Skip to main content
Springer Nature Link
Log in

Modified Brans–Dicke cosmology with minimum length uncertainty

  • Research
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

We consider a modification of the Brans–Dicke gravitational Action Integral inspired by the existence of a minimum length uncertainty for the scalar field. In particular, the kinetic part of the Brans–Dicke scalar field is modified such that the equation of motion for the scalar field is modified according to the quadratic Generalized Uncertainty Principle (GUP). For the background geometry, we assume the homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker metric. We investigate the dynamics and the cosmological evolution of the dynamical variables of the theory, and we compare the results with the unmodified Brans–Dicke theory. It follows that in consideration because of the additional degrees of freedom in the energy-momentum tensor the dynamical variables describe various aspects of the cosmological history. This is one of the first studies on the effects of GUP in a Machian gravitational theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: This is a theoretical work, so, no observational data-sets are associated with this work.]

References

  1. Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Phys. Rep. 1, 513 (2012)

    Google Scholar 

  2. Ratra, B., Peebles, P.J.E.: Phys. Rev. D 37, 3406 (1988)

    Article  ADS  Google Scholar 

  3. Linder, E.V.: Phys. Rev. D 70, 023511 (2004)

    Article  ADS  Google Scholar 

  4. Christodoulidis, P., Roest, D., Sfakianakis, E.I.: JCAP 12, 059 (2019)

    Article  ADS  Google Scholar 

  5. Horava, P.: Phys. Rev. D 79, 084008 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. Barrow, J.D., Ottewill, A.C.: J. Phys. A 16, 2757 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  7. Buchdahl, H.A.: Mon. Not. Roy. Astron. Soc. 150, 1 (1970)

    Article  ADS  Google Scholar 

  8. Harko, T., Lobo, F.S.N., Nojiri, S., Odintsov, S.D.: Phys. Rev. D 84, 024020 (2011)

    Article  ADS  Google Scholar 

  9. Ferraro, R., Fiorini, F.: Phys. Rev. D 75, 084031 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  10. Bahamonde, S., Bohmer, C.G., Wright, M.: Phys. Rev. D 92, 104042 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  11. Paliathanasis, A.: JCAP 1708, 027 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  12. Clifton, T., Barrow, J.D.: Class. Quantum Gravity 23, 2951 (2006)

    Article  ADS  Google Scholar 

  13. Nojiri, S., Odintsov, S.D., Oikonomou, V.K.: Phys. Rep. 692, 1 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  14. Sotiriou, T.P., Faraoni, V.: Rev. Mod. Phys. 82, 451 (2010)

    Article  ADS  Google Scholar 

  15. Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011)

    Article  ADS  MathSciNet  Google Scholar 

  16. Sotiriou, T.P.: Gravity and scalar fields. In: Papantonopoulos, E. (ed.) Modifications of Einstein’s Theory of Gravity at Large Distances. Lecture Notes in Physics, vol. 892. Springer, Berlin (2015)

    Google Scholar 

  17. Leon, G., Franz Silva, F.O.: Class. Quantum Gravity 38, 015004 (2020)

    Article  ADS  Google Scholar 

  18. Leon, G., Paliathanasis, A., Morales-Martinez, J.L.: EPJC 78, 753 (2018)

    Article  ADS  Google Scholar 

  19. Amendola, L., Polarski, D., Tsujikawa, S.: Phys. Rev. Lett. 98, 131302 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  20. Garay, L.J.: Int. J. Mod. Phys. A 10, 145 (1995)

    Article  ADS  Google Scholar 

  21. Casadio, R., Micu, O., Nicolini, P.: Minimum length effects in black hole physics. In: Camlent, X. (ed.) Quantum Aspects of Black Holes. Fundamental Theories of Physics, vol. 178. Springer, Cham (2015)

    Chapter  Google Scholar 

  22. Chang, L.N., Lewis, Z., Mimic, D., Takeuchi, T.: Adv. High Energy Phys. 2011, 4935514 (2011)

    Google Scholar 

  23. Nassif, C.: Int. J. Mod. Phys. D 19, 539 (2010)

    Article  ADS  Google Scholar 

  24. Greensite, J.: Phys. Lett. B 255, 375 (1991)

    Article  ADS  Google Scholar 

  25. Maggiore, M.: Phys. Lett. B 304, 65 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  26. Ali, A.F., Das, S., Vagenas, E.C.: Phys. Lett. B 678, 497 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  27. Silagadge, Z.: Phys. Lett. A 373, 2643 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  28. Vagenas, E.C., Ali, A.F., Hemeda, M., Alshal, H.: EPJC 79, 398 (2019)

    Article  ADS  Google Scholar 

  29. Lu, F., Tao, J., Wang, P.: JCAP 12, 036 (2018)

    Article  ADS  Google Scholar 

  30. Casadio, R., Scardigli, F.: Phys. Lett. B 807, 135558 (2020)

    Article  MathSciNet  Google Scholar 

  31. Adler, R.J., Chen, P., Santiago, D.I.: Gen. Relativ. Gravit. 33, 2101 (2001)

    Article  ADS  Google Scholar 

  32. Paliathanasis, A., Tsamparlis, M.: J. Geom. Phys. 107, 45 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  33. Padmanabhan, T., Chakraborty, S., Kothawala, D.: Gen. Relativ. Gravit. 48, 5, 55 (2016)

