Bimetric truncations for quantum Einstein gravity and asymptotic safety. (English) Zbl 1186.83060
Summary: In the average action approach to the quantization of gravity the fundamental requirement of “background independence” is met by actually introducing a background metric but leaving it completely arbitrary. The associated Wilsonian renormalization group defines a coarse graining flow on a theory space of functionals which, besides the dynamical metric, depend explicitly on the background metric. All solutions to the truncated flow equations known to date have a trivial background field dependence only, namely via the classical gauge fixing term. In this paper, we analyze a number of conceptual issues related to the bimetric character of the gravitational average action and explore a first nontrivial bimetric truncation in the simplified setting of conformally reduced gravity. Possible implications for the Asymptotic Safety program and the cosmological constant problem are discussed in detail.
MSC:
| 83C45 | Quantization of the gravitational field |
| 81S10 | Geometry and quantization, symplectic methods |
References:
| [1] | Hamber, H., Quantum Gravitation (2008), Springer: Springer Berlin |
| [2] | Ashtekar, A.; Lewandowski, J., Class. Quant. Grav., 21, R53 (2004) · Zbl 1077.83017 |
| [3] | Rovelli, C., Quantum Gravity (2004), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0962.83507 |
| [4] | Thiemann, Th., Modern Canonical Quantum General Relativity (2007), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1129.83004 |
| [5] | S. Weinberg, hep-th/0903.0568.; S. Weinberg, hep-th/0903.0568. |
| [6] | Reuter, M., Phys. Rev. D, 57, 971 (1998), hep-th/9605030 |
| [7] | Dou, D.; Percacci, R., Class. Quant. Grav., 15, 3449 (1998) · Zbl 0946.83050 |
| [8] | Lauscher, O.; Reuter, M., Phys. Rev. D, 65, 025013 (2002), hep-th/0108040 |
| [9] | Reuter, M.; Saueressig, F., Phys. Rev. D, 65, 065016 (2002), hep-th/0110054 |
| [10] | Lauscher, O.; Reuter, M., Phys. Rev. D, 66, 025026 (2002), hep-th/0205062 |
| [11] | Lauscher, O.; Reuter, M., Class. Quant. Grav., 19, 483 (2002), hep-th/0110021 · Zbl 0993.83012 |
| [12] | Lauscher, O.; Reuter, M., Int. J. Mod. Phys. A, 17, 993 (2002), hep-th/0112089 |
| [13] | Souma, W., Prog. Theor. Phys., 102, 181 (1999) |
| [14] | Fortschr. Phys. 52 (2004) 650, hep-th/0311056.; Fortschr. Phys. 52 (2004) 650, hep-th/0311056. |
| [15] | Bonanno, A.; Reuter, M., JHEP, 02, 035 (2005), hep-th/0410191 |
| [16] | Lauscher, O.; Reuter, M., (Stamatescu, I.-O.; Seiler, E., Approaches to Fundamental Physics (2007), Springer: Springer Berlin) · Zbl 1125.81003 |
| [17] | Percacci, R.; Perini, D., Class. Quant. Grav., 21, 5035 (2004) · Zbl 1062.83036 |
| [18] | Codello, A.; Percacci, R.; Rahmede, C., Int. J. Mod. Phys. A, 23 (2008), hep-th/0805.2909 |
| [19] | Fischer, P.; Litim, D., AIP Conf. Proc., 861, 336 (2006) |
| [20] | Machado, P.; Saueressig, F., Phys. Rev. D, 77, 124045 (2008) |
| [21] | D. Benedetti, P. Machado, F. Saueressig, hep-th/0901.2984 and hep-th/0902.4630.; D. Benedetti, P. Machado, F. Saueressig, hep-th/0901.2984 and hep-th/0902.4630. |
| [22] | Lauscher, O.; Reuter, M., JHEP, 10, 050 (2005), hep-th/0508202 |
| [23] | Reuter, M.; Schwindt, J.-M., JHEP, 01, 070 (2006), hep-th/0511021 |
| [24] | Reuter, M.; Schwindt, J.-M., JHEP, 01, 049 (2007), hep-th/0611294 |
| [25] | Reuter, M.; Weyer, H., Gen. Rel. Grav., 41, 983 (2009), hep-th/0903.2971 |
| [26] | Reuter, M.; Weyer, H., Phys. Rev. D, 80, 025001 (2009), hep-th/0804.1475 |
