Astrophysics and Space Science

, 364:195 | Cite as

Bulk viscous string cosmological models in Saez-Ballester theory of gravity

  • R. K. MishraEmail author
  • Heena Dua
Original Article


In this communication, a new class of bulk viscous string cosmological models has been constructed in Saez-Ballester theory of gravitation. To obtain the deterministic solution of the field equations, we have considered deceleration parameter as a bilinear function of cosmic time \(t\) for model I and special parametrization of Hubble parameter for model II. The presented class of the cosmological models indicate phase conversion from early decelerated expansion phase to present accelerated expansion phase. To discuss the dynamicity of the universe, the behaviour of various physical parameters has also been studied and presented graphically. For stability analysis, the nature of various energy conditions is investigated. Statefinder pair analysis is used to discriminate the constructed models with other dark energy models and it is noticed that the proposed models are in good agreement with recent observational data.


Saez-Ballester theory Deceleration parameter Cosmological models Dark energy 


Conflict of interest

There is no conflict of interest among authors of this communication and will abide by ethical standards of this manuscript.


  1. Adhav, K.S., Ugale, M.R., Kale, C.B., Bhende, M.P.: Bianchi type VI string cosmological model in Saez-Ballester’s scalar tensor theory of gravitation. Int. J. Theor. Phys. 46, 3122–3127 (2007) zbMATHCrossRefGoogle Scholar
  2. Akarsu, Ö., Dereli, T.: Cosmological models with linearly varying deceleration parameter. Int. J. Theor. Phys. 51, 612 (2012) zbMATHCrossRefGoogle Scholar
  3. Armendariz-Picon, T., et al.: k-Inflation. Phys. Lett. B 458, 209 (1999) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  4. Avelino, A., Nucamendi, U.: Can a matter-dominated model with constant bulk viscosity drive the accelerated expansion of the universe. J. Cosmol. Astropart. 4, 006 (2009) ADSCrossRefGoogle Scholar
  5. Banerjee, N., Das, S.: Acceleration of the universe with a simple trigonometric potential. Gen. Relativ. Gravit. 37, 1695–1703 (2005) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  6. Barber, G.A.: On two “self creation” cosmologies. Gen. Relativ. Gravit. 14, 117–136 (1982) ADSMathSciNetCrossRefGoogle Scholar
  7. Bennet, C.L., et al.: First year Wilkinson microwave anisotropy probe (WMAP) observations: preliminary maps and basic results. Astrophys. J. Suppl. 148, 1 (2003) ADSCrossRefGoogle Scholar
  8. Brans, C., Dicke, R.H.: Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925–935 (1961) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  9. Brevik, I., Gorbunova, O.: Dark energy and viscous cosmology. Gen. Relativ. Gravit. 37, 2039–2045 (2005) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  10. Brevik, I., Odintsov, S.D.: Cardy-Verlinde entropy formula in viscous cosmology. Phys. Rev. D 65, 067302 (2002) ADSMathSciNetCrossRefGoogle Scholar
  11. Chand, A., Mishra, R.K., Pradhan, A.: FRW cosmological models in Brans-Dicke theory of gravity with variable \(q\) and dynamical \(\Lambda \)-term. Astrophys. Space Sci. 361, 81 (2016) ADSMathSciNetCrossRefGoogle Scholar
  12. Chawla, C., Mishra, R.K.: Bianchi Type-I viscous fluid cosmological models with variable deceleration parameter. Rom. J. Phys. 58, 75 (2013) MathSciNetGoogle Scholar
  13. Chawla, C., Mishra, R.K., Pradhan, A.: A new class of accelerating cosmological models with variable \(G\) and \(\Lambda \) in sáez and ballester theory of gravitation. Rom. J. Phys. 59, 12–25 (2014) Google Scholar
  14. Clocchiatti, A., et al.: Hubble space telescope and ground based observations of Type 1a supernovae at redshift 0.5: cosmological implications. Astrophys. J. 642, 1 (2006) ADSCrossRefGoogle Scholar
  15. Cunha, C.E., et al.: Estimating the redshift distribution of photometric galaxy samples II. Applications and tests of a new method. Mon. Not. R. Astron. Soc. 396, 2379–2398 (2009) ADSCrossRefGoogle Scholar
  16. de Bernardis, P., et al.: A flat universe from high-resolution maps of the cosmic microwave background radiation. Nature 404, 955–959 (2000) ADSCrossRefGoogle Scholar
