Isaac Scientific Publishing

Advances in Astrophysics

Higher Dimensional Topological Defect Solutions with Quark Matter in Gravitation Theories

Download PDF (517.4 KB) PP. 83 - 94 Pub. Date: May 1, 2017

DOI: 10.22606/adap.2017.22003

Author(s)

  • Halife Caglar*
    Institute for Natural and Applied Sciences, Çanakkale Onsekiz Mart University, 17020, Çanakkale, Turkey
  • Sezgin Aygün
    Çanakkale Onsekiz Mart University, Arts and Sciences Faculty, Department of Physics, Terzioglu Campus 17020, Turkey

Abstract

In this paper we have researched higher dimensional flat Friedmann-Robertson-Walker (FRW) cosmological model solutions for string cloud and domain walls coupled with quark and strange quark matters in Lyra and Riemann geometries. We have obtained that string tension density is zero in Lyra and Riemann geometries. Also, the displacement field vector behaves like a cosmological constant in our models. In addition to these, some physical and kinematical quantities have been generalized and discussed in Lyra and Riemann geometries. Also our results are consistent with the results of Yılmaz, Back et al. and Adcox et al. in four dimensions.

Keywords

Quark matter, FRW Universe, string cloud, higher dimension, Lyra geometry, domain wall.

References

[1] M. Tegmark, et al.,"Cosmological parameters from SDSS and WMAP," Phys. Rev. D, vol. 69, 103501-103528, 2004.

[2] G. Efstathiou, et al.,"Evidence for a non-zero  and a low matter density from a combined analysis of the 2dF Galaxy Redshift Survey and cosmic microwave background anisotropies," Mon. Not. Roy. Astron. Soc., vol. 330, pp. L29-L35, 2002.

[3] N. Bilic, "Thermodynamics of Dark Energy," arXiv:0812.5050v2.

[4] C. Aktas. , S. Aygün, I. Y?lmaz, "Behaviors of dark energy and mesonic scalar field for anisotropic universe in f(R) gravity," Physics Letters B, vol. 707, 237-242, 2012.

[5] B. M. Barker, "General scalar-tensor theory of gravity with constant G," Astrophysical Journal vol. 219, pp. 5-11, 1978.

[6] J. D. Bekenstein, "Relativistic gravitation theory for the modified Newtonian dynamics paradigm," Phys. Rev. D, vol. 70, no. 8, pp. 083509-083543, 2004.

[7] H. Weyl," Gravitation und Elektrizitat," in Preuss akad. Wissi Berlin, pp. 465-478, 1918.

[8] F. S. N. Lobo and M. A. Oliveira, "Wormhole geometries in f(R) modified theories of gravity" Phys. Rev. D., vol. 80, no. 10, pp. 104012-104020, 2009.

[9] C. Brans and R. H. Dicke, "Mach’s Principle and a Relativistic Theory of Gravitation*," Phys. Rev. vol. 124, no. 3, pp. 925-935 , 1961.

[10] H. Y?lmaz, "New Approach to General Relativity," Phys. Rev., vol. 111, no. 5, pp. 1417-1426, 1958.

[11] G. Lyra, "über eine Modifikation der Riemannschen Geometrie," Mathematische Zeitschrift, vol 54, no. 1, pp. 52-64, 1951.

[12] W. D. Halford, "Cosmological theory based on Lyra’s geometry," Australian Journal of Physics, vol. 23, pp. 863-869, 1970.

[13] A. Beesham, "Vacuum Friedmann cosmology based on Lyra’s manifold," Astrophys. Space Sci., vol. 127, pp. 189-191, 1986.

[14] S. Aygün, C. Aktas. and I. Y?lmaz, "Non-existence of a massive scalar field for the Marder universe in Lyra and Riemannian geometries," Journal of Geometry and Physics, vol. 62, no. 1, pp. 100-106, 2012.

[15] J. K. Singh, "String Cosmological Models in Lyra Geometry," Int. J. Theor. Phys., vol. 48, no. 3, pp. 905-912, 2009.

[16] P. Mahanta and A. Mukherjee, "String models in Lyra geometry," Indian J. Püre appl. Math. 32, 199 (2001).

[17] A. Chodos and S. Detweller, "Where has the fifth dimension gone?," Physical Review D, vol. 21, no. 8, pp. 2167-2170, 1980.

[18] F. Rahaman and S. Mandal, "Gravitational field of higher dimensional domain walls in Lyra geometry," arXiv:gr-qc/0608082.

[19] I. Y?lmaz, " String cloud and domain walls with quark matter in 5-D Kaluza Klein cosmological model," General Relativity and Gravitation, vol. 38, no. 9, pp. 1397-1406, 2006.

[20] G. P. Singh, R. V. Deshpande and T. Singh, "Higher-dimensional cosmological model with variable gravitational constant and bulk viscosity in Lyra geometry," Pramana, vol. 63, no. 5, pp. 937-945. 2004.