| [27] | P.F. Machado, R. Percacci, hep-th/0904.2510.; P.F. Machado, R. Percacci, hep-th/0904.2510. |
| [28] | Manrique, E.; Reuter, M., Phys. Rev. D, 79, 025008 (2009), hep-th/0811.3888 |
| [29] | E. Manrique, M. Reuter, hep-th/0905.4220.; E. Manrique, M. Reuter, hep-th/0905.4220. |
| [30] | E. Manrique, M. Reuter, F. Saueressig, in press.; E. Manrique, M. Reuter, F. Saueressig, in press. |
| [31] | J.-E. Daum, M. Reuter, hep-th/0806.3907.; J.-E. Daum, M. Reuter, hep-th/0806.3907. |
| [32] | Niedermaier, M., Class. Quant. Grav., 24, R171 (2007) · Zbl 1128.83001 |
| [33] | R. Percacci, hep-th/0709.3851.; R. Percacci, hep-th/0709.3851. |
| [34] | Wetterich, C., Phys. Lett. B, 301, 90 (1993) |
| [35] | Reuter, M.; Wetterich, C., Nucl. Phys. B, 417, 181 (1994) |
| [36] | Reuter, M., Mod. Phys. Lett. A, 12, 2777 (1997) · Zbl 0925.81330 |
| [37] | Reuter, M.; Wetterich, C., Phys. Rev. D, 56, 7893 (1997), hep-th/9708051 |
| [38] | Reuter, M.; Wetterich, C., Nucl. Phys. B, 506, 483 (1997) · Zbl 0925.81330 |
| [39] | Wetterich, C., Int. J. Mod. Phys. A, 16, 1951 (2001) · Zbl 1087.82505 |
| [40] | H. Gies, hep-ph/0611146.; H. Gies, hep-ph/0611146. |
| [41] | Regge, T.; Williams, R. M., J. Math. Phys., 41, 3964 (2000), gr-qc/0012035 · Zbl 0984.83016 |
| [42] | Ambjørn, J.; Jurkiewicz, J.; Loll, R., Phys. Rev. Lett., 93, 131301 (2004) |
| [43] | Ambjørn, J.; Jurkiewicz, J.; Loll, R., Phys. Lett. B, 607, 205 (2005) · Zbl 1247.83243 |
| [44] | Ambjørn, J.; Jurkiewicz, J.; Loll, R., Contemp. Phys., 47, 103 (2006) |
| [45] | Adler, S. L., Rev. Mod. Phys., 54, 729 (1982) |
| [46] | Bonanno, A.; Reuter, M., Phys. Rev. D, 60, 084011 (1999), gr-qc/9811026 |
| [47] | Reuter, M.; Tuiran, E., (Kleinert, H.; Jantzen, R.; Ruffini, R., Proceedings of the Eleventh Marcel Grossmann Meeting (2007), World Scientific: World Scientific Singapore), hep-th/0612037 |
| [48] | Reuter, M.; Saueressig, F., JCAP, 09, 012 (2005), hep-th/0507167 |
| [49] | Bentivegna, E.; Bonanno, A.; Reuter, M., JCAP, 01, 001 (2004), astro-ph/0303150 |
| [50] | Bonanno, A.; Reuter, M., J. Phys. Conf. Ser., 140, 012008 (2008), astro-ph/0803.2546 |
| [51] | Bonanno, A.; Esposito, G.; Rubano, C.; Scudellaro, P., Class. Quant. Grav., 24, 1443 (2007) · Zbl 1111.83048 |
| [52] | Reuter, M.; Weyer, H., Phys. Rev. D, 69, 104022 (2004) |
| [53] | Reuter, M.; Weyer, H., Phys. Rev. D, 70, 124028 (2004), hep-th/0410117 |
| [54] | Reuter, M.; Weyer, H., JCAP, 12, 001 (2004), hep-th/0410119 |
| [55] | Girelli, F.; Liberati, S.; Percacci, R.; Rahmede, C., Class. Quant. Grav., 24, 3995 (2007) · Zbl 1205.83028 |
| [56] | Litim, D.; Plehn, T., Phys. Rev. Lett., 100, 131301 (2008) |
| [57] | Brownstein, J. R.; Moffat, J., Mon. Not. Roy. Astron. Soc., 367, 527 (2006) |
| [58] | Floreanini, R.; Percacci, R., Phys. Rev. D, 46, 1566 (1992) |
| [59] | Lauscher, O.; Reuter, M.; Wetterich, C., Phys. Rev. D, 62, 125021 (2000), hep-th/0006099 |
| [60] | Litim, D., Int. J. Mod. Phys. A, 16, 2081 (2001) · Zbl 0980.81037 |
| [61] | Gies, H., Phys. Rev. D, 68, 085015 (2003) |
| [62] | A. Codello, R. Percacci, hep-th/0810.0715.; A. Codello, R. Percacci, hep-th/0810.0715. |
| [63] | Giulini, D., (Stamatescu, I.-O.; Seiler, E., Approaches to Fundamental Physics (2007), Springer: Springer Berlin) · Zbl 1125.81003 |
| [64] | Straumann, N., (Stamatescu, I.-O.; Seiler, E., Approaches to Fundamental Physics (2007), Springer: Springer Berlin) · Zbl 1125.81003 |
| [65] | Weinberg, S., Rev. Mod. Phys., 61 (1989) · Zbl 1129.83361 |
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.
