Skip to main content
SpringerLink
Log in

Particle creation and bulk viscosity in Bianchi-I universe in Saez–Ballester theory with different deceleration parameters

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

Abstract

In Saez–Ballester gravitational theory, we studied the role of particle creation and bulk viscosity in the evolution of a spatially homogeneous and anisotropic Bianchi type I universe. We treated particle creation and bulk viscosity as two distinct irreversible processes, and we modified the energy momentum tensor to account for viscous and particle creation pressures. We employed constant and variable deceleration parameters to obtain average scale factor solutions for the Bianchi type I model. The use of constant deceleration parameter resulted in two unique scale factor solutions that led to singular and non-singular natures of the universe with power-law and exponential laws, respectively. Furthermore, the variable deceleration parameter yielded a de Sitter like solution representing a non-singular universe. We also explored the temporal evolution of the bulk viscosity coefficient in Eckart’s theory, truncated theory, and full causal theory for all three models.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22

Similar content being viewed by others

Data Availability

Data sharing is not applicable in this paper as no data were produced/reproduced or analysed in this work.

References

  1. Prigogine, I., Geheniau, J., Gunzig, E., Nordone, P.: Thermodynamics of matter creation. Proc. Natl. Acad. Sci. 85, 7428 (1988)

    ADS  MathSciNet  Google Scholar 

  2. Prigogine, I.: Thermodynamics and cosmology. Int. J. Theor. Phys. 28, 927 (1989)

    MATH  Google Scholar 

  3. Zeldovich, Ya.B.: Particle production in cosmology. J. Exp. Theor. Phys. 12(2), 370 (1970)

    Google Scholar 

  4. Hu, B.L.: Vacuum viscosity description of quantum processes in the early universe. Phys. Lett. A 90(7), 375–380 (1982)

    ADS  Google Scholar 

  5. Lima, J.A.S., Germano, A.S.M.: On the equivalence of bulk viscosity and matter creation. Phys. Lett. A 170(5), 373–378 (1992)

    ADS  Google Scholar 

  6. Zimdahl, W., Pavón, D.: Cosmology with adiabatic matter creation. Int. J. Mod. Phys. D 3(01), 327–330 (1994)

    ADS  Google Scholar 

  7. Birrell, N.D., Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Camb. Univer. Press, Cambridge (1984)

    MATH  Google Scholar 

  8. Parker, L.: Particle creation in expanding universes. Phys. Rev. Lett. 21(8), 562–564 (1968)

    ADS  Google Scholar 

  9. Hoyle, F., Narlikar, J.V.: On the avoidance of singularity in C field cosmology. Proc. R. Soc. Lond. A Math. Phys. Sci. 278(1375), 465–478 (1964)

    ADS  MATH  Google Scholar 

  10. Pope, A.C., Matsubara, T., Szalay, A.S., Blanton, M.R., Eisenstein, D.J., Gray, J., Jain, B., Bahcall, N.A., Brinkmann, J., Budavari, T., Connolly, A.J.: Cosmological parameters from eigenmode analysis of sloan digital sky survey galaxy redshifts. Astrophys. J. 607(2), 655 (2004)

    ADS  Google Scholar 

  11. Percival, W.J., Baugh, C.M., Bland-Hawthorn, J., Bridges, T., Cannon, R., Cole, S., Colless, M., Collins, C., Couch, W., Dalton, G., De Propris, R.: The 2dF Galaxy Redshift Survey: the power spectrum and the matter content of the Universe. Mon. Not. R. Astron. Soc. 327(4), 1297–1306 (2001)

    ADS  Google Scholar 

  12. Kumar, S., Singh, C.P.: Exact Bianchi Type-I cosmological models in a scalar-tensor theory. Int. J. Theor. Phys. 47, 1722–1730 (2008)

    MathSciNet  MATH  Google Scholar 

  13. Ellis, G.F.R.: Republication of relativistic cosmology. Gen. Relativ. Gravit. 41, 581–660 (2009)

    ADS  MATH  Google Scholar 

  14. Hu, B.L.: Quantum dissipative processes and gravitational entropy of the universe. Phys. Lett. A. 97(9), 368–374 (1983)

    ADS  Google Scholar 

  15. Grøn, Ø.: Viscous inflationary Universe models. Astrophys. Space Sci. 173, 191–225 (1990)

    ADS  MathSciNet  MATH  Google Scholar 

  16. Maartens, R., Mendez, V.: Non-Linear bulk viscosity and inflation. Phys. Rev. D. 55(4), 1937–1942 (1997)

    ADS  Google Scholar 

  17. Zimdahl, W.: “Understanding’’ cosmological bulk viscosity. Mon. Not. Roy. Astron. Soc. 280(4), 1239–1243 (1996)

    ADS  Google Scholar 

  18. Oikonomou, V.K.: Constraints on singular evolution from gravitational baryogenesis. Int. J. Geom. Meth. Mod. Phys. 13(3), 1937–1942 (1997)

