RT Journal Article
T1 Quantum corrections to unimodular gravity
A1 Álvarez, Enrique
A1 González Martín, Sergio
A1 Herrero Valea, Mario
A1 Pérez Martín, Carmelo
AB The problem of the comological constant appears in a new light in Unimodular Gravity. In particular, the zero momentum piece of the potential (that is, the constant piece independent of the matter fields) does not automatically produce a cosmological constant proportional to it. The aim of this paper is to give some details on a calculation showing that quantum corrections do not renormalize the classical value of this observable.
PB Springer
SN 1029-8479
YR 2015
FD 2015-08
LK https://hdl.handle.net/20.500.14352/24281
UL https://hdl.handle.net/20.500.14352/24281
LA eng
NO [1] J.J. van der Bij, H. van Dam and Y.J. Ng, The exchange of massless spin two particles, Physica 116A (1982) 307 [INSPIRE].[2] E. Álvarez, D. Blas, J. Garriga and E. Verdaguer, Transverse Fierz-Pauli symmetry, Nucl. Phys. B 756 (2006) 148 [hep-th/0606019] [INSPIRE].[3] A. Einstein, The principle of relativity, Dover (1952).[4] G.F.R. Ellis, H. van Elst, J. Murugan and J.-P. Uzan, On the trace-free einstein equations as a viable alternative to general relativity, Class. Quant. Grav. 28 (2011) 225007 [arXiv:1008.1196] [INSPIRE].[5] S. Deser, Selfinteraction and gauge invariance, Gen. Rel. Grav. 1 (1970) 9 [gr-qc/0411023] [INSPIRE].[6] C. Barceló, R. Carballo-Rubio and L.J. Garay, Unimodular gravity and general relativity from graviton self-interactions, Phys. Rev. D 89 (2014) 124019 [arXiv:1401.2941] [INSPIRE].[7] I.A. Batalin and G.A. Vilkovisky, Quantization of gauge theories with linearly dependent generators, Phys. Rev. D 28 (1983) 2567 [Erratum ibid. D 30 (1984) 508] [INSPIRE].[8] W. Siegel, Hidden ghosts, Phys. Lett. B 93 (1980) 170 [INSPIRE].[9] A. Eichhorn, The renormalization group flow of unimodular f(R) gravity, JHEP 04 (2015) 096 [arXiv:1501.05848] [INSPIRE].[10] I.D. Saltas, UV structure of quantum unimodular gravity, Phys. Rev. D 90 (2014) 124052 [arXiv:1410.6163] [INSPIRE].[11] L. Smolin, Unimodular loop quantum gravity and the problems of time, Phys. Rev. D 84 (2011) 044047 [arXiv:1008.1759] [INSPIRE].[12] L. Smolin, The quantization of unimodular gravity and the cosmological constant problems, Phys. Rev. D 80 (2009) 084003 [arXiv:0904.4841] [INSPIRE].[13] W.G. Unruh, A unimodular theory of canonical quantum gravity, Phys. Rev. D 40 (1989) 1048 [INSPIRE].[14] M. Henneaux and C. Teitelboim, The cosmological constant and general covariance, Phys. Lett. B 222 (1989) 195 [INSPIRE].[15] E. Álvarez and A.F. Faedo, Unimodular cosmology and the weight of energy, Phys. Rev. D 76 (2007) 064013 [hep-th/0702184] [INSPIRE].[16] E. Álvarez, A.F. Faedo and J.J. Lopez-Villarejo, Ultraviolet behavior of transverse gravity, JHEP 10 (2008) 023 [arXiv:0807.1293] [INSPIRE].[17] E. Álvarez and M. Herrero-Valea, No conformal anomaly in unimodular gravity, Phys. Rev. D 87 (2013) 084054 [arXiv:1301.5130] [INSPIRE].[18] E. Álvarez, M. Herrero-Valea and C.P. Martin, Conformal and non conformal dilaton gravity, JHEP 10 (2014) 115 [arXiv:1404.0806] [INSPIRE].[19] A.O. Barvinsky and G.A. Vilkovisky, The generalized Schwinger-Dewitt technique in gauge theories and quantum gravity, Phys. Rept. 119 (1985) 1 [INSPIRE].[20] E.S. Fradkin and A.A. Tseytlin, Quantum properties of higher dimensional and dimensionally reduced supersymmetric theories, Nucl. Phys. B 227 (1983) 252 [INSPIRE].[21] E. Álvarez and A.F. Faedo, Renormalized Kaluza-Klein theories, JHEP 05 (2006) 046 [hep-th/0602150] [INSPIRE].[22] D.J. Toms, Quadratic divergences and quantum gravitational contributions to gauge coupling constants, Phys. Rev. D 84 (2011) 084016 [INSPIRE].[23] D.J. Toms, The background-field method and the renormalization of nonabelian gauge theories in curved space-time, Phys. Rev. D 27 (1983) 1803 [INSPIRE].[24] M.M. Anber and J.F. Donoghue, On the running of the gravitational constant, Phys. Rev. D 85 (2012) 104016 [arXiv:1111.2875] [INSPIRE].[25] 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].[26] M. Reuter, Nonperturbative evolution equation for quantum gravity, Phys. Rev. D 57 (1998) 971 [hep-th/9605030] [INSPIRE].[27] E. Álvarez and M. Herrero-Valea, Unimodular gravity with external sources, JCAP 01 (2013) 014 [arXiv:1209.6223] [INSPIRE].[28] J.M. Martín-García, D. Yllanes and R. Portugal, The Invar tensor package: differential invariants of Riemann, Comput. Phys. Commun. 179 (2008) 586 [arXiv:0802.1274] [INSPIRE].[29] S.M. Christensen and M.J. Duff, Quantizing gravity with a cosmological constant, Nucl. Phys. B 170 (1980) 480 [INSPIRE].[30] F. Englert, C. Truffin and R. Gastmans, Conformal invariance in quantum gravity, Nucl. Phys. B 117 (1976) 407 [INSPIRE].[31] B. DeWitt, Dynamical theory of groups and fields, Gordon and Breach (1965).[32] V.P. Gusynin, Seeley-gilkey coefficients for the fourth order operators on a Riemannian manifold, Nucl. Phys. B 333 (1990) 296 [INSPIRE].[33] D.J. Toms, Renormalization of interacting scalar field theories in curved space-time, Phys. Rev. D 26 (1982) 2713.
NO © The Authors. © Springer Verlag.We are grateful for illuminating discussions with Andrei Barvinsky and Christian Steinwachs. This work has been partially supported by the European Union FP7 ITN INVISIBLES (Marie Curie Actions, PITN-GA-2011-289442) and (HPRN-CT-200-00148); COST action MP1405 (Quantum Structure of Spacetime), COST action MP1210 (The String Theory Universe) as well as by FPA2012-31880 (MICINN, Spain)), FPA2011-24568 (MICINN, Spain), and S2009ESP-1473 (CA Madrid). The authors acknowledge the support of the Spanish MINECO Centro de Excelencia Severo Ochoa Programme under grant SEV-2012-0249. The xAct package [28] has been extensively used in the computations of the present paper.
NO Unión Europea. FP7
NO Comunidad de Madrid
NO Marie Curie Action ITN INVISIBLES
NO COST Action Program (UE)
NO Ministerio de Ciencia e Innovación (MICINN), España
NO Programa Centro de Excelencia Severo Ochoa (MINECO)
NO Seventh Framework Programme for Research (FP7), UE
NO Ministerio de Economía y Competitividad (MINECO), España
DS Docta Complutense
RD 25 abr 2024