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

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Abstract

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.

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References

  • 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)

    MATH  Google Scholar 

  • Akarsu, Ö., Dereli, T.: Cosmological models with linearly varying deceleration parameter. Int. J. Theor. Phys. 51, 612 (2012)

    MATH  Google Scholar 

  • Armendariz-Picon, T., et al.: k-Inflation. Phys. Lett. B 458, 209 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Banerjee, N., Das, S.: Acceleration of the universe with a simple trigonometric potential. Gen. Relativ. Gravit. 37, 1695–1703 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  • Barber, G.A.: On two “self creation” cosmologies. Gen. Relativ. Gravit. 14, 117–136 (1982)

    ADS  MathSciNet  Google Scholar 

  • Bennet, C.L., et al.: First year Wilkinson microwave anisotropy probe (WMAP) observations: preliminary maps and basic results. Astrophys. J. Suppl. 148, 1 (2003)

    ADS  Google Scholar 

  • Brans, C., Dicke, R.H.: Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925–935 (1961)

    ADS  MathSciNet  MATH  Google Scholar 

  • Brevik, I., Gorbunova, O.: Dark energy and viscous cosmology. Gen. Relativ. Gravit. 37, 2039–2045 (2005)

    ADS  MathSciNet  MATH  Google Scholar 

  • Brevik, I., Odintsov, S.D.: Cardy-Verlinde entropy formula in viscous cosmology. Phys. Rev. D 65, 067302 (2002)

    ADS  MathSciNet  Google Scholar 

  • 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)

    ADS  MathSciNet  Google Scholar 

  • Chawla, C., Mishra, R.K.: Bianchi Type-I viscous fluid cosmological models with variable deceleration parameter. Rom. J. Phys. 58, 75 (2013)

    MathSciNet  Google Scholar 

  • 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 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • de Bernardis, P., et al.: A flat universe from high-resolution maps of the cosmic microwave background radiation. Nature 404, 955–959 (2000)

    ADS  Google Scholar 

  • De Sitter, W.: Einstein’s theory of gravitation and astronomical consequences. Mon. Not. R. Astron. Soc. 78, 3–28 (1917)

    ADS  Google Scholar 

  • Einstein, A.: Kosmologische Betrachtugen zur algemeinen Relativitatstheorie. Sitz.ber. Preuss. Akad. Wiss. 1, 142–152 (1917)

    MATH  Google Scholar 

  • Everett, A.E.: Cosmic strings in unified gauge theories. Phys. Rev. D 24, 858–868 (1981)

    ADS  Google Scholar 

  • 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)

    ADS  MathSciNet  MATH  Google Scholar 

  • Feng, B., et al.: Dark energy constraints from the cosmic age and supernova. Phys. Lett. B 607, 35 (2005)

    ADS  Google Scholar 

  • Gamow, G.: My Worldline, vol. 44. Viking Press, New York (1970)

    Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Harko, T., Lobo, F.S.N., Nojiri, S., Odintsov, S.D.: \(f(R,T)\) gravity. Phys. Rev. D 84, 024020 (2011)

    ADS  Google Scholar 

  • Khoury, J., Weltman, A.: Chameleon fields: awaiting surprises for tests of gravity in space. Phys. Rev. Lett. 93, 171104 (2004)

    ADS  Google Scholar 

  • Kibble, T.W.B.: Topology of cosmic domains and strings. J. Phys. A, Math. Gen. 9, 1387 (1976)

    ADS  MATH  Google Scholar 

  • Kibble, T.W.B.: Some implications of a cosmological phase transition. Phys. Rep. 67, 183–199 (1980)

    ADS  MathSciNet  Google Scholar 

  • 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)

    MATH  Google Scholar 

  • Letelier, P.S.: String cosmologies. Phys. Rev. D 28, 2414–2419 (1983)

    ADS  MathSciNet  Google Scholar 

  • Maartens, R.: Dissipative cosmology. Class. Quantum Gravity 12, 1455 (1995)

    ADS  MathSciNet  MATH  Google Scholar 

  • Meng, X.H., Dou, X.: Friedmann cosmology with bulk viscosity: a concrete model for dark energy. Commun. Theor. Phys. 52, 377 (2009)

    ADS  MATH  Google Scholar 

  • 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)