    MathSciNet  Google Scholar 

  19. Arbab, A.I.: Cosmological models with variable cosmological and gravitational constants and bulk viscous models. Gen. Relativ. Gravit. 29, 61–74 (1997)

    ADS  MathSciNet  MATH  Google Scholar 

  20. Singh, G.P., Kotambkar, S.: Higher-dimensional dissipative cosmology with varying G and Lambda. Grav. Cosmol. 9(3), 206–210 (2003)

    ADS  MATH  Google Scholar 

  21. Singh, G.P., Deshpande, R.V., Singh, T.: Higher-dimensional cosmological model with variable gravitational constant and bulk viscosity in Lyra geometry. Pramana 63(5), 937–945 (2004)

    ADS  Google Scholar 

  22. Israel, W.: Nonstationary irreversible thermodynamics: a causal relativistic theory. Ann. Phys. 100(1–2), 310–331 (1976)

    ADS  MathSciNet  Google Scholar 

  23. Israel, W., Stewart, J.M.: Transient relativistic thermodynamics and kinetic theory. Ann. Phys. 118(2), 341–372 (1979)

    ADS  MathSciNet  Google Scholar 

  24. Stewart, J.M.: On transient relativistic thermodynamics and kinetic theory. Proc. R. Soc. Lond. A. Math. Phys. Sci. 357(1688), 59–75 (1977)

    ADS  MathSciNet  Google Scholar 

  25. Maartens, R.: Dissipative cosmology. Class. Quantum Gravit. 12(6), 1455 (1995)

    ADS  MathSciNet  MATH  Google Scholar 

  26. Muller, I.: Zum paradoxon der wärmeleitungstheorie. Z. Phys. 198(4), 329–344 (1967)

    ADS  MATH  Google Scholar 

  27. Pavon, D., Jou, D., Casas-Vázquez, J.: On a covariant formulation of dissipative phenomena. In Annales de l’IHP Physique théorique 36(1), 79–88 (1982)

    MathSciNet  Google Scholar 

  28. Bali, R.: Bianchi type V magnetized string dust bulk viscous fluid cosmological model with variable magnetic permeability. Int. J. Theor. Phys. 48(2), 476–486 (2009)

    MathSciNet  MATH  Google Scholar 

  29. Tyagi, A., Sharma, K.: Bianchi type-II bulk viscous string cosmological models in general relativity. Int. J. Theor. Phys. 49(8), 1712–1718 (2010)

    MathSciNet  MATH  Google Scholar 

  30. Mohan, N.J., Mathew, T.K.: On the feasibility of truncated Israel-Stewart model in the context of late acceleration. Class. Quantum Gravit. 38(14), 145016 (2021)

    ADS  MathSciNet  MATH  Google Scholar 

  31. Singh, J.P., Singh, P., Bali, R.: Bulk viscosity and decaying vacuum density in Friedmann universe. Int. J. Theor. Phys. 51(12), 3828–3838 (2012)

    MathSciNet  MATH  Google Scholar 

  32. Johri, V.B., Desikan, K.: Cosmological models with constant deceleration parameter in Brans–Dicke theory. Gen. Relativ. Gravit. 26(12), 1217–1232 (1994)

    ADS  MathSciNet  Google Scholar 

  33. Krori, K.D., Mukherjee, A.: Bianchi cosmologies with particle creation and bulk viscosity. Gen. Relativ. Gravit. 32(8), 1429–1438 (2000)

    ADS  MathSciNet  MATH  Google Scholar 

  34. Desikan, K.: Cosmological models with bulk viscosity in the presence of particle creation. Gen. Relativ. Gravit. 29(4), 435–443 (1997)

    ADS  MathSciNet  MATH  Google Scholar 

  35. Johri, V.B., Pandey, S.K.: Cosmological models with matter creation in open thermodynamic systems. Int. J. Theor. Phys. 38(7), 1981–1991 (1999)

    MATH  Google Scholar 

  36. Singh, G.P., Beesham, A.: Bulk viscosity and particle creation in Brans–Dicke theory. Aust. J. Phys. 52(6), 1039–1049 (1999)