    ADS  Google Scholar 

  34. Miao, Y.-G., Zhao, Y.-J.: Int. J. Phys. D. 23, 1450062 (2014)

    Article  ADS  Google Scholar 

  35. Garattini, R., Faizal, M.: Nucl. Phys. B 905, 313 (2016)

    Article  ADS  Google Scholar 

  36. Diab, A.M., Tawfik, A.N.: Astron. Nachr. 342, 49 (2021)

    Article  ADS  Google Scholar 

  37. Zeynali, K., Darabi, F., Motavalli, H.: JCAP 12, 033 (2012)

    Article  ADS  Google Scholar 

  38. Chang, L.N., Minic, D., Okamura, N., Takeuchi, T.: Phys. Rev D 65, 125028 (2002)

    Article  ADS  Google Scholar 

  39. Paliathanasis, A., Pan, S., Pramanik, S.: Class. Quantum Grav. 32, 245006 (2015)

    Article  ADS  Google Scholar 

  40. Giacomini, A., Leon, G., Paliathanasis, A., Pan, S.: EPJC 80, 931 (2020)

    Article  ADS  Google Scholar 

  41. Paliathanasis, A., Leon, G., Khyllep, W., Dutta, J., Pan, S.: EPJC 81, 607 (2021)

    Article  ADS  Google Scholar 

  42. Barca, G., Giovannetti, E., Montani, G.: arXiv:2112.08905 [gr-qc]

  43. Brans, C., Dicke, R.H.: Phys. Rev. 124, 195 (1961)

    Article  Google Scholar 

  44. Bondi, H., Samuel, J.: Phys. Lett. A 228, 121 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  45. Gasco, E.: Mach’s Principle: the original Einstein’s considerations (1907-12). Il Principio di Mach: le prime considerazioni di Einstein (1907–12). Ital. Phys. Soc. 13, 75 (2005)

    Google Scholar 

  46. Faraoni, V.: Phys. Rev. D 59, 084021 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  47. O’Hanlon, J.: Phys. Rev. Lett. 29, 137 (1972)

    Article  ADS  Google Scholar 

  48. Sotiriou, T.P.: Gravity and Scalar fields. In: Papantonopoulos, E. (ed.) Proceedings of the 7th Aegean Summer School: Beyond Einstein’s theory of gravity, Modifications of Einstein’s Theory of Gravity at Large Distances, Paros, Greece. Lecture Notes in Physics, vol. 892 (2015)

  49. Alonso, J.L., Cortes, J.L., Laliena, V.: Phys. Rev. D 67, 024023 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  50. Faraoni, V.: Exact solutions of scalar-tensor cosmology. In: Cosmology in Scalar-Tensor Gravity. Fundamental Theories of Physics, vol 139. Springer, Dordrecht, pp 93–114. https://doi.org/10.1007/978-1-4020-1989-0_4

  51. Tsamparlis, M., Paliathanasis, A., Basilakos, S., Capozziello, S.: Gen. Relativ. Gravit. 45, 2003 (2013)

    Article  ADS  Google Scholar 

  52. Morganstern, R.E.: Phys. Rev. D 4, 946 (1971)

    Article  ADS  Google Scholar 

  53. Obregn, O., Chauvet, P.: Astroph. Space Sci. 56, 335 (1978)

    Article  ADS  Google Scholar 

  54. Faraoni, V.: Fundam. Theor. Phys. 139 (2004)

  55. Paliathanasis, A., Tsamparlis, M., Basilakos, S., Capozziello, S.: Phys. Rev. D 93, 043528 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  56. Papagiannopoulos, G., Barrow, J.D., Basilakos, S., Giacomini, A., Paliathanasis, A.: Phys. Rev. D 95, 024021 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  57. Morganstern, R.E.: Phys. Rev. D 4, 282 (1971)

    Article  ADS  Google Scholar 

  58. Montenegro, A.E., Jr., Carneiro, S.: Class. Quantum Gravity 24, 313 (2007)

    Article  ADS  Google Scholar 

  59. Johri, V.B., Goswami, G.K.: J. Math. Phys. 21, 2269 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  60. Chauvineau, B.: J. Math. Phys. 43, 1487 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  61. Paliathanasis, A., Tsamparlis, M., Basilakos, S., Barrow, J.D.: Phys. Rev. D 93, 043528 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  62. Hrycyna, O., Szydlowski, M.: JCAP 12, 016 (2013)

    Article  ADS  Google Scholar 

  63. Giacomini, F., Castro-Euiz, E., Brunke, C.: Nature Commun. 10(1), 494 (2019)

    Article  ADS  Google Scholar 

  64. Cid, A., Leon, G., Leyva, Y.: JCAP 16, 027 (2016)

    Article  Google Scholar 

  65. Leon, G., Paliathanasis, A., Velazquez, L.: Gen. Relativ. Gravit. 52, 71 (2020)

    Article  ADS  Google Scholar 

  66. Quesne, C., Tkachuk, V.M.: J. Phys. A 39, 10909 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  67. Das, S., Vagenas, E.C.: Phys. Rev. Lett. 101, 221301 (2008)

