Bianchi type-II string cosmological models in normal gauge for Lyra’s manifold with constant deceleration parameter

The present study deals with a spatially homogeneous and anisotropic Bianchi-II 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 form. 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 (Phys Rev D 28:2414, 1983) is used to construct massive string cosmological models for which we assume that the expansion (θ) in the model is proportional to the component σ11 of the shear tensor σij. 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 with the recent observations. It has been found that the displacement vector β behaves like cosmological term \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Uplambda$$\end{document} 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 decelerating universe, whereas strings dominate in the accelerating universe. Some physical and geometric behaviours of these models are also discussed.