    ADS  MATH  Google Scholar 

  37. Singh, G.P., Deshpande, R.V., Singh, T.: Viscous cosmological models with particle creation in Brans–Dicke theory. Astrophys. Space Sci. 282(3), 489–498 (2002)

    ADS  Google Scholar 

  38. Singh, G.P., Kale, A.Y.: Anisotropic bulk viscous cosmological models with particle creation. Astrophys. Space Sci. 331(1), 207–219 (2011)

    ADS  MATH  Google Scholar 

  39. Singh, G.P., Kale, A.Y.: Bianchi type I bulk viscous cosmological models with particle creation in Brans–Dicke theory. Eur. Phys. J. Plus 126(9), 1–17 (2011)

    ADS  Google Scholar 

  40. Chaubey, R.: Bianchi type-V bulk viscous cosmological models with particle creation in Brans–Dicke theory. Astrophys. Space Sci. 342(2), 499–509 (2012)

    ADS  MATH  Google Scholar 

  41. Rasouli, S.M.M.: Kasner solution in Brans–Dicke theory and its corresponding reduced cosmology. In: Progress in Mathematical Relativity, Gravitation and cosmology: Proceedings of the Spanish Relativity Meeting ERE2012, University of Minho, Guimaraes, Portugal, September 3-7, 371-375 (2012). Springer Berlin Heidelberg, Berlin, Heidelberg (2013)

  42. Rasouli, S.M.M., Vargas Moniz, P.: Extended anisotropic models in noncompact Kaluza-Kelin theory. Class. Quantum Gravit. 36(7), 075010 (2019)

    ADS  MATH  Google Scholar 

  43. Harko, T., Lobo, F., Mak, M.: Bianchi type I cosmological models in Eddington-inspired Born-Infeld gravity. Galaxies 2(4), 496–519 (2014)

    ADS  Google Scholar 

  44. Saez, D., Ballester, V.J.: A simple coupling with cosmological implications. Phys. Lett. A 113(9), 467–470 (1986)

    ADS  Google Scholar 

  45. Socorro, J., Sabido, M., Sánchez, M.A., Frías, Palos, M.G.: Anisotropic cosmology in Sáez-Ballester theory: classical and quantum solutions. Rev. Mex. Fis. 56(2), 166–171 (2010)

    Google Scholar 

  46. Rao, M., Santhi, M.V., Vinutha, T.: Exact Bianchi type II, VIII and IX string cosmological models in Saez–Ballester theory of gravitation. Astrophys. Space Sci. 314(1-3) (2008)

  47. Mishra, R.K., Dua, H.: Bulk viscous string cosmological models in Saez–Ballester theory of gravity. Astrophys. Space Sci. 364(11), 195 (2019)

    ADS  MathSciNet  Google Scholar 

  48. Mishra, R.K., Chand, A.: Cosmological models in Sáez–Ballester theory with bilinear varying deceleration parameter. Astrophys. Space Sci. 365(4), 76 (2020)

    ADS  Google Scholar 

  49. Naidu, R.L., Aditya, Y., Raju, K.D., Vinutha, T., Reddy, D.R.K.: Kaluza-Klein FRW dark energy models in Saez–Ballester theory of gravitation. New Astron. 85, 101564 (2021)

    Google Scholar 

  50. Quiros, I., Horta-Rangel, F.A.: Saez–Ballester and Einstein massless-scalar systems are one and the same theory! (2002) arXiv:2209.00157

  51. Quiros, I., DeArcia, R., García-Salcedo, R., Gonzalez, T., Horta-Rangel, F.A.: An issue with the classification of the scalar-tensor theories of gravity. Int. J. Mod. Phys. D. 29(07), 2050047 (2020)

    ADS  MathSciNet  MATH  Google Scholar 

  52. Rasouli, S.M.M., Sakellariadou, M., Moniz, P.V.: Geodesic deviation in Saez–Ballester theory. Phys. Dark Universe 37, 101112 (2022)

    Google Scholar 

  53. Rasouli, S.M.M.: Noncommutativity, Sáez–Ballester theory and kinetic inflation. Universe 8(3), 165 (2022)

    ADS  Google Scholar 

  54. Rasouli, S.M.M., Moniz, P.: Modified Saez–Ballester scalar tensor theory from 5D space time. Class. Quantum 35(2), 025004 (2017)

    ADS  MathSciNet  MATH  Google Scholar 

  55. Rasouli, S.M.M., Farhoudi, M., Sepangi, H.R.: An anisotropic cosmological model in a modified Brans–Dicke theory. Class. Quantum Gravit. 28(15), 155004 (2011)

