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Gravitational radiation in dynamical noncommutative spaces

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Abstract

We investigate gravitational radiation in dynamical noncommutative spaces. By including corrections to the gravitational potential due to dynamical noncommutativity, we calculate the power in gravitational radiation and use observational data to place an upper bound on the noncommutativity parameter. We also study quantum interference induced by gravitational potential in the usual and dynamical noncommutative spaces, and compare the resulting phase difference in these cases with that in commutative space.

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References

  1. Seiberg, N., Witten, E.: String theory and noncommutative geometry. JHEP 9909, 032 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Ardalan, F., Arfaei, H., Sheikh-Jabbari, M.M.: Noncommutative geometry from strings and branes. JHEP 9902, 016 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. Moffat, J. W.: Noncommutative quantum gravity. Phys. Lett. B 491 (2000)

  4. Cacciatori, S., Chamseddine, A.H., Klemm, D., Martucci, L., Sabra, W.A., Zanon, D.: Noncommutative gravity in two dimensions. Class. Quant. Gravit. 19, 4029–4042 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  5. Rychkov, V.S.: Observers and measurements in noncommutative space times. JCAP 0307, 006 (2003)

    Article  ADS  Google Scholar 

  6. Maceda, M., Madore, J., Manousselis, P., Zoupanos, G.: Can noncommutativity resolve the Big-Bang singularity? Eur. Phys. J. C 36, 529–534 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. Alavi, S.A., Nasseri, F.: Running of the spectral index in noncommutative inflation. Int. J. Mod. Phys. A 20, 4941–4950 (2005)

    Article  ADS  MATH  Google Scholar 

  8. Alvarez-Gaume, L., Meyer, F., Vazquez-Mozo, M.A.: Comments on noncommutative gravity. Nucl. Phys. B 753, 92–127 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  9. Cai, Y.F., Piao, Y.S.: Probing non-commutativity with inflationary gravitational waves. Phys. Lett. B 657, 1–9 (2007)

    ADS  Google Scholar 

  10. Fucci, G., Avramidi, I.G.: Noncommutative Einstein equations. Class. Quant. Gravit. 25, 025005 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Wang, D., Zhang, R.B., Zhang, X.: Exact solutions of noncommutative vacuum Einstein field equations and plane-fronted gravitational waves. Eur. Phys. J. C 64, 439–444 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  12. Szabo, R.J.: Quantum gravity, field theory and signatures of noncommutative space time. Gen. Rel. Gravit. 42, 1–29 (2010)

    Article  ADS  MATH  Google Scholar 

  13. Schenkel, A., Uhlemann, ChF: Field theory on curved noncommutative space times. SIGMA 6, 061 (2010)

    MATH  Google Scholar 

  14. Ohl, Th, Schenkel, A.: Algebraic approach to quantum field theory on a class of noncommutative curved space times. Gen. Rel. Gravit. 42, 2785–2798 (2010)

    Article  ADS  MATH  Google Scholar 

  15. Saha, A., Gangopadhyay, S., Saha, S.: Noncommutative quantum mechanics of a harmonic oscillator under linearized gravitational waves. Phys. Rev. D 83, 025004 (2011)

    Article  ADS  Google Scholar 

  16. Abreu, E.M.C., Amorim, R., Guzmán Ramírez, W.: Noncommutative particles in curved spaces. JHEP 1103, 135 (2011)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Anagnostopoulos, K.: Noncommutative quantum field theory and gravity. Gen. Rel. Gravit. 43, 2331 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  18. Miao, Y.G., Xue, Z., Zhang, ShJ: Tunneling of massive particles from noncommutative inspired Schwarzschild black hole. Gen. Relativ. Gravit. 44, 555–566 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  19. Faizal, M.: Noncommutative quantum gravity. Mod. Phys. Lett. A 28, 1350034 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  20. Devastato, A., Lizzi, F., Martinetti, P.: Higgs mass in noncommutative geometry. Forts Chritte der Physik 62, 863 (2014)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. Gangopadhyay, S., Saha, A., Saha, S.: Noncommutative quantum mechanics of simple matter systems interacting with circularly polarized gravitational waves. Gen. Rel. Gravit. 47(3), 28 (2015)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. Gouba, L.: A comparative review of four formulations of noncommutative quantum mechanics. Int. J. Mod. Phys. A 31, 1630025 (2016)

