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A comparative study of cosmological models in alternative theory of gravity with LVDP & BVDP

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Abstract

In this communication we have presented a comparative study of Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological models in alternative theory of gravity with linearly varying deceleration parameter (LVDP) and bilinearly varying deceleration parameter (BVDP) as suggested by Mishra and Chand (Astrophys. Space Sci. 361:259, 2016c). The role of viscosity in cosmology have been studied by several researchers. Under the influence of such study we have also studied bulk viscous fluid cosmological models in alternative \(f(R,T)\) theory of gravity along with comparison of results by taking LVDP and BVDP. The main conclusion of the paper is that BVDP law provides better results in comparative with Berman’s constant deceleration law (CDP) and LVDP law. Also the BVDP law provides an envelope for CDP law and LVDP law.

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References

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

    Article  MATH  Google Scholar 

  • Akarsu, Ö., Dereli, T.: A comparison of the LVDP and \(\varLambda \)CDM cosmological models. Int. J. Theor. Phys. 51, 2995 (2012b)

    Article  MATH  Google Scholar 

  • Akarsu, Ö., et al.: Probing kinematics and fate of the universe with linearly time-varying deceleration parameter. Eur. Phys. J. Plus 129, 22 (2014)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Arbab, A.I.: The universe with bulk viscosity. Chin. J. Astron. Astrophys. 3, 113 (2003)

    Article  ADS  Google Scholar 

  • Arbab, A.I.: Viscous dark energy model with variable \(G\) and \(\varLambda \). Chin. Phys. Lett. 25, 3834 (2008)

    Article  ADS  Google Scholar 

  • Astier, P., et al.: The supernova legacy survey: measurement of \(\varOmega_{\mathsf{M}}\), \(\varOmega_{\mathsf{\varLambda }}\) and \(w\) from the first year data set. Astron. Astrophys. 447, 31 (2006)

    Article  ADS  Google Scholar 

  • Berman, B.S.: Cosmological models with constant deceleration parameter. Gen. Relativ. Gravit. 20, 192 (1988)

    ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Chaubey, R., Shukla, A.K.: A new class of Bianchi cosmological models in \(f(R,T)\) gravity. Astrophys. Space Sci. 343, 415 (2013)

    Article  ADS  MATH  Google Scholar 

  • Chaubey, R., et al.: The general class of Bianchi cosmological models in \(f(R,T)\) gravity with dark energy in viscous cosmology. Indian J. Phys. 90, 233 (2016)

    Article  ADS  Google Scholar 

  • Cunha, J.V.: Kinematic constraints to the transition redshift from SNe Ia union data. Phys. Rev. D 79, 047301 (2009)

    ADS  Google Scholar 

  • Eckart, C.: The thermodynamics of irreversible processes. III. Relativ. Theory Simple Fluid Phys. Rev. 58, 919 (1940)

    MATH  Google Scholar 

  • Fabris, J.C., et al.: Bulk viscosity driving the acceleration of the universe. Gen. Relativ. Gravit. 38, 495 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Grøn, Ø., Hervik, S.: Einstein’s General Theory of Relativity: With Modern Applications in Cosmology. Springer, Berlin (2007)

    Book  MATH  Google Scholar 

  • Guth, A.: Inflationary universe, a possible solution to the horizon and flatness problems. Phys. Rev. D 23, 347 (1981)

    ADS  Google Scholar 

  • Harko, T., et al.: \(f(R,T)\) theory. Phys. Rev. D 84, 024020 (2011)

    ADS  Google Scholar 

  • Johri, V.B., Sudharsan, R.: BD-FRW cosmology with bulk viscosity. Aust. J. Phys. 42, 215 (1989)

    Article  ADS  Google Scholar 

  • Kazanas, D.: Dynamics of the universe and spontaneous symmetry breaking. Astrophys. J. Lett. 241, L59 (1980)

    Article  ADS  Google Scholar 

  • Klimek, Z.: Entropy per particle in the early Bianchi type-I universe. Nuovo Cimento B 35, 249 (1976)

    Article  ADS  Google Scholar 

  • Kowalski, M., et al.: Improved cosmological constraints from new, old and combined supernova data sets. Astrophys. J. 686(2), 749 (2008)

    Article  ADS  Google Scholar 

  • Landau, L., Lifshitz, E.: Fluid Mechanics. Pergamon, New York (1969)

    MATH  Google Scholar 

  • Mahanta, K.L.: Bulk viscous cosmological models in \(f(R,T)\) theory of gravity. Astrophys. Space Sci. 353, 683 (2014)

