk with a 1/r Force Law , 1983 .

[33]  Christoph Rahmede,et al.  Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation , 2008, 0805.2909.

[34]  Christoph Rahmede,et al.  ULTRAVIOLET PROPERTIES OF f(R)-GRAVITY , 2007, 0705.1769.

[35]  M. Niedermaier,et al.  Gravitational fixed points from perturbation theory. , 2009, Physical review letters.

[36]  R. W. Ogburn,et al.  Detection of B-mode polarization at degree angular scales by BICEP2. , 2014, Physical review letters.

[37]  Martin Reuter,et al.  Bare action and regularized functional integral of asymptotically safe quantum gravity , 2008, 0811.3888.

[38]  H. Gies,et al.  Asymptotically free scalar curvature-ghost coupling in quantum Einstein gravity , 2009, 0907.1828.

[39]  O. Zanusso,et al.  Higher Derivative Gravity from the Universal Renormalization Group Machine , 2011, 1111.1743.

[40]  S. Weinberg Asymptotically Safe Inflation , 2009, 0911.3165.

[41]  Martin Reuter,et al.  Background Independence and Asymptotic Safety in Conformally Reduced Gravity , 2008, 0801.3287.

[42]  C. A. Oxborrow,et al.  Planck 2013 results. I. Overview of products and scientific results , 2013, 1502.01582.

[43]  J. Jurkiewicz,et al.  Nonperturbative quantum gravity , 2012, 1203.3591.

[44]  C. Fischer,et al.  Analytic structure of the Landau-gauge gluon propagator. , 2004, Physical Review Letters.

[45]  Donoghue,et al.  General relativity as an effective field theory: The leading quantum corrections. , 1994, Physical review. D, Particles and fields.

[46]  R. Percacci,et al.  Matter matters in asymptotically safe quantum gravity , 2013, 1311.2898.

[47]  Daniel Becker,et al.  En route to Background Independence: Broken split-symmetry, and how to restore it with bi-metric average actions , 2014, 1404.4537.

[48]  H. Georgi Unparticle physics. , 2007, Physical review letters.

[49]  Martin Reuter,et al.  Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety , 2009, 0907.2617.

[50]  R. Percacci,et al.  Conformally reduced quantum gravity revisited , 2009, 0904.2510.

[51]  A. Bonanno An effective action for asymptotically safe gravity , 2012, 1203.1962.

[52]  C. Wetterich,et al.  Running gauge coupling in three dimensions and the electroweak phase transition , 1993 .

[53]  Martin Reuter,et al.  Scale-dependent metric and causal structures in Quantum Einstein Gravity , 2007 .

[54]  D. Litim Fixed points of quantum gravity , 2003, hep-th/0312114.

[55]  Roberto Percacci,et al.  Fixed points of higher-derivative gravity. , 2006, Physical review letters.

[56]  R. Percacci A Short introduction to asymptotic safety , 2011, 1110.6389.

[57]  Alfio Bonanno,et al.  Entropy signature of the running cosmological constant , 2007, 0706.0174.

[58]  J. R. Fisher,et al.  A New method of determining distances to galaxies , 1975 .

[59]  Frank Saueressig,et al.  Taming perturbative divergences in asymptotically safe gravity , 2009, 0902.4630.

[60]  Carlo Pagani,et al.  Quantization and fixed points of non-integrable Weyl theory , 2013, 1312.7767.

[61]  A. Ashtekar,et al.  Asymptotics and Hamiltonians in a first-order formalism , 2008, 0802.2527.

[62]  Nobuyoshi Ohta,et al.  Higher derivative gravity and asymptotic safety in diverse dimensions , 2013, 1308.3398.

[63]  M. Reuter,et al.  Running Immirzi Parameter and Asymptotic Safety , 2011, 1111.1000.

[64]  F. Hehl,et al.  Nonlocal gravity simulates dark matter , 2008, 0812.1059.

[65]  Jan M. Pawlowski,et al.  Global Flows in Quantum Gravity , 2014, 1403.1232.

[66]  M. Reuter,et al.  Ultraviolet fixed point and generalized flow equation of quantum gravity , 2001 .

[67]  F. Saueressig,et al.  Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation , 2002 .

[68]  C. Chicone,et al.  Nonlocal modification of Newtonian gravity , 2010, 1002.1425.

[69]  Frank Saueressig,et al.  Fixed-Functionals of three-dimensional Quantum Einstein Gravity , 2012, Journal of High Energy Physics.

[70]  Ericka Stricklin-Parker,et al.  Ann , 2005 .

[71]  Frank Saueressig,et al.  Ghost wavefunction renormalization in asymptotically safe quantum gravity , 2010, 1001.5032.

[72]  Nonlocal gravity: Modified Poisson's equation , 2011, 1111.4702.

[73]  F. Hehl,et al.  Gauge Theories of Gravitation , 2012, 1210.3775.

