Mathematical Models and Methods on Higher Dimensional Bulk Viscous String Cosmology with the Framework of Lyra Geometry
Keywords:Lyra geometry, bulk viscosity, evolution, early Universe, string
We investigate a cosmological scenario generated by a cloud of strings containing particles in the framework of the Lyra geometry by considering five-dimensional Bianchi type-III line element. We assume two physically plausible conditions (i) shear scalar (σ) proportional to the expansion factor (θ), which leads to P = Qn; n ≠ 0 is a constant, P and Q being scale factors and (ii) ξ = ξ0 = constant, ξ being the coefficient of bulk viscosity, deterministic models of our Universe are obtained. We have solved the modified Einstein’s field equations of a homogeneous Bianchi type-III metric. The bihaviors of cosmographic parameters for the different values of time (t) and redshift (z) are presented in detail to study the proposed model. It has been found that the displacement vector (β) behaves itself like the cosmological term, and the solution is consistent with the recent observations of SNeIa. The physical and geometrical properties of the model are premeditated, and it has been discussed in detail regarding the possibilities and prospects that can be happen throughout the evolution of the Universe. It is found that the bulk viscosity plays a crucial role in the evolution of the Universe, and the strings dominate in the early Universe and eventually disappear from the Universe during a sufficiently large time. So, our model can be treated as a realistic one.
P.S. Letelier. Clouds of strings in general relativity. Phys. Rev. 20, 1249 (1979).
P.S. Letelier. String cosmologies. Phys. Rev. D. 28, 2414 (1983).
J. Stachel. Thickening the string. I. The string perfect dust. Phys. Rev. D 21, 2171 (1980).
T.W.B. Kibble. Topology of cosmic domains and strings. J. Phys. A.: Math. Gen. 9, 1387 (1976).
T.W.B. Kibble. Some implications of a cosmological phase transition. Phys. Rept. 67, 183 (1980).
Y.B. Zel'dovich et al. Cosmological consequences of the spontaneous breakdown of discrete symmetry. Zh. Eksp. Teor. Fiz. 61, 3 (1974) [ISSN: 1090-6509].
Y.B. Zel'dovich et al. Cosmological fluctuations produced near a singularity. Mon. Not. R. Astron.Soc. 192, 663 (1980).
A.E. Everett. Cosmic strings in unified gauge theories. Phys. Rev. D 24, 858 (1981).
A. Vilenkin. Cosmic strings. Phys. Rev. D 24, 2082 (1981).
A. Vilenkin. Gravitational field of vacuum domain walls and strings. Phys. Rev. D 23, 852 (1981).
M. Goliath, G.F.R. Ellis. Homogeneous cosmologies with a cosmological constant. Phys. Rev. D 60, 023502 (1999).
G. Hinshaw et al. First year Wilkinson microwave anisotropy probe (WMAP1) observations; the angular power spectrum. Astrophys. J. Suppl. Ser. 148, 135 (2003).
G. Hinshaw et al. Three year Wilkinson microwave anisotropy probe (wmap1) observations; temperature analysis. Astrophys. J. Suppl. Ser. 170, 288 (2007).
M. Ryan, L. Shepley. Homogeneous Relativistic Cosmologies (Princeton Univ. Press, 1975) [ISBN: 9780691645209].
M.A.H. MacCallum. Anisotropic and Inhomogeneous Relativistic Cosmologies in: General Relativity-An Einstein Centenary Survey. Edit by S.W. Hawking, W. Tsrael (Cambridge Univ. Press, 1993).
H. Amirhashchi, H. Zainuddin, H.N.S. Dezfouli. Geometrical behaviors of LRS bianchi type-i cosmological model. E. J. Theor. Phys. 6, 79 (2009).
O. Akarsu, C.B. Kilinc. LRS bianchi type-i models with anisotropic dark energy and constant deceleration parameter. Gen. Rel. Grav. 42, 119 (2010).