  17. De Sitter, W.: Einstein’s theory of gravitation and astronomical consequences. Mon. Not. R. Astron. Soc. 78, 3–28 (1917) ADSCrossRefGoogle Scholar
  18. Einstein, A.: Kosmologische Betrachtugen zur algemeinen Relativitatstheorie. Sitz.ber. Preuss. Akad. Wiss. 1, 142–152 (1917) zbMATHGoogle Scholar
  19. Everett, A.E.: Cosmic strings in unified gauge theories. Phys. Rev. D 24, 858–868 (1981) ADSCrossRefGoogle Scholar
  20. Fabris, J.C., Gonalves, S.V.B., de Sá Ribeiro, R.: Bulk viscosity driving the acceleration of the universe. Gen. Relativ. Gravit. 38, 495 (2006) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  21. Feng, B., et al.: Dark energy constraints from the cosmic age and supernova. Phys. Lett. B 607, 35 (2005) ADSCrossRefGoogle Scholar
  22. Gamow, G.: My Worldline, vol. 44. Viking Press, New York (1970) Google Scholar
  23. Hanany, S., et al.: Maxima-1: a measurement of the cosmic microwave background anisotropy on angular scales of 10 arcminutes to 5 degrees. Astrophys. J. Lett. 545, L5 (2000) ADSCrossRefGoogle Scholar
  24. Harko, T., Lobo, F.S.N., Nojiri, S., Odintsov, S.D.: \(f(R,T)\) gravity. Phys. Rev. D 84, 024020 (2011) ADSCrossRefGoogle Scholar
  25. Khoury, J., Weltman, A.: Chameleon fields: awaiting surprises for tests of gravity in space. Phys. Rev. Lett. 93, 171104 (2004) ADSCrossRefGoogle Scholar
  26. Kibble, T.W.B.: Topology of cosmic domains and strings. J. Phys. A, Math. Gen. 9, 1387 (1976) ADSzbMATHCrossRefGoogle Scholar
  27. Kibble, T.W.B.: Some implications of a cosmological phase transition. Phys. Rep. 67, 183–199 (1980) ADSMathSciNetCrossRefGoogle Scholar
  28. Lemaître, G.: Un univers homogène de masse consttante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques. Ann. Soc. Sci. Brux. A 47, 49 (1927) zbMATHGoogle Scholar
  29. Letelier, P.S.: String cosmologies. Phys. Rev. D 28, 2414–2419 (1983) ADSMathSciNetCrossRefGoogle Scholar
  30. Maartens, R.: Dissipative cosmology. Class. Quantum Gravity 12, 1455 (1995) ADSMathSciNetzbMATHCrossRefGoogle Scholar
  31. Meng, X.H., Dou, X.: Friedmann cosmology with bulk viscosity: a concrete model for dark energy. Commun. Theor. Phys. 52, 377 (2009) ADSzbMATHCrossRefGoogle Scholar
  32. Meng, X.H., Ren, J., Hu, M.G.: Friedmann cosmology with a generalised equation of state and bulk viscosity. Commun. Theor. Phys. 47, 379 (2007) ADSzbMATHCrossRefGoogle Scholar
  33. Mishra, R.K., Chand, A.: Cosmological models in alternative theory of gravity with bilinear deceleration parameter. Astrophys. Space Sci. 361, 259 (2016) ADSMathSciNetCrossRefGoogle Scholar
  34. Mishra, R.K., Chand, A.: A comparative study of cosmological models in alternative theory of gravity with LVDP & BVDP. Astrophys. Space Sci. 362, 140 (2017) ADSMathSciNetCrossRefGoogle Scholar
  35. Mishra, R.K., Pradhan, A., Chawla, C.: Anisotropic viscous fluid cosmological models from deceleration to acceleration in string cosmology. Int. J. Theor. Phys. 52, 2546–2559 (2013) MathSciNetzbMATHCrossRefGoogle Scholar
  36. Mishra, R.K., Chand, A., Pradhan, A.: Dark energy models in \(f(R,T)\) theory with variable deceleration parameter. Int. J. Theor. Phys. 55, 1241–1256 (2016) MathSciNetzbMATHCrossRefGoogle Scholar
  37. Mishra, R.K., Dua, H., Chand, A.: Bianchi-III cosmological model with BVDP in modified \(f(R,T)\) theory. Astrophys. Space Sci. 363, 112 (2018a) ADSMathSciNetCrossRefGoogle Scholar
  38. Mishra, B., Tripathy, S.K., Ray, P.P.: Bianchi-V string cosmological models with dark energy anisotropy. Astrophys. Space Sci. 363, 86 (2018b) ADSMathSciNetCrossRefGoogle Scholar
  39. Nagpal, R., Pacif, S.K.J., Singh, J.K., Bamba, K., Beesham, A.: Analysis with observational constraints in \(\Lambda \) cosmology in \(f(R,T)\) gravity. Eur. Phys. J. C 78, 496 (2018) CrossRefGoogle Scholar
  40. Padmanabhan, T.: Accelerated expansion of the universe driven by tachyonic matter. Phys. Rev. D 66, 021301 (2002) ADSCrossRefGoogle Scholar
  41. Perlmutter, S., et al.: Measurements of \(\Omega \) and \(\Lambda \) from 42 high redshift supernovae. Astrophys. J. 517, 565 (1999) ADSzbMATHCrossRefGoogle Scholar