[74]  Frank Saueressig,et al.  RG flows of Quantum Einstein Gravity on maximally symmetric spaces , 2014, 1401.5495.

[75]  Howard Georgi,et al.  Another odd thing about unparticle physics , 2007, 0704.2457.

[76]  M. Reuter,et al.  The role of background independence for asymptotic safety in Quantum Einstein Gravity , 2009, 0903.2971.

[77]  A. Bonanno,et al.  Proper time flow equation for gravity , 2005 .

[78]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[79]  M.Reuter,et al.  Renormalization group flow of the Holst action , 2010, 1012.4280.

[80]  Martin Reuter,et al.  Effective average action for gauge theories and exact evolution equations , 1994 .

[81]  Frank Saueressig,et al.  Fractal space-times under the microscope: a renormalization group view on Monte Carlo data , 2011, 1110.5224.

[82]  G. Kallen On the definition of the Renormalization Constants in Quantum Electrodynamics , 1952 .

[83]  ON QUANTUM GRAVITY, ASYMPTOTIC SAFETY AND PARAMAGNETIC DOMINANCE , 2012, 1212.4325.

[84]  M. Reuter,et al.  Flow equation of quantum Einstein gravity in a higher derivative truncation , 2002 .

[85]  M. Reuter,et al.  Running boundary actions, Asymptotic Safety, and black hole thermodynamics , 2012, 1205.3583.

[86]  Frank Saueressig,et al.  On the Renormalization Group Flow of Gravity , 2007, 0712.0445.

[87]  Alfio Bonanno,et al.  Modulated Ground State of Gravity Theories with Stabilized Conformal Factor , 2013, 1302.2928.

[88]  Axel Maas,et al.  Gauge bosons at zero and finite temperature , 2011, 1106.3942.

[89]  J. Jurkiewicz,et al.  Renormalization group flow in CDT , 2014, 1405.4585.

[90]  M. Reuter,et al.  Is quantum Einstein gravity nonperturbatively renormalizable , 2002 .

[91]  Frank Saueressig,et al.  The R^2 phase-diagram of QEG and its spectral dimension , 2012, 1206.0657.

[92]  J. M. Irvine General Relativity – An Einstein Centenary Survey , 1980 .

[93]  C. Wetterich,et al.  Rotation symmetry breaking condensate in a scalar theory , 2000, hep-th/0006099.

[94]  M. Niedermaier,et al.  The Asymptotic Safety Scenario in Quantum Gravity , 2006, Living reviews in relativity.

[95]  Max Niedermaier,et al.  Gravitational fixed points and asymptotic safety from perturbation theory , 2010 .

[96]  M. Reuter,et al.  Cosmology of the Planck era from a renormalization group for quantum gravity , 2002 .

[97]  S. Rahvar,et al.  Observational Tests of Nonlocal Gravity: Galaxy Rotation Curves and Clusters of Galaxies , 2014, 1401.4819.

[98]  H. Lehmann Über Eigenschaften von Ausbreitungsfunktionen und Renormierungskonstanten quantisierter Felder , 1954 .

[99]  M. Reuter,et al.  Quantum gravity at astrophysical distances , 2004 .

[100]  Frank Saueressig,et al.  Bimetric renormalization group flows in quantum Einstein gravity , 2010, 1006.0099.

[101]  Frank Saueressig,et al.  Asymptotically safe Lorentzian gravity. , 2011, Physical review letters.

[102]  M. Reuter,et al.  From big bang to asymptotic de Sitter: complete cosmologies in a quantum gravity framework , 2005, hep-th/0507167.

[103]  Juergen A. Dietz,et al.  The local potential approximation in the background field formalism , 2013, Journal of High Energy Physics.

[104]  F. Saueressig,et al.  Four‐derivative Interactions in Asymptotically Safe Gravity , 2009, 0909.3265.

[105]  D. Zwanziger,et al.  Infrared saturation and phases of gauge theories with BRST symmetry , 2013, The European physical journal. C, Particles and fields.

[106]  R. Percacci,et al.  Asymptotic safety of gravity coupled to matter , 2003, hep-th/0304222.

[107]  G. West Confinement, the Wilson loop and the gluon propagator , 1982 .

[108]  D. Benedetti On the number of relevant operators in asymptotically safe gravity , 2013, 1301.4422.

[109]  C. Wetterich,et al.  Exact evolution equation for scalar electrodynamics , 1994 .

[110]  Functional integration over geometries , 1995, hep-th/9502109.

[111]  M. Reuter,et al.  Fractal spacetime structure in asymptotically safe gravity , 2005 .

[112]  Wataru Souma,et al.  Non-Trivial Ultraviolet Fixed Point in Quantum Gravity , 1999, hep-th/9907027.

[113]  Roberto Percacci,et al.  The running gravitational couplings , 1998 .