Bianchi type-II space-times with constant deceleration parameter in self creation cosmology

Abstract

The properties of locally rotationally symmetric Bianchi type-II perfect fluid space-times are analyzed in Barber's second self-creation theory by using a special law of variation for Hubble's parameter that yields a constant value of deceleration parameter. By assuming the equation of state p = γρ, many new solutions are obtained for different era-Zel'dovich, radiation, vacuum and vacuum energy dominated. The solutions with power-law and exponential expansion are discussed. A detailed study of geometrical and physical parameters is carried out. The nature of singularity is also clarified in each case.

LRS Bianchi type -V cosmology with heat flow in scalar: tensor theory

“…Rahaman et al [41] and Reddy et al [13] have studied LRS Bianchi type -I models with negative deceleration parameter. In a series of recent papers, Singh and Kumar [42][43][44] and Kumar and Singh [45,46] have extended the work to anisotropic Bianchi type -I and II cosmological models and obtained the solutions of field equations in general relativity and some scalar tensor theories.…”

Bianchi type-I models in self-creation cosmology with constant deceleration parameter

“…The assumed variation of Hubble parameter is consistent with observation. Recently Singh and Kumar (2007) used a similar type of law of variation for Hubble parameter in Bianchi type-II space time in self-creation cosmology that yields a constant value of deceleration parameter. To find out determinate solutions of the field equations (10)-(14), we assume the variation of the Hubble parameter given by Berman (1982):…”

“…Recently, Singh and Kumar (2007) have studied LRS Bianchi type-II models with perfect fluid in Barber's second self-creation theory of gravitation by using a special law of variation for Hubble parameter. Bianchi type-I space times being anisotropic generalization of FRW models with flat space sections are the simplest homogeneous models of the universe.…”

Bianchi type-II cosmological model: some remarks

“…In search of a realistic picture of the early Universe such models have been widely studied within a framework of General Relativity. In this note we confine our study to the scope of a Bianchi type-II (BII) space-time, which has recently been studied by a number of authors: Christodoulakis et al [1] investigated the set of space˛time general coordinate transformations which leave the line element of a generic Bianchi-type geometry quasiform invariant; Einstein's field equations for stationary BII models with a perfect fluid source were investigated by Nilsson and Uggla [2]; Ram and Singh [3] presented analytical solutions of the Einstein-Maxwell equations for cosmological models of LRS Bianchi type-II, VIII and IX; two-fluid BII cosmological models were studied by Pant and Oli [4]; a BII cosmological model with constant deceleration parameter was considered by Singh and Kumar [5]; Belinchon [6,7] studied a massive cosmic string within the scope of a BII model, while LRS BII cosmological models in the presence of a massive cosmic string and varying cosmological constant were studied by Pradhan et al [8], Kumar [9] and Yadav et al [10], respectively. Other recent work includes exact solutions for BII cosmological model in the Jordan Brans-Dicke scalar-tensor theory of gravitation were obtained in [11], study of a BII Lyttleton-Bondi Universe [12], and determination of an anisotropic BII cosmological model in the presence of source-free electromagnetic fields in Lyra's manifold [13].…”