[21] G. C. Samanta and S. Debata, Journal of Mod. Phys. 3, 180 (2012).

[22] F. Rahaman, S. Chakraborty, S. Das, M. Hossain and J. Bera, "Higher-dimensional string theory in Lyra geometry," Pramana, vol. 60, no. 3, pp. 453-459, 2003.

[23] F. Rahaman, S. Das, N. Begum, M. Hossain, "Higher dimensional homogeneous cosmology in Lyra geometry," Pramana, vol. 61, no. 1, pp. 153-159 2003.

[24] S. D. Katore, S. V. Thakare and K. S. Adhav, "Bianchi Type-I cosmological mesonic stiff fluid models in Lyra’s geometry,", Pramana, vol. 71, no. 1, pp. 15-22, 2008.

[25] A. K. Yadav, "Lyra’s cosmology of inhomogeneous universe with electromagnetic field," Fizika B, vol. 19, pp. 53-80, 2010.

[26] A. Pradhan and P. Ram, "A Plane-Symmetric Magnetized Inhomogeneous Cosmological Models of Perfect Fluid Distribution with Variable Magnetic Permeability in Lyra Geometry," Int. J. Theor. Phys., vol. 48, pp. 3188-3201, 2009.

[27] A. Pradhan, "Some Magnetized Bulk Viscous String Cosmological Models in Cylindrically Symmetric Inhomogeneous Universe with Variable -Term," Commun. Theor. Phys., vol. 51, pp. 367-374, 2009.

[28] A. Pradhan, "Cylindrically symmetric viscous fluid universe in Lyra geometry," Jour. Math. Phys., vol. 50, pp. 022501-022512, 2009.

[29] A. Pradhan and A. K. Singh, "Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter," Int. J. of Theor. Phys., vol. 50, no. 3 pp. 916-913, 2011.

[30] S. Agarwal, R. K. Pandey and A. Pradhan, "Bianchi type-II string cosmological models in normal gauge for Lyra’s manifold with constant deceleration parameter," Indian J. Phys., vol. 86, no. 1, pp. 61-70, 2012.

[31] A. Pradhan, H. Amirhashchi and H. Zainuddin, "Exact solution of perfect fluid massive string cosmology in Bianchi type III space-time with decaying vacuum energy density ," Astrophy. and Space Sci., vol. 331, no. 2, pp. 679-687, 2011.

[32] I. Yavuz, I. Y?lmaz and H. Baysal, "Strange Quark Matter Attached to the String Cloud in the Spherical Symmetric Space-Time Admitting Conformal Motion," Int. J. Mod. Phys. D, vol. 14, no. 08, pp. 1365-1372, 2005.

[33] K. S. Adhav, A. S. Nimkar, M. V. Dawande, "String Cloud and Domain Walls with Quark Matter in n-Dimensional Kaluza-Klein Cosmological Model," Int. J. Theor. Phys., vol. 47, no. 7, pp. 2002-2010, 2008.

[34] H.C. aˉglar and S. Aygün, "Non-existence of Brans-Dicke theory in higher dimensional FRW universe," Astrophys. and Space Sci., vol. 361, no. 6, pp. 200-2005, 2016.

[35] A. R. Bodmer, "Collapsed Nuclei," Phys. Rev. D, vol. 4, no. 6, pp. 1601-1606, 1971.

[36] E. Witten, "Cosmic separation of phases," Phys. Rev. D , vol. 30, no. 2, pp. 272-285, 1984.

[37] N. Itoh, "Hydrostatic Equilibrium of Hypothetical Quark Stars," Prog. Theor. Phys., vol. 44, no. 1, pp. 291-292, 1970.

[38] A. Pradhan, G. S. Khadekar, M. M. Kumar and S. Kumbhare, "Higher Dimensional Strange Quark Matter Coupled to the String Cloud with Electromagnetic Field Admitting One Parameter Group of Conformal Motion," Chin. Phys. Lett., vol. 24, no. 10, pp. 3013-3016, 2007.

[39] B. B. Back, et al., "The PHOBOS perspective on discoveries at RHIC," Nucl Phys. A, vol 757, no. 1, pp. 28-101, 2005.

[40] K. Adcox, et al., "Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX Collaboration," Nucl Phys. A, vol. 757, no. 1, pp. 184-283, 2005.

[41] G. S. Khadekar, R. Wanjari and C. Ozel, "Domain Wall with Strange Quark Matter in Kaluza-Klein Type Cosmological Model," Int. J. Theor. Phys., vol. 48, no. 9, pp. 2550-2557, 2009.

[42] K. S. Adhav, A. S. Nimkar, V. B. Raut and R. S. Thakare, "Strange quark matter attached to string cloud in Bianchi type-III space time," Astrophys. Space Sci., vol. 319, no. 1, pp. 81-84, 2009.

[43] K. L. Mahanta, S. V. Biswal, P. K. Sahoo and M. C. Adhikary, "String Cloud with Quark Matter in Self-creation Cosmology," Int. J. Theor. Phys., vol. 51, no. 5, pp. 1538-1544, 2012.

