Abstract
Quantum Field Theory is the standard framework for the description of the weak, electromagnetic and strong interactions, and results in an extremely well tested theory known as Standard Model (SM) of particle physics. Similarly, General Relativity provides a successful description of the gravitational interaction and most of its predictions have been confirmed by observations. Although Standard Model and General Relativity show a very good agreement with experimental observations, there are several inconsistencies and unsolved problems suggesting that these theories are incomplete and may not be able to describe all fundamental aspects of our universe. For instance, the SM cannot explain the observed baryon asymmetry characterizing the observable universe and cannot incorporate the neutrino masses, required to explain neutrino flavor oscillation, in a natural way.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
S. Weinberg, Critical phenomena for field theorists, in Proceedings 14th International School of Subnuclear Physics, Erice (1976), p. 1. https://doi.org/10.1007/978-1-4684-0931-4_1 (cit. on p. 4)
K.G. Wilson, J. Kogut, The renormalization group and the \(\epsilon \) expansion. Phys. Rep. 12, 75–199 (1974). https://doi.org/10.1016/0370-1573(74)90023-4 (cit. on p. 4)
K.G. Wilson, Renormalization group and critical phenomena. I. Renormalization group and the Kadanoff scaling picture. Phys. Rev. B 4, 3174–3183 (1971). https://doi.org/10.1103/PhysRevB.4.3174 (cit. on p. 4)
F.J. Wegner, A. Houghton, Renormalization group equation for critical phenomena. Phys. Rev. A 8, 401–412 (1973). https://doi.org/10.1103/PhysRevA.8.401 (cit. on p. 5)
C. Wetterich, Exact evolution equation for the effective potential. Phys. Lett. B 301, 90–94 (1993). https://doi.org/10.1016/0370-2693(93)90726-X (cit. on p. 5)
T.R. Morris, The exact renormalization group and approximate solutions. Int. J. Mod. Phys. A 9, 2411–2449 (1994). https://doi.org/10.1142/S0217751X94000972. eprint: hep-ph/9308265 (cit. on p. 5)
M. Reuter, C. Wetterich, Effective average action for gauge theories and exact evolution equations. Nucl. Phys. B 417, 181–214 (1994). https://doi.org/10.1016/0550-3213(94)90543-6 (cit. on p. 5)
M. Reuter, Nonperturbative evolution equation for quantum gravity. Phys. Rev. D 57, 971–985 (1998). https://doi.org/10.1103/PhysRevD.57.971. eprint: hep-th/9605030 (cit. on p. 5)
W. Souma, Non-trivial ultraviolet fixed point in quantum gravity. Prog. Theor. Phys. 102, 181–195 (1999). https://doi.org/10.1143/PTP.102.181. eprint: hep-th/9907027 (cit. on p. 5)
O. Lauscher, M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity. Phys. Rev. D 65(2), 025013 (2002). https://doi.org/10.1103/PhysRevD.65.025013. eprint: hep-th/0108040 (cit. on p. 5)
M. Reuter, F. Saueressig, Renormalization group flow of quantum gravity in the Einstein–Hilbert truncation. Phys. Rev. D 65(6), 065016 (2002). https://doi.org/10.1103/PhysRevD.65.065016. eprint: hep-th/0110054 (cit. on p. 5)
D.F. Litim, Fixed points of quantum gravity. Phys. Rev. Lett. 92(20), 201301 (2004). https://doi.org/10.1103/PhysRevLett.92.201301. eprint: hep-th/0312114 (cit. on p. 5)
O. Lauscher, M. Reuter, Flow equation of Quantum Einstein Gravity in a higher-derivative truncation. Phys. Rev. D 66(2), 025026 (2002). https://doi.org/10.1103/PhysRevD.66.025026. eprint: hep-th/0205062 (cit. on p. 5)
A. Codello, R. Percacci, C. Rahmede, Ultraviolet properties of f(R)-gravity. Int. J. Mod. Phys. A 23, 143–150. https://doi.org/10.1142/S0217751X08038135. arXiv:0705.1769 [hep-th] (cit. on p. 5)