    ADS  MathSciNet  MATH  Google Scholar 

  56. Zeyauddin, M., Saha, B.: Bianchi type V bulk viscous cosmological models with particle creation in general relativity. Eur. Phys. J. Plus 129(8), 1–23 (2014)

    Google Scholar 

  57. Chandel, S., Ram, S.: Anisotropic cosmological models with bulk viscosity and particle creation in Saez–Ballester theory of gravitation. Pramana 86(3), 681–699 (2016)

    ADS  Google Scholar 

  58. Bertone, G., Hooper, D., Silk, J.: Particle dark matter: evidence, candidates and constraints. Phys. Rep. 405(5–6), 279–390 (2005)

    ADS  Google Scholar 

  59. Feng, J.: Dark matter candidates from particle physics and methods of detection. Ann. Rev. Astron. Astrophys. 48, 495–545 (2010)

    ADS  Google Scholar 

  60. Bekenstein, J., Modrdehai, M.: Does the missing mass problem signal the breakdown of Newtonian gravity? Astrophys. J. Part I 286, 7–14 (1984)

    ADS  Google Scholar 

  61. Trippe, S.: The ‘missing mass problem’ in astronomy and the need for a modified law of gravity. Z. NAturforsch. A 69(3–4), 173–187 (2014)

    ADS  Google Scholar 

  62. Hodson, A., Hongsheng, Z.: Generalizing MOND to explain the missing mass in galaxy clusters. Astron. Astrophys. 598, A127 (2017)

    Google Scholar 

  63. Wang, X.: Bianchi type I string cosmological models with bulk viscosity and magnetic field. Astrophys. Space Sci. 293(4), 433–440 (2004)

    ADS  Google Scholar 

  64. Chaubey, R.: Bianchi type-V bulk viscous cosmological models with particle creation in Brans–Dicke theory. Astrophys. Space Sci. 342(2), 499–509 (2012)

    ADS  MATH  Google Scholar 

  65. Rao, V.U.M., Sireesha, K.V.S.: Bianchi types II, VIII and IX string cosmological models with bulk viscosity in Brans–Dicke theory of gravitation. Int. J. Theor. Phys. 51, 3013–3020 (2012)

    MathSciNet  MATH  Google Scholar 

  66. Zeyauddin, M., Saha, B.: Bianchi type V bulk viscous cosmological models with particle creation in general relativity. Eur. Phys. J. Plus 129, 1–23 (2014)

    Google Scholar 

  67. Singh, G.P., Kale, A.Y.: Anisotropic bulk viscous cosmological models with particle creation in general relativity. Astrophys. Space Sci. 331, 207–219 (2011)

    ADS  MATH  Google Scholar 

  68. Naidu, R.L., Reddy, D., Ramprasad, T., Ramana, K.V.: Bianchi type-V bulk viscous string cosmological model in f(R, T) gravity. Astrophys. Space Sci. 348, 247–252 (2013)

    ADS  Google Scholar 

  69. Eckart, C.: The thermodynamics of irreversible processes. III. Relativistic theory of the simple fluid. Phys. Rev. 58(10), 919 (1940)

    ADS  MATH  Google Scholar 

  70. Landau, L.D., Lifshitz, E.M.: Fluid Mechanics Addison (1959)

  71. Belinchón, J.A., Cornejo-Pérez, O., Cruz, N.: Exact solutions of a causal viscous FRW cosmology within the Israel-Stewart theory through factorization. Gen. Relativ. Gravit. 54(1), 1–22 (2022)

    ADS  MathSciNet  MATH  Google Scholar 

  72. Murphy, G.L.: Big-bang model without singularities. Phys. Rev. D 8(12), 4231 (1973)

    ADS  Google Scholar 

  73. Brevik, I., Grøn, Ø.: Universe models with negative bulk viscosity. Astrophys. Space Sci. 347(2), 399–404 (2013)

    ADS  Google Scholar 

  74. Bolotin, Y.L., Kostenko, A., Lemets, O.A., Yerokhin, D.A.: Cosmological evolution with interaction between dark energy and dark matter. Int. J. Mod. Phys. D 24(03), 1530007 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  75. Ram, S., Zeyauddin, M., Singh, C.P.: Anisotropic Bianchi type V perfect fluid cosmological models in Lyra’s geometry. J. Geom. Phys. 60(11), 1671–1680 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  76. Saha, B., Rikhvitsky, V.: Bianchi type I universe with viscous fluid and a \(\Lambda \) term: a qualitative analysis. Phys. D: Nonlinear Phenom. 219(2), 168–176 (2006)