  42. Ramesh, G., Umadevi, S.: LRS bianchi type-II minimally interacting holographic dark energy model in Saez-Ballester theory of gravitation. Astrophys. Space Sci. 361, 50 (2016) MathSciNetCrossRefGoogle Scholar
  43. Rao, V.U.M., Prasanthi, U.Y.D., Aditya, Y.: Plane symmetric modified holographic Ricci dark energy model in Saez-Ballester theory of gravitation. Results Phys. 10, 469–475 (2018) ADSCrossRefGoogle Scholar
  44. Ratra, B., Peebles, P.J.E.: Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37, 3406 (1988) ADSCrossRefGoogle Scholar
  45. Reddy, D.R.K., Naidu, R.L., Sobhan Babu, K., Naidu, K.D.: Bianchi type-V bulk viscous string cosmological model in Saez-Ballester scalar tensor theory of gravitation. Astrophys. Space Sci. 349, 473–477 (2013) ADSCrossRefGoogle Scholar
  46. Ren, J., Meng, X.H.: Cosmological model with viscosity media (dark fluid) described by an effective equation of state. Phys. Lett. B 633, 1 (2006) ADSzbMATHCrossRefGoogle Scholar
  47. Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998) ADSCrossRefGoogle Scholar
  48. Saez, D., Ballester, V.J.: A simple coupling with cosmological implications. Phys. Lett. A 113, 467–470 (1986) ADSCrossRefGoogle Scholar
  49. Sahni, V., Saini, T.D., Starobinsky, A., Alam, U.: Statefinder—a new geometrical diagnostic of dark energy. JETP Lett. 77, 201–206 (2003) ADSCrossRefGoogle Scholar
  50. Sahoo, P.K., Mishra, B., Sahoo, P., Pacif, S.K.J.: Bianchi type string cosmological models in \(f(R,T)\) gravity. Eur. Phys. J. Plus 131, 333 (2016) CrossRefGoogle Scholar
  51. Sahoo, P.K., Sahoo, P., Bishi, B.K.: Anisotropic cosmological models in \(f(R,T)\) gravity with variable deceleration parameter. Int. J. Geom. Methods Mod. Phys. 14, 1750097 (2017) MathSciNetzbMATHCrossRefGoogle Scholar
  52. Sahoo, P.K., Tripathy, S.K., Sahoo, P.: A periodic varying deceleration parameter in \(f(R,T)\) gravity. Mod. Phys. Lett. A 33, 1850193 (2018) ADSzbMATHCrossRefGoogle Scholar
  53. Santhi, M.V., Rao, V.U.M., Aditya, Y.: Bulk viscous string cosmological models in \(f(R)\) gravity. Can. J. Phys. 96, 55–61 (2018) ADSCrossRefGoogle Scholar
  54. Sen, A.: Tachyon matter. J. High Energy Phys. 0207, 065 (2002) ADSMathSciNetCrossRefGoogle Scholar
  55. Sharma, U.K., Zia, R., Pradhan, A.: Transit cosmological models with perfect fluid and heat flow in Saez-Ballester theory of gravitation. J. Astrophys. Astron. 40, 2 (2018) ADSCrossRefGoogle Scholar
  56. Singh, C.P.: Bulk viscous cosmology in early universe. Pramana J. Phys. 71, 33 (2008a) ADSCrossRefGoogle Scholar
  57. Singh, J.P.: A cosmological model with both deceleration and acceleration. Astrophys. Space Sci. 318, 103–107 (2008b) ADSCrossRefGoogle Scholar
  58. Singh, P., Sami, M., Dadhich, N.: Cosmological dynamics of phantom field. Phys. Rev. D 68, 023522 (2003) ADSCrossRefGoogle Scholar
  59. Thorne, P.S.: Primordial element formation, primordial magnetic fields and the isotropy of the universe. Astrophys. J. 148, 51 (1967) ADSCrossRefGoogle Scholar
  60. Tiwari, R.K., Singh, R., Shukla, B.K.: A cosmological model with variable deceleration parameter. Afr. Rev. Phys. 10, 395 (2015) Google Scholar
  61. Tonry, J.L., et al.: Cosmological results from high-z supernovae. Astrophys. J. 594, 1–24 (2003) ADSCrossRefGoogle Scholar
  62. Vilenkin, A.: Cosmic strings. Phys. Rev. D 24, 2082–2089 (1981) ADSMathSciNetCrossRefGoogle Scholar
  63. Vinutha, T., Rao, V.U.M., Getaneh, B., Mengesha, M.: Dark energy cosmological models with cosmic string. Astrophys. Space Sci. 363, 188 (2018) ADSMathSciNetCrossRefGoogle Scholar
  64. Zel’dovich, Ya.B.: Cosmological fluctuations produced near a singularity. Mon. Not. R. Astron. Soc. 192, 663–667 (1980) ADSCrossRefGoogle Scholar
  65. Zel’dovich, Ya.B., et al.: Cosmological consequences of a spontaneous breakdown of a discrete symmetry. Sov. Phys. JETP 40, 1–5 (1975) ADSGoogle Scholar
  66. Zia, R., Maurya, D.C., Pradhan, A.: Transit dark energy string cosmological models with perfect fluid in \(f(R,T)\) gravity. Int. J. Geom. Methods Mod. Phys. 15, 1850168 (2018) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Deemed University, Under MHRDGovt. of IndiaLongowalIndia

Personalised recommendations