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Kantowski–Sachs Cosmological Model with Anisotropic Dark Energy in Lyra Geometry

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Proceedings of the National Academy of Sciences, India Section A: Physical Sciences Aims and scope Submit manuscript

Abstract

This paper deals with the study of Kantowski–Sachs universe in the presence of an anisotropic dark energy within the framework of Lyra geometry. A special form of time-varying deceleration parameter and present non-singular cosmological model were used to obtain exact solutions of Einstein's field equations. The physical and geometric features of the cosmological model were discussed. Under suitable condition, it was observed that the anisotropy parameter of the universe and the skewness parameter of the dark energy approach to zero for large cosmic time. The results were found to be consistent with the recent observations on the present-day universe.

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References

  1. Perlmutter S, Aldering G, Goldhaber G, Knop RA, Nugent P, Castro PG, Deustua S, Fabbro S, Goobar A, Groom DE, Hook IM, Kim AG, Kim MY, Lee JC, Nunes NJ, Pain R, Pennypacker CR, Quimby R, Lidman C, Ellis RS, Irwin M, McMahon RG, Ruiz-Lapuente P, Walton N, Schaefer B, Boyle BJ, Filippenko AV, Matheson T, Fruchter AS, Panagia N, Newberg HJM, Couch WJ (1999) Measurements of \(\Omega \) and \(\Lambda \) from 42 high-redshift supernovae. Astrophys J 517:565–586

    Article  ADS  Google Scholar 

  2. Riess AG, Adam G, Filippenko Alexei V, Peter Challis, Clocchiatti A, Garnavich Diercks AM, Gilliland RL, Hogan CJ, Jha S, Kirshner RP, Leibundgut B, Phillips MM, Reiss D, Schmidt BP, Schommer RA, Smith RC, Spyromilio J, Stubbs C, Suntzeff NB (1998) An accelerating universe and a cosmological constant. Astron J 116:1009–1038

    Article  ADS  Google Scholar 

  3. Purlmuter S (1998) Discovery of supernova explosion at half the age of the universe. Nature 391:51–54

    Article  ADS  Google Scholar 

  4. Ade PAR et al (2009) Plank 2013 results XVI cosmological parameters (2013) arXiv:13033.5076

  5. Cunha V (2009) Kinematic constrains to transition redshift from supernova type Ia union data. Phys Rev D 79:47301–47311

    Article  ADS  Google Scholar 

  6. Copeland EJ et al (2006) Dynamics of dark energy. Int J Mod Phys D 15:1753–1936

    Article  ADS  MathSciNet  Google Scholar 

  7. Overduin JM, Cooperstock FJ (1998) Evolution of scale factor with variable cosmological term. Phys Rev D 58:043506

    Article  ADS  Google Scholar 

  8. Rodrigues DC (2008) Anisotropic cosmological constant and the CMB quadrupole anomaly. Phys Rev D 77:0243534–0243538

    Article  ADS  Google Scholar 

  9. Kovisto T, Mota DF (2008) Accelerating cosmologies with an anisotropic equation of state. Astrophys J 679:1–5

    Article  ADS  Google Scholar 

  10. Gupta RC, Pradhan A (2010) Genesis of dark energy: dark energy as consequence of release and two-stage tracking of cosmological nuclear energy. Int J Theor Phys 49:821–834

    Article  Google Scholar 

  11. Harko T et al (2011) f(R, T) gravity. Phys Rev D 84:024020

    Article  ADS  Google Scholar 

  12. Ahrmed A, Pradhan A (2013) Bianchi type-V cosmology in f(R, T) gravity with \(\Lambda (t)\). Int J Theor Phys 53:289–306

    Article  MathSciNet  Google Scholar 

  13. Bamba K (2012) Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests. Astrophys Space Sci 342:155–228

    Article  ADS  Google Scholar 

  14. Sarkar S (2014) Holographic dark energy model with variable deceleration parameter, cosmic coincidence and the future singularity of the Kantowski–Sachs universe. Astrophys Space Sci 351:361–369

    Article  ADS  Google Scholar 

  15. Weyl N (1918) Reine infinitesimalgeo metrics. Math Z 2:384–411

    Article  ADS  MathSciNet  Google Scholar 

  16. Lyra G (1951) Uber eine modifikation der Riemannschen geometric. Math Z 54:52–64

    Article  MathSciNet  Google Scholar 

  17. Sen DK (1957) A static cosmological model. Z Phys Hadrons Nucl 149:311–323

    MathSciNet  MATH  Google Scholar 

  18. Sen DK, Dunn KA (1972) A scalar–tensor theory o gravitation in a modified Reemannian manifold. J Math Phys 13:578–586

    Article  Google Scholar 

  19. Halford WD (1972) Scalar–tensor theory of gravitation in Lyra manifold. J Maths Phys 13:1699–1703

    Article  ADS  Google Scholar 

  20. Soleng HH (1987) Self-creation cosmological solution. Astrophys Space Sci 139:13–19

    Article  ADS  MathSciNet  Google Scholar 

  21. Adhav KS, Bansod AS, Ajmire HG (2013) Early deceleration & late time accelerating anisotropic cosmological models with dynamical EoS parameter. Astrophys Space Sci 345:405–413