    Article  ADS  Google Scholar 

  68. Quesne, C., Tkackuk, V.M.: J. Phys. A: Math. Gen. 39, 10909 (2006)

    Article  ADS  Google Scholar 

  69. Moayedi, S.K., Setare, M.R., Moayeri, H.: Int. J. Theor. Phys. 49, 2080 (2010)

    Article  Google Scholar 

  70. Bishop, M., Lee, J., Singleton, D.: Phys. Lett. B 802, 135209 (2020)

    Article  MathSciNet  Google Scholar 

  71. Lake, M.J., Miller, M., Ganardi, R.F., Liu, Z., Liang, S.-D., Paterek, T.: Class. Quantum Gravity 36(15), 155012 (2019)

    Article  ADS  Google Scholar 

  72. Lake, M.J., Miller, M., Liang, S.-D.: Universe 6, 56 (2020)

    Article  ADS  Google Scholar 

  73. Lake, M.J.: A new approach to generalised uncertainty relations. In: Nicolini, P. (ed.) Touring the Planck Scale: Antonio Aurilia Memorial Volume. Springer (2021). arXiv:2008.13183

  74. Kempf, A.: J. Phys. A: Math. Gen. 30, 2093 (1997)

    Article  ADS  Google Scholar 

  75. Hinrichen, H., Kempf, A.: J. Math. Phys. 37, 2121 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  76. Jizba, P., Kleinert, H., Scardigli, F.: Phys. Rev. D 81, 084030 (2010)

    Article  ADS  Google Scholar 

  77. Buoninfante, L., Luciano, G.G., Petruzziello, L.: EPJC 79, 663 (2019)

    Article  ADS  Google Scholar 

  78. Scardigli, F., Lambiase, G., Vagenas, E.: Phys. Lett. B 767, 242 (2012)

    Article  ADS  Google Scholar 

  79. Buoninfante, L., Lambiase, G., Luciano, G.G., Petruzziello, L.: EPJC 80, 853 (2020)

    Article  ADS  Google Scholar 

  80. Pedram, P.: Phys. Lett. B 718, 638 (2012)

    Article  ADS  Google Scholar 

  81. Vagenas, E.C., Ali, A.F., Hemeda, M., Alshal, H.: EPJC 79, 398 (2019)

    Article  ADS  Google Scholar 

  82. Aghababaei, S., Moradpour, H., Vagenas, E.C.: Eur. Phys. J. Plus 136, 997 (2021)

    Article  Google Scholar 

  83. Shababi, H., Chung, W.S.: Phys. Lett. B 770, 445 (2017)

    Article  ADS  Google Scholar 

  84. Paliathanasis, A., Pan, S., Pramanik, S.: Class. Quantum Gravity 32, 245006 (2015)

    Article  ADS  Google Scholar 

  85. Giacomini, A., Leon, G., Paliathanasis, A., Pan, S.: EPJC 80, 931 (2020)

    Article  ADS  Google Scholar 

  86. Miao, Y.-G., Zhao, Y.-J.: Int. J. Mod. Phys. D. 23, 1450062 (2014)

    Article  ADS  Google Scholar 

  87. Diab, A.M., Tawfik, A.N.: Aston. Nachr. 342, 49 (2021)

    Article  ADS  Google Scholar 

  88. Kerachian, M., Acquaviva, G., Lukes-Gerakopoulos, G.: Phys. Rev. D 101, 043535 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  89. Dabrowski, M.P., Denkiewicz, T., Blaschke, D.: Annalen Phys. 16, 237 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  90. Perko, L.: Differential Equations and Dynamical Systems. Springer-Verlag, New York (1991)

    Book  MATH  Google Scholar 

  91. Guckenheimer, J., Holmes, P.: Nonlinear Oscillations. Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York (1983)

    Book  MATH  Google Scholar 

Download references

Acknowledgements

This work is based on the research supported in part by the National Research Foundation of South Africa (Grant Number 131604). Additionally, the research of Genly Leon is funded by Vicerrectoría de Investigación y Desarrollo Tecnológico (Vridt) at Universidad Católica del Norte. He also thanks Vridt support through Concurso De Pasantías De Investigación Año 2022, Resolución Vridt N0040/2022 and through Resolución Vridt N 054/2022. The authors thank the support of Núcleo de Investigación Geometría Diferencial y Aplicaciones, Resolución Vridt N\(\circ \)096/2022.

Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile

    Genly Leon

  2. Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban, 4000, South Africa

    Andronikos Paliathanasis & Genly Leon

  3. Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile

    Andronikos Paliathanasis

Authors
  1. Andronikos Paliathanasis
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Genly Leon
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Genly Leon.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Paliathanasis, A., Leon, G. Modified Brans–Dicke cosmology with minimum length uncertainty. Gen Relativ Gravit 55, 12 (2023). https://doi.org/10.1007/s10714-022-03059-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-022-03059-3

Keywords

Search

Navigation