O. Akarsu, C.B. Kilinc. Bianchi type-iii models with anisotropic Dark energy. Gen. Rel. Grav. 42, 763(2010).
A. Pradhan, H. Amirhashchi, B. Saha. Bianchi type-i anisotropic Dark energy model with constant deceleration parameter. Int. J. Theor. Phys. 50, 2923 (2011).
S.K. Sahu, T. Kumar. Tilted bianchi type-i cosmological model in lyra geometry. Int. J. Theor. Phys. 52, 793 (2013).
P.K. Sahoo, B. Mishra. Higher-dimensional bianchi typeiii universe with strange quark matter attached to string cloud in general relativity. Turk. J. Phys. 39, 43 (2015).
T. Harko et al. Bianchi type-i cosmological models in eddington-inspired Born-infeld gravity. Galaxies 2, 496 (2014).
P. Sahoo. LRS bianchi type-i string cosmological model in f (R, T) gravity. Fortschr. Phys. 64, 414 (2016).
G.P. Singh et al. Bianchi type-i bulk viscous cosmology with chaplygin gas in Lyra geometry. Chin. J. Phys. 54, 895 (2016).
S.K. Sahu et al. Cosmic transit and anisotropic models in f (R, T) gravity. Chin. J. Phys. 55, 862 (2017).
S. Kotambkar et al. Anisotropic bianchi type i cosmological models with chaplygin gas and dynamical gravitational and cosmological constants. Commun. Theor. Phys. 67,222 (2017).
S. Choudhury. Bianchi type i universe in brane world scenario with non-zero weyl tensor of the bulk. Eur. Phys. J. C 77, 619 (2017).
V.F. Panov et al. Bianchi type ii cosmological model of the universe's evolution. IJGMMP 15, 1850016 (2018).
F. Naderiet al. Noncritical anisotropic bianchi type-i string cosmology with ' α corrections. Phys. Rev. D 15, 026009 (2018).
N. Kaiser, A. Stebbins. Microwave anisotropy due to cosmic strings. Nature 310, 391 (1984).
A. Vilenkin, S.W. Hawking, W. Israel. Three Hundred Years of Gravitation (Cambridge University Press, 1989) [ISBN: 9780521379762].
A. Banerjeeet al. String cosmology in bianchi i space-time. Pramana J. Phys. 34, 1 (1990).
G.P. Singh, T. Singh. String cosmological models with magnetic field. Gen. Rel. Grav. 31, 371 (1999).
A. Pradhan, P. Mathur. Magnetized string cosmological model in cylindrically symmetric inhomogeneous universerevisited. Astrophys. Space Sci. 318, 255 (2008).
P.K. Sahoo, B. Mishra. String cloud and domain walls with quark matter in kink cosmological model. J. Theor. Appl. Phys. 7, 62 (2013).
R. Bali, S. Singh. LRS bianchi type-ii massive string cosmological model for stiff fluid distribution with decaying vacuum energy (Λ). Int. J. Theor. Phys. 53, 2082 (2014).
S.K. Tripathy, L.K. Mahanta. Cosmic acceleration and anisotropic models with magnetic field. Eur. Phys. J. Plus. 130, 30, (2015).
B. K. Bishi, K.L. Mahanta. Bianchi type-v bulk viscous cosmicstring in f (r, t) gravity with time varying deceleration parameter. Adv. High Energy Phys. 130, Article ID 491403 (2015).
G.K. Goswami et al. Anisotropic string cosmological models in heckmann-suchuking space-time. Astrophys. Space Sci. 361, 47 (2016).
P.K. Sahoo et al. Bianchi type string cosmological models in f (R, T) gravity. Eur. Phys. J. Plus. 131, 333 (2016).
K.D. Krori et al. Some exact solutions in string cosmology. Gen. Rel. Grav. 22, 123 (1990).