    ADS  MathSciNet  MATH  Google Scholar 

  77. Berman, M.S.: A special law of variation for Hubble’s parameter. II Nuovo Cimento B (1971-1996) 74(2), 182–186 (1983)

  78. Berman, M.S., Gomide, F.M.: Cosmological models with constant deceleration parameter. Gen. Relativ. Gravit. 20(2), 191–198 (1988)

    ADS  MathSciNet  Google Scholar 

  79. Tiwari, R.K., Singh, R., Shukla, B.K.: A cosmological model with variable deceleration parameter. African Rev. Phys. 10 (2016)

  80. Tiwari, R.K., Beesham, A., Shukla, B.K.: Cosmological models with viscous fluid and variable deceleration parameter. Eur. Phys. J. Plus 132(1), 20–29 (2017)

    Google Scholar 

  81. Mishra, R.K., Dua, H.: Bianchi type-I cosmological model in Sáez–Ballester theory with variable deceleration parameter. Astrophys. Space Sci. 366(5), 47 (2021)

    ADS  Google Scholar 

  82. Shukla, B.K., Khare, S., Shukla, S.N., Singh, A.: Bianchi Type-I cosmological model in Saez–Ballester theory with varying cosmological constant. Prespacetime J. 13(3), 327–335 (2022)

    Google Scholar 

  83. Johri, V.B., Sudarshan, R.: Friedmann universes with bulk viscosity. Phys. Lett. A 132(6–7), 316–320 (1988)

    ADS  MathSciNet  Google Scholar 

  84. Triginer, J., Pavón, D.: Particle production in a viscous cosmological fluid. Gen. Relativ. Gravit. 26(5), 513–524 (1994)

    ADS  MATH  Google Scholar 

  85. Reddy, D.R.K.: A string cosmological model in Brans–Dicke theory of gravitation. Astrophys. Space Sci. 286(3), 365–371 (2003)

    ADS  MATH  Google Scholar 

  86. Chen, C., Kao, W.: Stability analysis of anisotropic infationary cosmology. Phys. Rev. D 64(12), 124019 (2001)

    ADS  MathSciNet  Google Scholar 

  87. Kao, W.: Bianchi type-I space and the stability of the inflationary Friedmann–Robertson–Walker solution. Phys. Rev. D 64(10), 107301 (2001)

    ADS  MathSciNet  Google Scholar 

  88. Mishra, R.K., Dua, H.: Bianchi type I cosmological model in Saez–Ballester theory with variable deceleration parameter. Astrophys. Space Sci. 366 (2021)

  89. Mohanty, S.: Astroparticle Physics and Cosmology; Perspectives in the multimessenger era, in Lecture notes in Physics. Springer 975 (2020)

  90. Luciano, G.: Saez–Ballester gravity in Kantowski–Sachs Universe: a new reconstruction paradigm for Barrow Holographic Dark Energy. Phys. Dark. Univ. 41, 101237 (2023)

    Google Scholar 

  91. Jesus, J., Oliveira, F.A., Basilakos, S., Lima, J.A.S.: Newtonian perturbations on models with matter creation. Phys. Rev. D. 84(6), 063511 (2011)

    ADS  Google Scholar 

  92. Bhattacharya, K., Chatterjee, A., Hussain, S.: The nature of cosmological metric perturbations in presence of gravitational particle production. Gen. Relativ. Gravit. 54(8), 84 (2022)

    ADS  MathSciNet  MATH  Google Scholar 

  93. Basilakos, S., Lima, J.A.: Constraints on cold dark matter accelerating cosmologies and cluster formation. Phys. Rev. D. 82(2), 023504 (2010)

    ADS  Google Scholar 

Download references

Acknowledgements

The author thanks the referee for their valuable time and needful suggestions.

Author information

Authors and Affiliations

  1. Department of Physics, Dibrugarh University, Dibrugarh, Assam, 786004, India

    Chayanika Chetia, Mrinnoy M. Gohain & Kalyan Bhuyan

Authors
  1. Chayanika Chetia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mrinnoy M. Gohain
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Kalyan Bhuyan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chayanika Chetia.

Ethics declarations

Conflict of interest

The authors hereby certify that there are no actual or potential conflict of interest of any of the authors in relation to this article

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

Chetia, C., Gohain, M.M. & Bhuyan, K. Particle creation and bulk viscosity in Bianchi-I universe in Saez–Ballester theory with different deceleration parameters. Gen Relativ Gravit 55, 107 (2023). https://doi.org/10.1007/s10714-023-03155-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-023-03155-y

Keywords

Search

Navigation