P.F. Machado, F. Saueressig, On the renormalization group flow of f(R)-gravity. Phys. Rev.D 77, 124045 (2008). https://doi.org/10.1103/PhysRevD.77.124045. eprint:arXiv:0712.0445 (cit. on p. 5)
A. Codello, R. Percacci, C. Rahmede, Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation. Ann. Phys. 324, 414–469 (2009). https://doi.org/10.1016/j.aop.2008.08.008. arXiv:0805.2909 [hep-th] (cit. on p. 5)
K. Falls et al., Further evidence for asymptotic safety of quantum gravity. Phys. Rev. D 93(10), 104022 (2016). https://doi.org/10.1103/PhysRevD.93.104022 (cit. on p. 5)
M. Demmel, F. Saueressig, O. Zanusso, RG flows of Quantum Einstein Gravity in the linear-geometric approximation. Ann. Phys. 359, 141–165 (2015). https://doi.org/10.1016/j.aop.2015.04.018. arXiv:1412.7207 [hep-th] (cit. on p. 5)
A. Codello, R. Percacci, Fixed points of higher-derivative gravity. Phys. Rev. Lett. 97(22), 221301 (2006). https://doi.org/10.1103/PhysRevLett.97.221301. eprint: hep-th/0607128 (cit. on p. 5)
D. Benedetti, P.F. Machado, F. Saueressig, Asymptotic safety in higher-derivative gravity. Mod. Phys. Lett. A 24, 2233–2241 (2009). https://doi.org/10.1142/S0217732309031521. arXiv:0901.2984 [hep-th] (cit. on p. 5)
D. Benedetti, P.F. Machado, F. Saueressig, Taming perturbative divergences in asymptotically safe gravity. Nucl. Phys. B 824, 168–191 (2010). https://doi.org/10.1016/j.nuclphysb.2009.08.023. arXiv:0902.4630 [hep-th] (cit. on p. 5)
F. Saueressig et al., Higher derivative gravity from the universal renormalization group machine, in PoS EPS-HEP2011 (2011), p. 124. arXiv:1111.1743 [hep-th] (cit. on p. 5)
D. Benedetti, F. Caravelli, The local potential approximation in quantum gravity. J. High Energy Phys. 6, 17 (2012). https://doi.org/10.1007/JHEP06(2012)017. arXiv:1204.3541 [hep-th] (cit. on p. 5)
M. Demmel, F. Saueressig, O. Zanusso, Fixed-functionals of three dimensional Quantum Einstein Gravity. J. High Energy Phys. 11, 131 (2012). https://doi.org/10.1007/JHEP11(2012)131. arXiv: 1208.2038 [hep-th] (cit. on p. 5)
J.A. Dietz, T.R. Morris, Asymptotic safety in the f(R) approximation. J. High Energy Phys. 1, 108 (2013). https://doi.org/10.1007/JHEP01(2013)108. arXiv:1211.0955 [hep-th] (cit. on p. 5)
M. Demmel, F. Saueressig, O. Zanusso, Fixed functionals in asymptotically safe gravity, in Proceedings of the 13th Marcel Grossmann Meeting, Stockholm, Sweden (2015), pp. 2227–2229. https://doi.org/10.1142/9789814623995_0404. arXiv:1302.1312 [hep-th] (cit. on p. 5)
J.A. Dietz, T.R. Morris, Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety. J. High Energy Phys. 7, 64 (2013). https://doi.org/10.1007/JHEP07(2013)064 (cit. on p. 5)
D. Benedetti, F. Guarnieri, Brans-Dicke theory in the local potential approximation. New J. Phys. 16(5), 053051 (2014). https://doi.org/10.1088/1367-2630/16/5/053051. arXiv:1311.1081 [hep-th] (cit. on p. 5)
M. Demmel, F. Saueressig, O. Zanusso, RG flows of Quantum Einstein Gravity on maximally symmetric spaces. J. High Energy Phys. 6, 26 (2014). https://doi.org/10.1007/JHEP06(2014)026. arXiv:1401.5495 [hep-th] (cit. on p. 5)
R. Percacci, G.P. Vacca, Search of scaling solutions in scalar-tensor gravity. Eur. Phys. J. C 75, 188 (2015). https://doi.org/10.1140/epjc/s10052-015-3410-0. arXiv:1501.00888 [hep-th] (cit. on p. 5)
J. Borchardt, B. Knorr, Global solutions of functional fixed point equations via pseudospectral methods. Phys. Rev. D 91(10), 105011 (2015). https://doi.org/10.1103/PhysRevD.91.105011. arXiv:1502.07511 [hep-th] (cit. on p. 5)
M. Demmel, F. Saueressig, O. Zanusso, A proper fixed functional for four-dimensional Quantum Einstein Gravity. J. High Energy Phys. 8, 113 (2015). https://doi.org/10.1007/JHEP08(2015)113. arXiv:1504.07656 [hep-th] (cit. on p. 5)
