Renormalization group flow in scalar-tensor theories: II

We study the UV behaviour of actions including integer powers of scalar curvature and even powers of scalar fields with functional renormalization group techniques. We find UV fixed points where the gravitational couplings have nontrivial values while the matter ones are Gaussian. We prove several properties of the linearized flow at such a fixed point in arbitrary dimensions in the one-loop approximation and find recursive relations among the critical exponents. We illustrate these results in explicit calculations in d = 4 for actions including up to four powers of scalar curvature and two powers of the scalar field. In this setting we note that the same recursive properties among the critical exponents, which were proven at one-loop order, still hold, in such a way that the UV critical surface is found to be five dimensional. We then search for the same type of fixed point in a scalar theory with minimal coupling to gravity in d = 4 including up to eight powers of scalar curvature. Assuming that the recursive properties of the critical exponents still hold, one would conclude that the UV critical surface of these theories is five dimensional.

[1]  R. Percacci.  Further evidence for a gravitational fixed point , 2005, hep-th/0511177.

[2]  High-accuracy scaling exponents in the local potential approximation , 2007, hep-th/0701172.

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

[4]  Huang,et al.  Halpern and Huang Reply. , 1996, Physical review letters.

[5]  M. Shaposhnikov,et al.  The Standard Model Higgs boson as the inflaton , 2007, 0710.3755.

[6]  F. Wilczek,et al.  Gravitational correction to running of gauge couplings. , 2005, Physical review letters.

[7]  Conformal transformations in classical gravitational theories and in cosmology , 1998, gr-qc/9811047.

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

[9]  C. Burgess,et al.  Power-counting and the validity of the classical approximation during inflation , 2009, 0902.4465.

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

[11]  Holger Gies.  Running coupling in Yang-Mills theory: A flow equation study , 2002 .

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

[13]  D. Litim.  Optimisation of the exact renormalisation group , 2000, hep-th/0005245.

[14]  Fixed points of quantum gravity in extra dimensions , 2006, hep-th/0602203.

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

[16]  P. Mazur,et al.  Conformal Invariance and Cosmic Background Radiation , 1996, astro-ph/9611208.

[17]  S. Weinberg.  Effective field theory for inflation , 2008, 0804.4291.

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

[19]  The Cosmon model for an asymptotically vanishing time dependent cosmological 'constant' , 1994, hep-th/9408025.

[20]  Sergei D. Odintsov,et al.  Effective Action in Quantum Gravity , 1992 .

[21]  Renormalization and asymptotic safety in truncated quantum Einstein gravity , 2002, hep-th/0207143.

[22]  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.

[23]  S. Deser,et al.  One-loop divergences of quantized Einstein-Maxwell fields , 1974 .

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

[25]  S. Deser,et al.  Nonrenormalizability of the Quantized Einstein-Maxwell System , 1974 .

[26]  1/R gravity and scalar-tensor gravity , 2003, astro-ph/0307338.

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

[28]  Dimensionally reduced gravity theories are asymptotically safe , 2003, hep-th/0304117.

[29]  C. Bervillier,et al.  Exact renormalization group equations. An Introductory review , 2000 .

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

[31]  Brian Whitt.  Fourth-order gravity as general relativity plus matter , 1984 .

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

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

[36]  F. Wilczek,et al.  Running inflation in the Standard Model , 2008, 0812.4946.

[37]  E. Elizalde,et al.  One-loop f(R) gravity in de Sitter universe , 2005, hep-th/0501096.

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

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

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

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

[42]  Fractal geometry of quantum spacetime at large scales , 1998, hep-th/9808070.

[43]  J. McDonald,et al.  Gauge singlet scalar as inflaton and thermal relic dark matter , 2009, 0909.0520.

[44]  Macroscopic effects of the quantum trace anomaly , 2006, gr-qc/0604051.

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

[46]  D. Litim.  Optimized renormalization group flows , 2001, hep-th/0103195.

[47]  R. Percacci.  The Higgs phenomenon in quantum gravity , 1991, 0712.3545.

[48]  Daniel F. Litim.  Critical exponents from optimised renormalisation group flows , 2002 .

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

[50]  P. Mazur,et al.  Cosmological dark energy: prospects for a dynamical theory , 2006, gr-qc/0612068.

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

[52]  N. Mavromatos,et al.  LECT NOTES PHYS , 2002 .

[53]  C. Wetterich,et al.  Non-perturbative renormalization flow in quantum field theory and statistical physics , 2002 .

[54]  T. Morris.  On Truncations of the Exact Renormalization Group , 1994, hep-th/9405190.

[55]  S. Deser,et al.  Nonrenormalizability of the quantized Dirac-Einstein system , 1974 .

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

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

[58]  P. Nieuwenhuizen,et al.  Nonrenormalizabilily of quantized fermiongravitation interactions , 1974 .

[59]  Michael E. Fisher,et al.  Critical Exponents in 3.99 Dimensions , 1972 .

[60]  Sokolowski,et al.  Physical equivalence between nonlinear gravity theories and a general-relativistic self-gravitating scalar field. , 1994, Physical review. D, Particles and fields.

[61]  S. Deser,et al.  One-loop divergences of the Einstein-Yang-Mills system , 1974 .

[62]  Tianjun Li,et al.  ATIC and PAMELA Results on Cosmic e+- Excesses and Neutrino Masses , 2009, 0901.0176.

[63]  K. Maeda,et al.  Towards the Einstein-Hilbert action via conformal transformation. , 1989, Physical review. D, Particles and fields.

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

[65]  Daniel F Litim.  Fixed points of quantum gravity. , 2004, Physical review letters.

[66]  S. Hawking,et al.  General Relativity; an Einstein Centenary Survey , 1979 .

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

[68]  S. Deser,et al.  Nonrenormalizability of Einstein-Yang-Mills interactions at the one-loop level , 1974 .

[69]  Jared Kaplan,et al.  The Effective Field Theory of Inflation , 2007, 0709.0293.

[70]  E. Fradkin,et al.  Renormalizable asymptotically free quantum theory of gravity , 1982 .

[71]  S. Odintsov,et al.  TWO-LOOP APPROACH TO THE EFFECTIVE ACTION IN QUANTUM GRAVITY , 1992 .

[72]  Tim R. Morris.  Derivative expansion of the exact renormalization group , 1994 .

[73]  R. Percacci,et al.  Fixed points of nonlinear sigma models in d > 2 , 2008, 0810.0715.