Advertisement

Foundations of Physics

, Volume 48, Issue 10, pp 1364–1379 | Cite as

Unimodular quantum gravity and the cosmological constant

  • R. PercacciEmail author
Article
Part of the following topical collections:
  1. Black holes, Gravitational waves and Space Time Singularities

Abstract

It is shown that the one-loop effective action of unimodular gravity is the same as that of ordinary gravity, restricted to unimodular metrics. The only difference is in the treatment of the global scale degree of freedom and of the cosmological term. A constant vacuum energy does not gravitate, addressing one aspect of the cosmological constant problem.

Keywords

Cosmological constant Quantum gravity Unimodular 

Notes

Acknowledgements

This paper is based in part on joint work with R. de León Ardón and N. Ohta. I also thank M. Henneaux and S. Gielen for discussions and D. Benedetti and A. Eichhorn for reading parts of the manuscript and making useful suggestions.

References

  1. 1.
    Akhmedov, E.K.: Vacuum energy and relativistic invariance. arXiv:hep-th/0204048
  2. 2.
    Ossola, G., Sirlin, A.: Considerations concerning the contributions of fundamental particles to the vacuum energy density. Eur. Phys. J. C 31, 165 (2003). arXiv:hep-th/0305050 ADSCrossRefGoogle Scholar
  3. 3.
    Shapiro, I.L., Sola, J.: Scaling behavior of the cosmological constant: Interface between quantum field theory and cosmology. JHEP 0202, 006 (2002). arXiv:hep-th/0012227
  4. 4.
    Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989)ADSMathSciNetCrossRefGoogle Scholar
  5. 5.
    Burgess, C.P.: The cosmological constant problem: why it’s hard to get dark energy from micro-physics. arXiv:1309.4133 [hep-th]
  6. 6.
    Anderson, J.L., Finkelstein, D.: Cosmological constant and fundamental length. Am. J. Phys. 39, 901 (1971)ADSCrossRefGoogle Scholar
  7. 7.
    Ng, Y.J., van Dam, H.: A Small but nonzero cosmological constant. Int. J. Mod. Phys. D 10, 49 (2001). arXiv:hep-th/9911102 ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    Finkelstein, D.R., Galiautdinov, A.A., Baugh, J.E.: Unimodular relativity and cosmological constant. J. Math. Phys. 42, 340 (2001). arXiv:gr-qc/0009099 ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    Buchmuller, W., Dragon, N.: Einstein gravity from restricted coordinate invariance. Phys. Lett. B 207, 292 (1988)ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    Buchmuller, W., Dragon, N.: Gauge fixing and the cosmological constant. Phys. Lett. B 223, 313 (1989)ADSCrossRefGoogle Scholar
  11. 11.
    Ellis, G.F.R., van Elst, H., Murugan, J., Uzan, J.P.: On the trace-free einstein equations as a viable alternative to general relativity. Class. Quant. Grav. 28, 225007 (2011). arXiv:1008.1196 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Percacci, R., Vacca, G.P.: Asymptotic safety, emergence and minimal length. Class. Quant. Grav. 27, 245026 (2010). arXiv:1008.3621 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Henneaux, M., Teitelboim, C.: The cosmological constant and general covariance. Phys. Lett. B 222, 195 (1989)ADSCrossRefGoogle Scholar
  14. 14.
    Henneaux, M., Teitelboim, C., Zanelli, J.: Gauge invariance and degree of freedom count. Nucl. Phys. B 332, 169 (1990)ADSMathSciNetCrossRefGoogle Scholar
  15. 15.
    Burger, D.J., Ellis, G.F.R., Murugan, J., Weltman, A.: The KLT relations in unimodular gravity. arXiv:1511.08517 [hep-th]
  16. 16.
    Álvarez, E., González-Martín, S., Martin, C.P.: Unimodular trees versus einstein trees. Eur. Phys. J. C 76(10), 554 (2016). arXiv:1605.02667 [hep-th]
  17. 17.
    Álvarez, E., Faedo, A.F., Lopez-Villarejo, J.J.: Transverse gravity versus observations. JCAP 0907, 002 (2009). arXiv:0904.3298 [hep-th]Google Scholar
  18. 18.
    Fiol, B., Garriga, J.: Semiclassical unimodular gravity. JCAP 1008, 015 (2010). arXiv:0809.1371 [hep-th]Google Scholar