    Article  ADS  Google Scholar 

  • Mak, M.K., et al.: Viscous fluid cosmological models in a Bianchi type-I universe. Astrophys. Space Sci. 249, 43 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Mishra, R.K., Chandra, R.: Cosmological models with \(G\rho \propto H^{2}\) and \(\varLambda \propto H^{2}\). Math. Educ. 38, 202 (2004)

    Google Scholar 

  • Mishra, R.K., et al.: String cosmological models from early deceleration to current acceleration phase with varying \(G\) and \(\varLambda \). Eur. Phys. J. Plus 127, 137 (2012)

    Article  Google Scholar 

  • Mishra, R.K., et al.: Bianchi type-I viscous fluid cosmological models with variable deceleration parameter. Rom. J. Phys. 58, 75 (2013a)

    MathSciNet  Google Scholar 

  • Mishra, R.K., et al.: Anisotropic viscous fluid cosmological models from deceleration to acceleration in string cosmology. Int. J. Theor. Phys. 52, 2546 (2013b)

    Article  MathSciNet  MATH  Google Scholar 

  • Mishra, R.K., et al.: Dark energy models in \(f(R,T)\) theory with variable deceleration parameter. Int. J. Theor. Phys. 55, 1241 (2016a)

    Article  MathSciNet  MATH  Google Scholar 

  • Mishra, R.K., et al.: FRW cosmological models in Brans-Dicke theory of gravity with variable \(q\) and dynamical \(\varLambda \)-term. Astrophys. Space Sci. 361, 81 (2016b)

    Article  ADS  MathSciNet  Google Scholar 

  • Mishra, R.K., et al.: Cosmological models in alternative theory of gravity with bilinear deceleration parameter. Astrophys. Space Sci. 361(8), 259 (2016c). doi:10.1007/s10509-016-2837-6

    Article  ADS  MathSciNet  Google Scholar 

  • Mostafapoor, N., Grøn, Ø.: Viscous \(\varLambda \)CDM models. Astrophys. Space Sci. 333, 357 (2011)

    Article  ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

  • Peebles, P.J.E., Ratra, B.: The cosmological constant and dark energy. Rev. Mod. Phys. 75, 559 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Perlmutter, S., et al.: Discovery of a supernova explosion at half the age of the universe. Nature 391, 51 (1998)

    Article  ADS  Google Scholar 

  • Perlmutter, S., et al.: Measurements of \(\varOmega \) and \(\varLambda \) from 42 high-redshift supernova. Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  • Riess, A.G., et al.: The farthest known supernova: support for an accelerating universe and a glimpse of the epoch of deceleration. Astrophys. J. 560, 49 (2001)

    Article  ADS  Google Scholar 

  • Sahni, V., et al.: The case for a positive cosmological \(\varLambda \)-term. Int. J. Mod. Phys. D 9, 373 (2000)

    ADS  Google Scholar 

  • Sahni, V., et al.: Statefinder—a new geometrical diagnostic of dark energy. JETP Lett. 77, 201 (2003)

    Article  ADS  Google Scholar 

  • Sahoo, P.K., Sivakumar, M.: LRS Bianchi type-I cosmological model in \(f(R,T)\) theory of gravity with \(\varLambda (T)\). Astrophys. Space Sci. 357, 60 (2015)

    Article  ADS  Google Scholar 

  • Sahoo, P.K., et al.: Anisotropic Bianchi-III cosmological model in \(f(R,T)\) gravity. Eur. Phys. J. Plus 131, 18 (2016)

    Article  ADS  Google Scholar 

  • Sato, K.: First-order phase transition of a vacuum and the expansion of the universe. Mon. Not. R. Astron. Soc. 195, 467 (1981)

    Article  ADS  Google Scholar 

  • Speergel, D.N., et al.: First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters. Astron. Astrophys. Suppl. Ser. 148, 175 (2003)

    Article  ADS  Google Scholar 

  • Visser, M.: Jerk, snap and the cosmological equation of state. Class. Quantum Gravity 21, 2603 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Weinberg, S.: Entropy generation and the survival of protogalaxies in an expanding universe. Astrophys. J. 168, 175 (1971)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Authors are very indebted to the editor and the anonymous referees for their constructive comments and suggestions to improve the research quality of this manuscript.

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Correspondence to R. K. Mishra.

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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). https://doi.org/10.1007/s10509-017-3117-9

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