[44] S. D. Katore and A. Y. Shaikh, "Cosmological Model with Strange Quark Matter Attached to Cosmic String for Axially Symmetric Space-Time," Int. J. Theor. Phys., vol. 51, no. 6, pp. 1881-1888, 2012.

[45] I. Yilmaz and C. Aktas. , "Space-Time Geometry of Quark and Strange Quark Matter," Chin. J. Astron. Astrophys., vol. 7, no. 6, pp. 757-763, 2007.

[46] D. K. Sen and K. A. Dunn,"A Scalar-Tensor Theory of Gravitation in a Modified Riemannian Manifold," J. Math. Phys., vol. 12, no. 4, pp. 578-586, 1971.

[47] D. R. K. Reddy, "Plane Symmetric Cosmic Strings In Lyra Manifold," Astrophys. Space Sci., vol. 300, no. 4, pp. 381-386, 2005.

[48] F. Rahaman, S. Chakraborty, N. Begum, M. Hossain, and M. Kalam, "Bianchi-IX string cosmological model in Lyra geometry," Pramana J. Phys., vol. 60, no.6, pp. 1153-1159, 2003.

[49] G. P. Singh, S. Kotambkar and A. Pradhan, "Higher Dimensional Cosmological Model in Lyra Geometry," Int. J. Mod. Phys. D., vol. 12, no. 05, pp. 853-860, 2003.

[50] C. P. Singh and A. Beesham, "Particle Creation in Higher Dimensional Space-time with Variable G and," Int. J. Theor. Phys., vol. 51, no. 12, pp. 3951-3962, 2012.

[51] P. S. Letelier, "String cosmologies," Phys. Rev. D, vol. 28, no. 10, pp. 2414-2419, 1983.

[52] K. S. Adhav, "LRS Bianchi type-I cosmological model with linearly varying deceleration parameter," Eur. Phys. J. Plus, vol. 126, pp. 122-126, 2011.

[53] ?. Akarsu, T. Dereli, "Cosmological Models with Linearly Varying Deceleration Parameter," Int. J. Theor. Phys., vol. 51, no. 2, pp. 612-621, 2012.

[54] P. S. Letelier, "Clouds of strings in general relativity," Physical Review D, vol. 20, no. 6, pp. 1294-1302, 1979.

[55] M. Kalb, P. Ramond, "Classical direct interstring action," Phys. Rev. D 9, 2273 (1974). ; M. Kalb, ibid. 17, 2713 (1978).

[56] P. S. Letelier, "Gauge-invariant theory of direct interaction between strings," Phys. Rev. D, vol. 15, no. 4, pp. 1055-1062, 1977.

[57] K. S. Adhav, P. S. Gadodia snd A. S. Bansod, "Bianchi Type-I String Cosmological Model in Creation-Field," Int. J. of Theo. Phys., vol. 50, no. 9, pp. 2720-2736, 2009.

[58] M. Kiran and D. R. K. Reddy, "Non-existence of Bianchi type-III bulk viscous string cosmological model in f( R, T) gravity," Astrophys Space Sci., vol. 346, no. 2, pp. 521-524, 2013.

[59] K. D. Krori, T. Chaudhury and C. R. Mahanta, "Strings in some Bianchi type cosmologies," Gen. Rel. and Grav., vol. 26, no. 3, pp. 265-274, 1994.

[60] D. R. K. Reddy, "Non-existence of cosmic strings in bimetric theory of gravitation," Astrophys. and Space Sci., vol. 286, no. 3, pp. 397-400, 2003.

[61] P. K. Sahoo, B. Mishra, "String cloud and domain walls with quark matter for plane symmetric cosmological model in bimetric theory," Journal of Theoretical and Applied Physics vol. 7, no. 1, pp. 12-16, 2013.

[62] P.K. Sahoo, B. Mishra, "Axially symmetric space-time with strange quark matter attached to string cloud in bimetric theory," Int. J.Pure and Applied Math. 82, 87 (2013).

[63] G. Mohanty, R. R. Sahoo and B. K. Bishi, "Non-existence of five dimensional string cosmological models in Riemannian and Lyra geometries," Astrophys. Space Sci., vol. 319, no. 1, pp. 75-79, 2009.

[64] P. M. Garnavich, et al., "Supernova Limits on the Cosmic Equation of State," Astrophys. J., vol. 509, no. 1, pp. 74-79, 1998.

[65] S. Perlmutter, et al., "Measurements of the Cosmological Parameters and  from the First Seven Supernovae at z > 0.35," Astrophys. J., vol. 483, no. 2, pp. 565-581, 1997. 0.35," Astrophys. J., vol. 483, no. 2, pp. 565-581, 1997.

[66] B. P. Schmidt, "The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Curvature of the Universe Using Type IA Supernovae" Astrophys J., vol. 507, no. 1, pp. 46-63, 1998.