Abstract
We argue that the true nature of the renormalizability of Horava-Lifshitz gravity lies in the presence of higher order spatial derivatives and not in the anisotropic Lifshitz scaling of space and time. We discuss the possibility of constructing a higher order spatial derivatives model that has the same renormalization properties of Horava-Lifshitz gravity but that does not make use of the Lifshitz scaling. In addition, the state-of-the-art of the Lorentz symmetry restoration in Horava-Lifshitz-type theories of gravitation is reviewed.
Similar content being viewed by others
Notes
With spatial derivatives we mean covariant derivatives constructed with the spatial components of the metric tensor.
References
Smolin, L.: Three Roads to Quantum Gravity. Weidenfeld & Nicolson, London (2000)
Hořava, P.: Phys. Rev. D 79, 084008 (2009)
Mukohyama, S.: Class. Quantum Gravity 27, 223101 (2010)
Izumi, K., Mukohyama, S.: Phys. Rev. D 84, 064025 (2011)
Gumrukcuoglu, A.E., Mukohyama, S., Wang, A.: Phys. Rev. D 85, 064042 (2012)
Hořava, P., Melby-Thompson, C.M.: Phys. Rev. D 82, 064027 (2010)
Biswas, R., Chakraborty, S.: Gen. Relativ. Gravit. 43, 41 (2011)
Janke, W., Johnston, D.A., Kenna, R.: J. Phys. A 43, 425206 (2010)
Cao, Q.-J., Chen, Y.-X., Shao, K.-N.: Phys. Rev. D 83, 064015 (2011)
Quevedo, H., Sánchez, A., Taj, S., Vázquez, A.: J. Phys. A 45, 055211 (2012)
Stelle, K.S.: Phys. Rev. D 16, 953 (1977)
Moffat, J.W.: Eur. Phys. J. Plus 126, 43 (2011)
Tomboulis, E.T.: arXiv:hep-th/9702146
Modesto, L.: arXiv:1107.2403 [hep-th]
Modesto, L.: arXiv:1206.2648 [hep-th]
Modesto, L.: arXiv:1202.3151 [hep-th]
Pospelov, M., Shang, Y.: Phys. Rev. D 85, 105001 (2012)
Bogdanos, C., Saridakis, E.N.: Class. Quantum Gravity 27, 075005 (2010)
Bemfica, F.S., Gomes, M.: Phys. Rev. D 84, 084022 (2011)
Bemfica, F.S., Gomes, M.: arXiv:1111.5779 [hep-th]
Visser, M.: Phys. Rev. D 80, 025011 (2009)
Weinfurtner, S., Sotiriou, T.P., Visser, M.: J. Phys. Conf. Ser. 222, 012054 (2010)
Arnowitt, R., Deser, S., Misner, C.W.: Gravitation: an Introduction to Current Research. Wiley, New York (1962)
Gomes, H., Gryb, S., Koslowski, T.: Class. Quantum Gravity 28, 045005 (2011)
Orlando, D., Reffert, S.: Class. Quantum Gravity 26, 155021 (2009)
Charmousis, C., Niz, G., Padilla, A., Saffin, P.M.: J. High Energy Phys. 0908, 070 (2009)
Iengo, R., Russo, J.G., Serone, M.: J. High Energy Phys. 0911, 020 (2009)
Mukohyama, S., Nakayama, K., Takahashi, F., Yokoyama, S.: Phys. Lett. B 679, 6 (2009)
Xiao, Z., Ma, B.-Q.: Phys. Rev. D 80, 116005 (2009)
Shao, L., Xiao, Z., Ma, B.-Q.: Astropart. Phys. 33, 312 (2010)
Amelino-Camelia, G., et al.: Nature 393, 763 (1998)
Schaefer, B.E.: Phys. Rev. Lett. 82, 4964 (1999)
Biller, S.D., et al.: Phys. Rev. Lett. 83, 2108 (1999)
Kifune, T.: Astrophys. J. Lett. 518, L21 (1999)
Amelino-Camelia, G.: Nature 408, 661 (2000)
Abdo, A.A., et al.: Science 323, 1688 (2009)
Ellis, J., Mavromatos, N.E., Nanopoulos, D.V.: Phys. Lett. B 674, 83 (2009)
Amelino-Camelia, G., Smolin, L.: Phys. Rev. D 80, 084017 (2009)
Abdo, A.A., et al.: Nature 462, 331 (2009)
Amelino-Camelia, G.: Nature 462, 291 (2009)
Amelino-Camelia, G., Gualtieri, L., Mercati, F.: Phys. Lett. B 686, 283 (2010)
Amelino-Camelia, G., Lämmerzahl, C., Mercati, F., Tino, G.M.: Phys. Rev. Lett. 103, 171302 (2009)
Mercati, F., et al.: Class. Quantum Gravity 27, 215003 (2010)
Acknowledgements
We thank A. Marcianó, D.H. Lyth, S. Mukohyama, M. Sasaki, and M. de Llano for useful discussions during the edition of this Letter. F.B. is a UIS postdoctoral fellow. Y.R. is supported by DIEF de Ciencias (UIS) grant number 5177.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Briscese, F., Rodríguez, Y. & González, G.A. On the True Nature of Renormalizability in Horava-Lifshitz Gravity. Found Phys 42, 1444–1451 (2012). https://doi.org/10.1007/s10701-012-9677-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-012-9677-1