  19. 19.
    Smolin, L.: The Quantization of unimodular gravity and the cosmological constant problems. Phys. Rev. D 80, 084003 (2009). arXiv:0904.4841 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    Smolin, L.: Unimodular loop quantum gravity and the problems of time. Phys. Rev. D 84, 044047 (2011). arXiv:1008.1759 [hep-th]ADSCrossRefGoogle Scholar
  21. 21.
    Bufalo, R., Oksanen, M., Tureanu, A.: How unimodular gravity theories differ from general relativity at quantum level. Eur. Phys. J. C 75, 477 (2015). arXiv:1505.04978 [hep-th]ADSCrossRefGoogle Scholar
  22. 22.
    Álvarez, E., Faedo, A.F., Lopez-Villarejo, J.J.: Ultraviolet behavior of transverse gravity. JHEP 0810, 023 (2008). arXiv:0807.1293 [hep-th]Google Scholar
  23. 23.
    Álvarez, E., González-Martín, S., Herrero-Valea, M., Martin, C.P.: Unimodular gravity redux. Phys. Rev. D 92, 061502 (2015). arXiv:1505.00022 [hep-th]ADSCrossRefGoogle Scholar
  24. 24.
    Álvarez, E., González-Martín, S., Herrero-Valea, M., Martin, C.P.: Quantum corrections to unimodular gravity. JHEP 1508, 078 (2015). arXiv:1505.01995 [hep-th]Google Scholar
  25. 25.
    Upadhyay, S., Oksanen, M., Bufalo, R.: BRST Quantization of Unimodular Gravity. Braz. J. Phys. 47(3), 350 (2017). arXiv:1510.00188 [hep-th]ADSCrossRefGoogle Scholar
  26. 26.
    Eichhorn, A.: On unimodular quantum gravity. Class. Quant. Grav. 30, 115016 (2013). arXiv:1301.0879 [gr-qc]; The Renormalization Group flow of unimodular \(f(R)\) gravity. JHEP 1504, 096 (2015). arXiv:1501.05848 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Benedetti, D.: Essential nature of Newtons constant in unimodular gravity. Gen. Rel. Grav. 48(5), 68 (2016). arXiv:1511.06560 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    Saltas, I.D.: UV structure of quantum unimodular gravity. Phys. Rev. D 90(12), 124052 (2014). arXiv:1410.6163 [hep-th]ADSCrossRefGoogle Scholar
  29. 29.
    Padilla, A., Saltas, I.D.: A note on classical and quantum unimodular gravity. Eur. Phys. J. C 75(11), 561 (2015). arXiv:1409.3573 [gr-qc]ADSCrossRefGoogle Scholar
  30. 30.
    ’t Hooft, G., Veltman, M.J.G.: One loop divergencies in the theory of gravitation. Ann. Inst. Poincare Phys. Theor. A20, 69–94 (1974)Google Scholar
  31. 31.
    Christensen, S.M., Duff, M.J.: Quantizing gravity with a cosmological constant. Nucl. Phys. B 170, 480 (1980)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    González-Martín, S., Martin, C.P.: Unimodular gravity and general relativity UV divergent contributions to the scattering of massive scalar particles. arXiv:1711.08009 [hep-th]
  33. 33.
    de León Ardón, R., Ohta, N., Percacci, R.: The path integral of unimodular gravity. Phys. Rev. D arXiv:1710.02457 [gr-qc]
  34. 34.
    Ellis, G.F.R.: The trace-free einstein equations and inflation. Gen. Rel. Grav. 46, 1619 (2014). arXiv:1306.3021 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    Machado, P.F., Percacci, R.: Conformally reduced quantum gravity revisited. Phys. Rev. D 80, 024020 (2009). arXiv:0904.2510 [hep-th]ADSCrossRefGoogle Scholar
  36. 36.
    Percacci, R.: Renormalization group flow of Weyl invariant dilaton gravity. New J. Phys. 13, 125013 (2011). arXiv:1110.6758 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Codello, A., D’Odorico, G., Pagani, C., Percacci, R.: The Renormalization Group and Weyl-invariance. Class. Quant. Grav. 30, 115015 (2013). arXiv:1210.3284 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Nieto, C.M., Percacci, R., Skrinjar, V.: Split Weyl transformations in quantum gravity. Phys. Rev. D 96, 106019 (2017). arXiv:1708.09760 [gr-qc]ADSCrossRefGoogle Scholar
  39. 39.
    Percacci, R., Vacca, G.P.: Search of scaling solutions in scalar-tensor gravity. Eur. Phys. J. C 75, 188 (2015). arXiv:1501.00888 [hep-th]ADSCrossRefGoogle Scholar
  40. 40.
