Abstract
The present study explores the Bianchi type I universe in the frame work of f(R) theory of gravity by considering strange quark matter attached to string cloud and domain walls in the presence and absence of magnetism. Field equations are solved by choosing a constant curvature method. It is found that obtained cosmological models are relevant to the early era of evolution of the universe. The strange quark matter may be a source of string cloud and domain walls.
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Perlmutter, S., et al.: Measurement of \(\Omega \) and \(\Lambda \) from 42 high-redshift supernovae. Astrophys J. 517, 565 (1999)
Riess, A.G.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998)
Spergel, D.N., et al.: First year Wilkinson microwave anisotropy probe observational: determination of cosmological parameters. Astrophys. J. Suppl. 148, 175 (2003)
Tegmark, M., et al.: Cosmological parameters from SDSS and WMAP. Phys. Rev. D. 69, 103501 (2004)
Caldwell, R.R., Dave, R.: Cosmological imprint of an energy component with general equation of state. Phys. Rev. Lett. 82, 1582–1585 (1988)
Peebles, P.J.E., Ratra, B.: Cosmological consequences of a rolling homogeneous scalar field. Phys. Rev. D 37, 3406 (1998)
Carroll, S.M., DeFelice, A., Duvvuri, V., Easson, V.D.A., Trodden, M., Turner, M.S.: Cosmology of generalized modified gravity models. Phys. Rev. D. 71, 063513 (2005)
Shojai, A., Shojai, F.: Some static sherically symmetric interior solutions of \(f(R)\) gravity. Gen. Relat. Grav. 44, 211–223 (2012)
Fairbain, M., Rydbeck, S.: Expansion History and \(f(R)\) modified gravity. J. Cosm. Astropart. Phys. 5(12), 1–15 (2007)
Appleby, S.A., Battye, R.A.: Aspects of cosmological expansion in \(f(R)\) gravity models. J. Assoc. Chest Phys. 05, 019 (2008)
Girones, Z., Marchetti, A., Mena, O., Pena-Garay, C., Rius, N.: Cosmological data analysis of \(f(R)\) gravity models. arXiv:0912.5474v1 (2009)
Sharif, M., Shamir, M.F.: Non-vacuum Bianchi type I and V in \(f(R)\) gravity. Gen. Relat. Gravit. 42, 2643–2655 (2010)
Sancheti, M.M., Katore, S.D., Hatkar, S.P.: Anisotropic homogeneous hypersurface with bulk viscosity in \(f(R)\) gravity. Int. J. Math. Sci. Eng. Appl. 7, 391–402 (2013)
Vilenkin, A.: Cosmic string and domain walls. Phys. Rep. 121, 263–315 (1985)
Rajaraman, R.: Solutions & Instantons. North Holland Publishing, Amsterdam (1987)
Nielsen, H.B., Olesen, P.: Vortex-line models for dual strings. Nucl. Phys. B 61, 45 (1973)
Bachs, C., Tomaras, N.: Higgs-sector solitons. Phys. Rev. D 51, 5356 (1995)
Hooft, Gt: A two-dimensional model for mesons. Nucl. Phys. B 75, 276 (1974)
Itoh, N.: Hydrostatic equilibrium of hypothetical quark stars. Prog. Theor. Phys. 44, 291 (1970)
Bodmer, A.R.: Collapsed nuclei. Phys. Rev. D. 4, 1601 (1971)
Witten, E.: Cosmic separation of phases. Phys. Rev. D. 30, 272 (1984)
Kapusta, J.: Finite Temperature Field Theory. Cambridge University Press, Cambridge (1994)
Sotani, H., Kohri, K., Harada, T.: Restricting quark matter models by gravitational wave observation. Phys. Rev. D. 69, 084008 (2004)
Yilmaz, I.: String cloud and domain walls with quark matter in 5-D Kaluza–Klein cosmological model. Gen. Relat. Grav. 38, 1397–1406 (2006)
Katore, S.D., Shaikh, A.Y.: Einstein–Rosen string cosmological model in Barber’s second self creasion theory. Int. J. Mod. Phys. A 26, 1651–1657 (2011)
Katore, S.D., Adhav, K.S., Shaikh, A.Y., Sarkate, N.K.: Higher dimensional LRS Bianchi type-I domain walls in a scalar-tensor theory of gravitation. Int. J. Theor. Phys. 49(10), 2358–2363 (2010)
Manhanta, K.L., Biswal, A.K.: String cloud and Domain walls with quark matter in Lyra geometry. J. Mod. Phys. 3, 1479–1486 (2012)
Yilmaz, I., Baysal, H., Aktas, C.: Quark and strange quark matter in \(f(R)\) gravity for Bianchi type I and V space times. Gen. Relat. Gravit. 44, 2313–2328 (2012)
Letelier, P.S.: String cosmologies. Phys. Rev. D. 28, 2414 (1983)
Saha, B., Visinescu, M.: Bianchi type I magnetic string cosmological model. Phys. AUC 18, 46–52 (2008)
Thorne, K.S.: Primordial element formation, primordial magnetic fields, and the isotropy of the universe. Astrophys. J. 148, 51–68 (1967)
Kantowski, R., Sachs, R.K.: Some spatially homogeneous anisotropic relativistic cosmological models. J. Math. Phys. 7, 433–446 (1966)
Kristian, J., Sachs, R.K.: Observations in cosmology. Astrophys. J. 143, 379 (379)
Pradhan, A., Kumar, S.S., Jotania, K.: Anisotropic Bianchi type I massive string cosmological models in general relativity. Palestine J. Math. 1(2), 118–132 (2012)
Larranaga, A.: A rotating charged black hole solution in \(f(R)\) gravity. Pramana J. Phys. 78, 697–703 (2012)
Zel’dovich, YaB: Cosmological fluctuations produced near a singularity. Mon. Not. R. Astron. Soc. 1 192, 663 (1980)
Bali, R.: Bianchi type V magnetized string dust universe with variable magnetic permeability. Electron. J. Theor. Phys. 5(9), 105–114 (2008)
Singh, C.P.: The role of magnetic field in anisotropic string cosmological model. Int. J. Theor. Phys. 53, 1533–1546 (2014)
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Mrs. R.J.Baxi is grateful to the Department of Science and Technology (DST) New Delhi, India, for providing INSPIRE fellowship (No.IF140404). We are very much thankful to referee for his valuable suggestions and guidelines for the up gradation of the manuscript.
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Katore, S.D., Hatkar, S.P. & Baxi, R.J. Unified Description of Bianchi Type-I Universe in \(f\,(R)\) Gravity. Found Phys 46, 409–427 (2016). https://doi.org/10.1007/s10701-015-9970-x
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DOI: https://doi.org/10.1007/s10701-015-9970-x