    ADS  MATH  Google Scholar 

  • Mishra, R.K., Chand, A.: Cosmological models in alternative theory of gravity with bilinear deceleration parameter. Astrophys. Space Sci. 361, 259 (2016)

    ADS  MathSciNet  Google Scholar 

  • 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)

    ADS  MathSciNet  Google Scholar 

  • 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)

    MathSciNet  MATH  Google Scholar 

  • 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)

    MathSciNet  MATH  Google Scholar 

  • 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)

    ADS  MathSciNet  Google Scholar 

  • Mishra, B., Tripathy, S.K., Ray, P.P.: Bianchi-V string cosmological models with dark energy anisotropy. Astrophys. Space Sci. 363, 86 (2018b)

    ADS  MathSciNet  Google Scholar 

  • 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)

    Google Scholar 

  • Padmanabhan, T.: Accelerated expansion of the universe driven by tachyonic matter. Phys. Rev. D 66, 021301 (2002)

    ADS  Google Scholar 

  • Perlmutter, S., et al.: Measurements of \(\Omega \) and \(\Lambda \) from 42 high redshift supernovae. Astrophys. J. 517, 565 (1999)

    ADS  MATH  Google Scholar 

  • 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)

    MathSciNet  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Ratra, B., Peebles, P.J.E.: Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37, 3406 (1988)

    ADS  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • 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)

    ADS  MATH  Google Scholar 

  • Riess, A.G., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  • Sahni, V., Saini, T.D., Starobinsky, A., Alam, U.: Statefinder—a new geometrical diagnostic of dark energy. JETP Lett. 77, 201–206 (2003)

    ADS  Google Scholar 

  • 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)

    Google Scholar 

  • 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)

    MathSciNet  MATH  Google Scholar 

  • 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)

    ADS  MATH  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Sen, A.: Tachyon matter. J. High Energy Phys. 0207, 065 (2002)

    ADS  MathSciNet  Google Scholar 

  • 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)

    ADS  Google Scholar 

  • Singh, C.P.: Bulk viscous cosmology in early universe. Pramana J. Phys. 71, 33 (2008a)

    ADS  Google Scholar 

  • Singh, J.P.: A cosmological model with both deceleration and acceleration. Astrophys. Space Sci. 318, 103–107 (2008b)

    ADS  Google Scholar 

  • Singh, P., Sami, M., Dadhich, N.: Cosmological dynamics of phantom field. Phys. Rev. D 68, 023522 (2003)

    ADS  Google Scholar 

  • Thorne, P.S.: Primordial element formation, primordial magnetic fields and the isotropy of the universe. Astrophys. J. 148, 51 (1967)

    ADS  Google Scholar 

  • Tiwari, R.K., Singh, R., Shukla, B.K.: A cosmological model with variable deceleration parameter. Afr. Rev. Phys. 10, 395 (2015)

    Google Scholar 

  • Tonry, J.L., et al.: Cosmological results from high-z supernovae. Astrophys. J. 594, 1–24 (2003)

    ADS  Google Scholar 

  • Vilenkin, A.: Cosmic strings. Phys. Rev. D 24, 2082–2089 (1981)

    ADS  MathSciNet  Google Scholar 

  • Vinutha, T., Rao, V.U.M., Getaneh, B., Mengesha, M.: Dark energy cosmological models with cosmic string. Astrophys. Space Sci. 363, 188 (2018)

    ADS  MathSciNet  Google Scholar 

  • Zel’dovich, Ya.B.: Cosmological fluctuations produced near a singularity. Mon. Not. R. Astron. Soc. 192, 663–667 (1980)

    ADS  Google Scholar 

  • Zel’dovich, Ya.B., et al.: Cosmological consequences of a spontaneous breakdown of a discrete symmetry. Sov. Phys. JETP 40, 1–5 (1975)

    ADS  Google Scholar 

  • 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)

    MathSciNet  MATH  Google Scholar 

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  1. Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Deemed University, Under MHRD, Govt. of India, Longowal, 148 106, Punjab, India

    R. K. Mishra & Heena Dua

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  1. R. K. Mishra
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  2. Heena Dua
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Correspondence to R. K. Mishra.

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Mishra, R.K., Dua, H. Bulk viscous string cosmological models in Saez-Ballester theory of gravity. Astrophys Space Sci 364, 195 (2019). https://doi.org/10.1007/s10509-019-3689-7

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