    Nink, A.: Field parametrization dependence in asymptotically safe quantum gravity. Phys. Rev. D 91, 044030 (2015). arXiv:1410.7816 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Demmel, M., Nink, A.: Phys. Rev. D 92, 104013 (2015). arXiv:1506.03809 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    Mazur, P.O., Mottola, E.: The gravitational measure, solution of the conformal factor problem and stability of the ground state of quantum gravity. Nucl. Phys. B 341, 187 (1990)ADSCrossRefGoogle Scholar
  43. 43.
    Bern, Z., Mottola, E., Blau, S.K.: General covariance of the path integral for quantum gravity. Phys. Rev. D 43, 1212 (1991)ADSMathSciNetCrossRefGoogle Scholar
  44. 44.
    Mottola, E.: Functional integration over geometries. J. Math. Phys. 36, 2470 (1995). arXiv:hep-th/9502109 ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Percacci, R.: Gravity from a Particle Physicists’ perspective. PoS ISFTG 011 (2011). arXiv:0910.5167 [hep-th]
  46. 46.
    Floreanini, R., Percacci, R.: Canonical algebra of \(GL(4)\)-invariant gravity. Class. Quant. Grav. 7, 975 (1990)ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    Dabrowski, L., Percacci, R.: Spinors and diffeomorphisms. Commun. Math. Phys. 106(4), 691 (1986)ADSMathSciNetCrossRefGoogle Scholar
  48. 48.
    Álvarez, E., Blas, D., Garriga, J., Verdaguer, E.: Transverse Fierz-Pauli symmetry. Nucl. Phys. B 756, 148 (2006). arXiv:hep-th/0606019 ADSMathSciNetCrossRefGoogle Scholar
  49. 49.
    Álvarez, E., Vidal, R.: Weyl transverse gravity (WTDiff) and the cosmological constant. Phys. Rev. D 81, 084057 (2010). arXiv:1001.4458 [hep-th]ADSCrossRefGoogle Scholar
  50. 50.
    Bonifacio, J., Ferreira, P.G., Hinterbichler, K.: Transverse diffeomorphism and Weyl invariant massive spin 2: Linear theory. Phys. Rev. D 91, 125008 (2015). arXiv:1501.03159 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    Oda, I.: Fake conformal symmetry in unimodular gravity. Phys. Rev. D 94(4), 044032 (2016). arXiv:1606.01571 [gr-qc]ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    Ohta, N., Percacci, R., Pereira, A.D.: Gauges and functional measures in quantum gravity I: Einstein theory. JHEP 1606, 115 (2016). arXiv:1605.00454 [hep-th]ADSMathSciNetCrossRefGoogle Scholar
  53. 53.
    Ohta, N., Percacci, R., Pereira, A.D.: Gauges and functional measures in quantum gravity II: Higher derivative gravity. arXiv:1610.07991 [hep-th]
  54. 54.
    Donoghue, J.F.: Leading quantum correction to the Newtonian potential. Phys. Rev. Lett. 72, 2996 (1994). arXiv:gr-qc/9310024 ADSCrossRefGoogle Scholar
  55. 55.
    Donoghue, J.F.: General relativity as an effective field theory: the leading quantum corrections. Phys. Rev. D 50, 3874 (1994). arXiv:gr-qc/9405057 ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    Percacci, R.: An Introduction to Covariant Quantum Gravity and Asymptotic Safety. World Scientific, Singapore (2017)CrossRefGoogle Scholar
  57. 57.
    Labus, P., Percacci, R., Vacca, G.P.: Asymptotic safety in \(O(N)\) scalar models coupled to gravity. Phys. Lett. B 753, 274 (2016). arXiv:1505.05393 [hep-th]ADSCrossRefGoogle Scholar
  58. 58.
    Ohta, N., Percacci, R., Vacca, G.P.: Flow equation for \(f(R)\) gravity and some of its exact solutions. Phys. Rev. D 92, 061501 (2015). arXiv:1507.00968 [hep-th]ADSCrossRefGoogle Scholar
  59. 59.
    Ohta, N., Percacci, R., Vacca, G.P.: Renormalization Group Equation and scaling solutions for \(f(R)\) gravity in exponential parametrization. Eur. Phys. J. C 76, 46 (2016). arXiv:1511.09393 [hep-th]ADSCrossRefGoogle Scholar
  60. 60.
    Donà, P., Eichhorn, A., Labus, P., Percacci, R. R.: Asymptotic safety in an interacting system of gravity and scalar matter. Phys. Rev. D 93, 044049 (2016) Erratum: Phys. Rev. D 93(129904). arXiv:1512.01589 [gr-qc]

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.SISSATriesteItaly
  2. 2.INFN, Sezione di TriesteTriesteItaly

Personalised recommendations