Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter

Abstract

The present study deals with a spatially homogeneous and anisotropic Bianchi type-I (B-I) cosmological models representing massive strings in normal gauge for Lyra's manifold by applying the variation law for generalized Hubble's parameter that yields a constant value of deceleration parameter. The variation law for Hubble's parameter generates two types of solutions for the average scale factor, one is of power-law type and other is of the exponential-law type. Using these two forms, Einstein's modified field equations are solved separately that correspond to expanding singular and non-singular models of the universe respectively. The energy-momentum tensor for such string as formulated by Letelier, P.S.: Phys. Rev. D 28, 2414 is used to construct massive string cosmological models for which we assume that the expansion (θ ) in the model is proportional to the component σ 1 1 of the shear tensor σ j i . This condition leads to A = (BC) m , where A, B and C are the metric coefficients and m is proportionality constant. Our models are in accelerating phase which is consistent to the recent observations. It has been found that the displacement vector β behaves like cosmological term in the normal gauge treatment and the solutions are consistent with recent observations of SNe Ia. It has been found that massive strings dominate in the both decelerating and accelerating universes. The strings dominate in the early universe and eventually disappear from the universe for sufficiently large times. This is in consistent with the current observations. Some physical and geometric behaviour of these models are also discussed.

Higher Dimensional Topological Defect Solutions with Quark Matter in Gravitation Theories

“…According to Halford [12] the displacement vector field plays role of cosmological constant in Lyra geometry [29]. Also, recent cosmological observations of SNe Ia show that the value of the cosmological constant is a positive value ≈ 10 −123 [64], [65], [66], [29]. In this context, our results agree with Halford's study [12] as string cloud results.…”

“…Also ρ q , p q and σ w decrease for domain wall that includes strange quark matter and ρ m , p m and σ w increase for domain wall that includes quark matter in Lyra geometry. According to Halford [12] the displacement vector field plays role of cosmological constant in Lyra geometry [29]. Also, recent cosmological observations of SNe Ia show that the value of the cosmological constant is a positive value ≈ 10 −123 [64], [65], [66], [29].…”

“…Also, who researched cylindrically symmetric viscous fluid universe in Lyra geometry [28]. Using constant deceleration parameter, Bianchi I string cosmological models in Lyra geometry have been studied by Pradhan and Singh [29]. However Agarwal et al [30] have investigated massive strings in Lyra manifold for Bianchi type II universe.…”

The Measurement of and in Bianchi Type-I Anisotropic Dark Energy Cosmological Model with Constant Deceleration Parameter in Bimetric Theory of Gravitation

“…For closed universe, the Hubble parameter , H the matter energy density parameter M  and the dark energy density parameter ,   predicted by Tegmark [12] by Sahni et al [23][24].This parameter ) ( t  have been calculated with some reasoning with reduced to some simple parameterization of the dependences by many authors [25][26][27][28][29][30]. The results from SNe Ia data collaborated with CMBR anisotropy and galaxy clustering statistics (Tegmark et al [12] [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54].…”

New Class of Magnetized Inhomogeneous Bianchi Type-I Cosmological Model with Variable Magnetic Permeability in Lyra Geometry

“…Recently, Pradhan et al [21,22,23,24,25,26,27], Casama et al [6], Rahaman et al [28], Bali and Chandnani [2,3], Kumar and Singh [15], Yadav et al [35], Rao et al [29], Zia and Singh [37] have studied cosmological models based on Lyras geometry in various contexts.…”