N. Ohta, R. Percacci, G.P. Vacca, Flow equation for f(R) gravity and some of its exact solutions. Phys. Rev. D 92(6), 061501 (2015). https://doi.org/10.1103/PhysRevD.92.061501. arXiv:1507.00968 [hep-th] (cit. on p. 5)
N. Ohta, R. Percacci, G.P. Vacca, Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization. Eur. Phys. J. C 76, 46 (2016). https://doi.org/10.1140/epjc/s10052-016-3895-1. arXiv:1511.09393 [hep-th] (cit. on p. 5)
P. Labus, T.R. Morris, Z.H. Slade, Background independence in a background dependent renormalization group. Phys. Rev. D 94(2), 024007 (2016). https://doi.org/10.1103/PhysRevD.94.024007. arXiv:1603.04772 [hep-th] (cit. on p. 5)
J.A. Dietz, T.R. Morris, Z.H. Slade, Fixed point structure of the conformal factor field in quantum gravity. Phys. Rev. D 94(12), 124014 (2016). https://doi.org/10.1103/PhysRevD.94.124014. arXiv:1605.07636 [hep-th] (cit. on p. 5)
P. Horava, Spectral dimension of the universe in quantum gravity at a Lifshitz point. Phys. Rev. Lett. 102(16), 161301 (2009). https://doi.org/10.1103/PhysRevLett.102.161301. arXiv:0902.3657 [hep-th] (cit. on p. 5)
J. Ambjrn, J. Jurkiewicz, R. Loll, The spectral dimension of the universe is scale dependent. Phys. Rev. Lett. 95(17), 171301 (2005). https://doi.org/10.1103/PhysRevLett.95.171301. eprint: hep-th/0505113 (cit. on p. 5)
L. Modesto, Fractal spacetime from the area spectrum. Class. Quantum Gravity 26(24), 242002 (2009). https://doi.org/10.1088/0264-9381/26/24/242002. arXiv:0812.2214 [gr-qc] (cit. on p. 5)
G. Amelino-Camelia et al., Planck-scale dimensional reduction without a preferred frame. Phys. Lett. B 736, 317–320 (2014). https://doi.org/10.1016/j.physletb.2014.07.030. arXiv:1311.3135 [gr-qc] (cit. on p. 5)
C.J. Isham, Canonical quantum gravity and the problem of time (1992), pp. 0157–288. arXiv:gr-qc/9210011 [gr-qc] (cit. on p. 5)
E. Manrique, S. Rechenberger, F. Saueressig, Asymptotically safe Lorentzian gravity. Phys. Rev. Lett. 106(25), 251302 (2011). https://doi.org/10.1103/PhysRevLett.106.251302. arXiv:1102.5012 [hep-th] (cit. on p. 6)
S. Rechenberger, F. Saueressig, A functional renormalization group equation for foliated spacetimes. J. High Energy Phys. 3, 10 (2013). https://doi.org/10.1007/JHEP03(2013)010. arXiv:1212.5114 [hep-th] (cit. on p. 6)
R. Loll, Discrete Lorentzian quantum gravity. Nucl. Phys. B Proc. Suppl. 94, 96–107 (2001). https://doi.org/10.1016/S0920-5632(01)00957-4. eprint: hep-th/0011194 (cit. on p. 6)
A. Bonanno, F. Saueressig, Asymptotically safe cosmology—a status report. Comptes Rendus Phys. 18, 254–264 (2017). https://doi.org/10.1016/j.crhy.2017.02.002. arXiv:1702.04137 [hep-th] (cit. on p. 6)
J. Biemans, A. Platania, F. Saueressig, Quantum gravity on foliated spacetimes: asymptotically safe and sound. Phys. Rev. D 95(8), 086013 (2017). https://doi.org/10.1103/PhysRevD.95.086013. arXiv:1609.04813 [hep-th] (cit. on pp. 6, 7, 9)
J. Biemans, A. Platania, F. Saueressig, Renormalization group fixed points of foliated gravity-matter systems. J. High Energy Phys. 5, 93 (2017). https://doi.org/10.1007/JHEP05(2017)093. arXiv:1702.06539 [hep-th] (cit. on pp. 6, 9)
A. Platania, F. Saueressig, Functional renormalization group flows on Friedman–Lemaitre–Robertson–Walker backgrounds (2017). arXiv:1710.01972 [hep-th] (cit. on pp. 7, 9)
Planck Collaboration et al., Planck 2015 results. XIII. Cosmological parameters. A&A 594, A13 (2016). https://doi.org/10.1051/0004-6361/201525830. arXiv:1502.01589 (cit. on pp. 7, 8)