    Article  ADS  MATH  Google Scholar 

  23. Gomes, M., Kupriyanov, V.G.: Position-dependent non-commutativity in quantum mechanics. Phys. Rev. D 79, 125011 (2009)

    ADS  Google Scholar 

  24. Gomes, M., Kupriyanov, V.G., da Silva, A.J.: Dynamical non-commutativity. J. Phys. A: Math. Theor. 43, 285301 (2010)

    Article  MATH  Google Scholar 

  25. Fring, A., Gouba, L., Scholtz, F.G.: Strings form position-dependent non-commutativity. J. Phys. A: Math. Theor. 43, 345401 (2010)

    Article  MATH  Google Scholar 

  26. Chaichian, M., Sheikh-Jabbari, M.M., Tureanu, A.: Hydrogen atom spectrum and the Lamb shift in noncommutative QED. Phys. Rev. Lett. 86(2716), 2–3 (2001)

    Google Scholar 

  27. Alavi, S.A., Abbaspour, S.: Dynamical noncommutative quantum mechanics. J. Phys. A: Math. Theor. 47, 045303 (2014)

    Article  ADS  MATH  Google Scholar 

  28. Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Pergamon Press, Oxford (1982)

    MATH  Google Scholar 

  29. Cheng, T.P.: Relativity, Gravitation, and Cosmology. Oxford University Press, Oxford (2005)

    MATH  Google Scholar 

  30. Jahan, A., Sadeghnezhad, N.: Gravitational radiation in noncommutative gravity. Rom. J. Phys. 58, 866 (2013)

    MathSciNet  Google Scholar 

  31. Essen, L., et al.: Nature 229, 110 (1971)

    Article  ADS  Google Scholar 

  32. Speliotopoulos, A.D.: Phys. Rev. D 51, 1701–1709 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  33. Sakurai, J.J.: Modern Quantum Mechanics Addison, vol. 128. Wesley Publishing Company, Boston (1994)

    Google Scholar 

  34. Yi-Fu, Cai, Yi, Wang: Testing quantum gravity effects with latest CMB observations. Phys. Lett. B 735, 108–111 (2014)

    Article  ADS  Google Scholar 

  35. Yi-Fu, Cai, Yun-Song, Piao: Probing noncommutativity with inflationary gravitational. Phys. Lett. B 657, 9 (2007)

    Google Scholar 

  36. Ferrari, A.F., et al.: Lorentz violation in the linearized gravity. Phys. Lett. B 652, 174 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Gamboa, J., Lopez-Sarrion, J.: U (1) noncommutative gauge fields and magnetogenesis. Phys. Rev. D 71, 067702 (2005)

    Article  ADS  Google Scholar 

  38. Nelson, W., Ochoa, J., Sakellariadou, M.: Constraining the Noncommutative Spectral Action via Astrophysical Observations. Phys. Rev. Lett. 105, 101602 (2010)

    Article  ADS  Google Scholar 

  39. Chamseddine, A., Connes, A.: The spectral action principle. Commun. Math. Phys. 186, 731 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  40. Chamseddine, A., Connes, A., Mukhanov, V.: Quanta of geometry : noncommutative aspects. Phys. Rev. Lett. 114, 091302 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  41. Sakellariadou, M.: Noncommutative spectral geometry: a short review. Conf. Ser. 442, 012015 (2013). arXiv:1301.4687

    Article  Google Scholar 

  42. Ardalan, F., Arfaei, H., Sheikh-Jabbari, M.M.: Mixed Branes and M(atrix) Theory on Noncommutative Torus, IPM-98-280. arXiv:hep-th/9803067

  43. Landi, G., Lizzi, F., Szabo, R.J.: String geometry and the noncommutative torus. Commun. Math. Phys. 206, 603 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  44. Kostelecky, A., Melissinos, A.C., Mewes, M.: Searching for photon-sector Lorentz violation using gravitational-wave detectors. Phys. Lett. B 761, 1 (2016)

    Article  ADS  Google Scholar 

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Acknowledgements

S. A. Alavi would like to thank “INFN, Sezione di Torino and Dipartimento di Fisica” for kind hospitality and support during his visit to INFN where part of this work was done. We are also very grateful to Dr. Estiri and Prof. Rouzbeh Allahverdi (University of New Mexico, USA) for careful reading of the manuscript and valuable comments.

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Alavi, S.A., Nasab, M.A. Gravitational radiation in dynamical noncommutative spaces. Gen Relativ Gravit 49, 5 (2017). https://doi.org/10.1007/s10714-016-2167-6

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