    Article  ADS  Google Scholar 

  22. Kumar S, Singh CP (2011) Anisotropic dark energy models constant deceleration parameter. Gen Relativ Gravit 43:1427–1442

    Article  ADS  MathSciNet  Google Scholar 

  23. Yadav AK, Yadav L (2011) Bianchi type-III anisotropic dark energy with constant deceleration parameter. Int J Theor Phys 50:218–227

    Article  Google Scholar 

  24. Kumar S, Yadav AK (2011) Some Bianchi type-V models of accelerating universe with dark energy. Mod Phys Lett A 26:647–659

    Article  ADS  Google Scholar 

  25. Adhav KS, Bansod AS, Nakwal SLRG (2012) Bianchi type VI\(_{0}\) cosmological model with anisotropic dark energy. Astrophys Space Sci 332:497–502

    Article  ADS  Google Scholar 

  26. Pradhan A, Jaiswal R, Jotania K, Khare AK (2012) dark energy models with anisotropic fluid in Bianchi type-VI\(_{0}\) space–time with time dependent deceleration parameter. Astrophys Space Sci 337:401–413

    Article  ADS  Google Scholar 

  27. Akarsu O, Kilinc CB (2012) Bianchi type-III models with dark energy. Gen Relative Gravit 42:763–775

    Article  ADS  MathSciNet  Google Scholar 

  28. Katore SD, Adhav KS, Shaikh AY, Sancheti MM (2011) Plane symmetric cosmological models with perfect fluid and dark energy. Astrophys Space Sci 333:333–341

    Article  ADS  Google Scholar 

  29. Naidu RL, Satyararayana B, Reddy DRK (2012) LRS Bianchi type II dark energy model in a scalar–tensor of gravitation. Astrophys Space Sci 338:333–336

    Article  ADS  Google Scholar 

  30. Ram Shri, Chandel S, Verma MK (2015) Hypersurface–homogeneous cosmological models with dynamical equation of state parameter in Lyra geometry. Can J Phys 93:1100–1105

    Article  ADS  Google Scholar 

  31. Ram Shri, Chandel S, Verma MK (2016) LRS bianchi type-II universe with anisotropic dark energy with dynamical equation of state. Prespacetime J 7:15

    Google Scholar 

  32. Pawar DD, Solanke YS (2014) Exact Kantowski–Sachs anisotropic dark energy cosmological models in Brans–Dicke theory of gravitation. Int J Theor Phys 53:3052–3065

    Article  MathSciNet  Google Scholar 

  33. Pawar DD, Solanke YS (2014) Magnetized anisotropic dark energy model in Baber second self-creation theory. Adv High Energy Phys. https://doi.org/10.1155/859638

  34. Singh CP, Beesham A (2011) Hypersurface homogeneous space time with anisotropic dark energy. Gravit Cosmol 17:284–290

    Article  ADS  MathSciNet  Google Scholar 

  35. Sarkar S, Mahanta CR (2013) Dark energy, cosmic coincidence and future singularity of the universe. Gen Relativ Gravit 45:53–62

    Article  ADS  MathSciNet  Google Scholar 

  36. Adhav KS (2011) LRS Bianchi type-I universe with anisotropic dark enrgy in Lyra geometry. Int J Astron Astrophys 1:204–209

    Article  Google Scholar 

  37. Katore SD, Shaikh AY, Bhaskar AS (2014) Anisotropic dark energy cosmological model from early deceleration of late time acceleration in Lyra geometry. Bulg J Phys 41:34–59

    Google Scholar 

  38. Ram Shri, Chandel S, Verma MK (2016) Kantowski–Sachs universe with anisotropic dark energy in Lyra geometry. Chin J Phys 54:953–959

    Article  MathSciNet  Google Scholar 

  39. Abdussattar Prajapati SR (2011) Role of deceleration parameter and interacting dark energy in singularity. Astrophys Space Sci 331:657–663

    Article  ADS  Google Scholar 

  40. Vishwakarama RG (2003) Is the present expansion of the universe really accelerating. Mon Not R Astron Soc 345:545–551

    Article  ADS  Google Scholar 

  41. Verma MK, Chandel S, Ram Shri (2015) Anisotropic plane symmetric two-fluid cosmological model with time- varying G and cosmological constant. Chin Phys Lett 32:120401

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Sciences, IIT (BHU), Varanasi, 2210 05, India

    Shri Ram & S. Chandel

  2. Department of Mathematics, BBD NITM, Lucknow, 227105, India

    M. K. Verma

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  1. Shri Ram
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  2. S. Chandel
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  3. M. K. Verma
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Correspondence to Shri Ram.

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Ram, S., Chandel, S. & Verma, M.K. Kantowski–Sachs Cosmological Model with Anisotropic Dark Energy in Lyra Geometry. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. 90, 109–114 (2020). https://doi.org/10.1007/s40010-018-0549-8

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  • DOI: https://doi.org/10.1007/s40010-018-0549-8

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