B.P. Abbott et al., Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116(6), 061102 (2016). https://doi.org/10.1103/PhysRevLett.116.061102. arXiv:1602.03837 [gr-qc] (cit. on p. 7)
S. Coleman, E. Weinberg, Radiative corrections as the origin of spontaneous symmetry breaking. Phys. Rev. D 7, 1888–1910 (1973). https://doi.org/10.1103/PhysRevD.7.1888 (cit. on p. 7)
A.B. Migdal, Vacuum polarization in strong non-homogeneous fields. Nucl. Phys. B 52, 483–505 (1973). https://doi.org/10.1016/0550-3213(73)90575-0 (cit. on p. 7)
D.J. Gross, F. Wilczek, Asymptotically free gauge theories. I. Phys. Rev. D 8, 3633–3652 (1973). https://doi.org/10.1103/PhysRevD.8.3633 (cit. on p. 7)
H. Pagels, E. Tomboulis, Vacuum of the quantum Yang-Mills theory and magnetostatics. Nucl. Phys. B 143, 485–502 (1978). https://doi.org/10.1016/0550-3213(78)90065-2 (cit. on p. 7)
S.G. Matinyan, G.K. Savvidy, Vacuum polarization induced by the intense gauge field. Nucl. Phys. B 134, 539–545 (1978). https://doi.org/10.1016/0550-3213(78)90463-7 (cit. on p. 7)
S.L. Adler, Short-distance perturbation theory for the leading logarithm models. Nucl. Phys. B 217, 381–394 (1983). https://doi.org/10.1016/0550-3213(83)90153-0 (cit. on p. 7)
A. Bonanno, M. Reuter, Entropy signature of the running cosmological constant. JCAP 8, 024 (2007). https://doi.org/10.1088/1475-7516/2007/08/024. arXiv:0706.0174 [hep-th] (cit. on p. 8)
A. Bonanno, A. Platania, Asymptotically safe inflation from quadratic gravity. Phys. Lett. B 750, 638–642 (2015). https://doi.org/10.1016/j.physletb.2015.10.005. arXiv:1507.03375 [gr-qc] (cit. on pp. 8, 9)
A. Bonanno, A. Platania, Asymptotically safe \({{\rm R}+{{\rm R}^2}}\) gravity, in PoS CORFU2015 (2016), p. 159 (cit. on pp. 8, 9)
A. Kogut et al., The primordial inflation explorer (PIXIE): a nulling polarimeter for cosmic microwave background observations. JCAP 7, 025 (2011). https://doi.org/10.1088/1475-7516/2011/07/025. arXiv:1105.2044 (cit. on p. 8)
T. Matsumura et al., Mission design of LiteBIRD. J. Low Temp. Phys. 176, 733–740 (2014). https://doi.org/10.1007/s10909-013-0996-1. arXiv:1311.2847 [astro-ph.IM] (cit. on p. 8)
CORE Collaboration, F. Finelli et al., Exploring cosmic origins with CORE: inflation. ArXiv e-prints (2016). arXiv:1612.08270 (cit. on p. 8)
A. Bonanno, A. Platania, F. Saueressig, Cosmological bounds on the field content of asymptotically safe gravity-matter models. Phys. Lett. B (2018). https://doi.org/10.1016/j.physletb.2018.06.047. arXiv:1803.02355 [gr-qc] (cit. on pp. 8, 9)
F.J. Tipler, On the nature of singularities in general relativity. Phys. Rev. D 15, 942–945 (1977). https://doi.org/10.1103/PhysRevD.15.942 (cit. on p. 8)
A. Bonanno, B. Koch, A. Platania, Cosmic censorship in quantum Einstein gravity. Class. Quantum Gravity 34(9), 095012 (2017). https://doi.org/10.1088/1361-6382/aa6788. arXiv:1610.05299 [gr-qc] (cit. on pp. 8, 9)
A. Bonanno, B. Koch, A. Platania, Asymptotically safe gravitational collapse: Kuroda-Papapetrou RG-improved model, in PoS CORFU2016 (2017), p. 058 (cit. on pp. 8, 9)
A. Bonanno, B. Koch, A. Platania, Gravitational collapse in Quantum Einstein Gravity. Found. Phys. (2018). https://doi.org/10.1007/s10701-018-0195-7. arXiv:1710.10845 [gr-qc] (cit. on pp. 8, 9)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Platania, A.B. (2018). Introduction. In: Asymptotically Safe Gravity. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-98794-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-98794-1_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-98793-4
Online ISBN: 978-3-319-98794-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)