X.X. Wang. Exact solutions for string cosmology. Chin. Phys. Lett. 20, 615 (2003).
W. Xing-Xiang. Locally rotationally symmetric bianchi type-i string cosmological model with bulk viscosity. Chin. Phys. Lett. 21, 1205 (2004).
T. Vinutha et al. Dark energy cosmological model with cosmic string. Astrophys. Space Sci. 363, 1188 (2018).
K.S. Adhav et al. N-dimensional string cosmological model in brans-dicke theory of gravitation. Astrophys. Space Sci. 310, 231 (2007).
H. Baysal et al. Some string cosmological models in cylindrically symmetric inhomogeneous universe. Turk. J. Phys. 25, 283 (2001).
C.B. Kilinc, I. Yavuz. Inhomogeneous cylindrically-symmetric models in string cosmology. Astrophys. Space Sci. 238, 239 (1996).
A. Pradhan. Magnetized string cosmological model in cylindrically symmetric inhomogeneous universe with variable cosmological term Λ. Fizika B (Zagreb) 16, 205 (2007).
D.R.K. Reddy. A string cosmological model in Brans-Dicke theory of gravitation. Astrophys. Space Sci. 286, 365 (2003).
D.R.K. Reddy. Plane symmetric cosmic strings in lyra manifold. Astrophys. Space Sci. 300, 381 (2005).
D.R.K. Reddy, M.V.S. Rao. Axially symmetric string cosmological model in Brans-Dicke theory of gravitation. Astrophys. Space Sci. 305, 183 (2005).
D.R.K. Reddy, R.L. Naidu. Five dimensional string cosmological models in a scalar-tensor theory of gravitation. Astrophys. Space Sci. 307, 395 (2007).
A. Pradhan. Some magnetized bulk viscous string cosmological models in cylindrically symmetric inhomogeneous universe with variable λ-term. Commun. Theor. Phys. 51, 367 (2009).
A. Pradhan et al. Higher dimensional strange quark matter coupled to string cloud with electromagnetic field admitting one parameter group of conformal motion. Chin. Phys., Lett. 24, 3013 (2007).
V.U.M. Rao et al. Exact Bianchy type II, VIII and IX string cosmological models in saez-ballester theory of gravitation. Astrophys. Space Sci. 314, 73 (2008).
V.U.M. Rao et al. Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on lyra manifold. Astrophys. Space Sci. 314, 213 (2008).
V.U.M. Rao et al. Axially symmetric string cosmological models in Brans-Dicke theory of gravitation. Astrophys. Space Sci. 323, 401 (2009).
V.U.M. Rao, T. Vinutha. Plane symmetric string cosmological models in self-creation theory of gravitation. Astrophys. Space Sci. 325, 59 (2010).
A. Pradhan et al. Magnetized bulk viscous string cosmological model in cylindrically symmetric inhomogeneous universe with time dependent cosmological-term Λ. Braz. J. Phys. 38, 167. (2008a).
A. Pradhan, P. Mathur. Magnetized string cosmological model in cylindrically symmetric inhomogeneous universe revisited. Astrophys. Space Sci. 318, 255 (2008).
A. Pradhan et al. Cylindrically symmetric inhomogeneous string cosmological models of perfect fluid distribution with electromagnetic field. Elect. J. Theor. Phys. 7, 197 (2010).
S.K. Tripathi et al. Bulk viscous barotropic magnetized string cosmological models. Astrophys. Space Sci. 323, 281 (2009).
G.S. Khadekar, S.D. Tade. String cosmological models in five dimensional bimetric theory of gravitation. Astrophys. Space Sci. 310, 51 (2007).
V.K. Yadav et al. Bianchi type-III anisotropic universes with a cloud of strings in Lyra's geometry. Fizika B 19, 29 (2010).
M.C. Bento, O. Bertolami. String theory and cosmology. General Relativity and Gravitation 28, 565 (1996).
G.S. Khadekar, P. Vrishali. String dust cosmological model in higher-dimensional space time. Intern. J. Modern Phys. D 14, 1621 (2005).
G.S. Khadekar et al. String cosmological model with bulk viscosity in higher dimensional space time. J. Dynamical Systems and Geometric Theories 5, 117 (2007).
M.C. Bento, O. Bertolami. String-generated gravity model with cubic curvatureterm. Phys. Lett.B 228, 348 (1989).
J.A. Belinchon. Massive cosmic strings in bianchi type II. Astrophys. Space Sci. 323, 307 (2009).
H. Amirhashchi, H. Zainuddin. Some LRS Bianchi type ii string-dust cosmological models in general relativity. Elect. J. Theor. Phys. 7, 213 (2010).
A.K. Yadav et al. Bianchi type-V string cosmological models in general relativity. Pramana 76, 681 (2011).
C.P. Singh. String cosmology with magnetized bulk viscous fluid in bianchi I universe. Astrophys. Space Sci. 343, 773 (2013).
B.R. Tripathi et al. Bianchi type-I inhomogeneous string cosmological model with electromagnetic field in general relativity. Prespacetime J. 8, 474 (2017).
A. Pradhan, R. Jaiswal. Magnetized string cosmological models of acceleration. Int. J. Geom. Meth. Mod. Phys. 15, 1850076 (2018).
P.S. Wesson. A new approach to scale-invariant gravity /or: A variable-mass embedding for general relativity. Astron Astrophys. 119, 145 (1983).
O. Gron. Inflationary cosmology according to Wesson's gravitational theory. Astron Astrophys. 193, 1 (1988).
D.K. Sen. A static cosmological model. Z. Physik 149, 311 (1957).
D.K. Sen, K.A. Dunn. A scalartensor theory of gravitation in a modified riemannian manifold. J. Math. Phys. 12, 578 (1971).
K.S. Thorne. Primordial element formation, primrdial magnectic fields and isotropy of the universe. Astrophys. J. 148, 51 (1967).
J. Kristian, R.K. Sachs. Observations in cosmology. Astrophys. J. 143, 379 (1966).
C.B. Collins et al. Exact spatially homogeneous cosmologies. Gen. Rel. Grav. 12, 805 (1980).
M.S. Berman. A special law of variation for Hubble's parameter. Nuov. Cim. B 74, 182 (1983).
R.G. Vishwakarma. A study of angular size redshift relation for models in which Lambda decays as the energy density. Class Quantum Gravity 17, 3833 (2000).
G.S. Sharov, V.O. Vasiliev. How predictions of cosmological models depend on Hubble parameter data sets. Math. Model. Geom. 6, 1 (2018).
P. Biswas et al. Posing constraints on the free parameters of a new model of dark energy EoS: Responses through cosmological behaviours. Astrophys. Space Sci. 365, 117 (2020).
W.D. Halford. Cosmological theory based on Lyra's geometry. Austr. J. Phys. 23, 863 (1970).
S. Perlmutter et al. Measurements* of the cosmological parameters Ω and Λ from the first seven supernovae at z ≥ 0.35. Astrophys J. 483, 565 (1997).
P.M. Garnavich. Constraints on cosmological models from hubble space telescope observations of high-z supernovae. Astrophys J. 493, L53 (1998).
P.M. Garnavich. Supernova limits on the cosmic equation of state. Astrophys. J. 509, 74 (1998).
S. Perlmutter et al. Discovery of a supernova explosion at half the age of the Universe. Nature 391, 51 (1998).
B.P. Schmidt. The High-Z supernova search: Measuring cosmic deceleration and global curvature of the universe using type Ia supernovae. Astrophys. J. 507, 46 (1998).
A.G. Reiss et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998).
S. Perlmutter et al. Measurements of Ω and Λ from 42 high-redshift supernovae. Astrophys. J. 517, 565 (1999).
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