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H. R. Ghate^{1}, Atish S. Sontakke^{2}

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A Bianchi typeIX cosmological model has been investigated in the presence of perfect fluid with disordered radiation in Barbers (Gen. Relat. Gravit.14, 117, 1982) second selfcreation theory of gravitation. The field equations have been solved by applying special law of variation for generalized Hubble’s parameter given by Bermann (NuovoCimento 74, 182, 1983). Some physical properties of the models are also discussed.
Keywords 
SelfCreation Cosmology, Radiating Model, Bianchi typeIX 
INTRODUCTION 
Einstein’s theory of general relativity (Einstein 1916) is a very successful gravitational theory in describing the gravitational phenomena which also served as a basis for the models of the universe. Einstein pointed out that general relativity does not account satisfactorily for inertial properties of matter i.e. Mach’s principle is not substantiated by general relativity. There have been several attempts to generalize the general theory of gravitation by incorporating Mach’s principle and other desired features which were lacking in the original theory. Barber [1] has proposed two selfcreation theories of gravitation by modifying BransDicke theory and general relativity. Brans [2] has pointed out that Barber’s first theory is in agreement with experiment but is actually inconsistent in general as it violates equivalence principle. However second theory is a modification of general relativity to a variable Gtheory and predicts local effects that are within the observational limits. In this theory, the scalar field does not gravitate directly but simply divides the matter tensor, acting as a reciprocal gravitational constant. Here the scalar field couples to the trace of the energy momentum tensor. 
Pimentel [3] and Soleng [4] have discussed FRW models by using a power law relation between the expansion factor of the universe and the scalar field. Singh [5], Reddy [6] and Reddy et al. [7] have studied Bianchi type spacetimes solutions in Barber’s second theory of gravitation while Reddy and Venkateswarlu [8] presented Bianchi typeVI0 cosmological model in Barber’s second selfcreation theory of gravitation. Shanthi and Rao [9] studied Bianchi type II and III spacetimes in this theory, both in vacuum as well as in presence of stiff fluid. Ram and Singh [10] have discussed the spatially homogeneous and isotropic RobertsonWalker and Bianchi typeII models of the universe in Barber’s selfcreation theory in presence of perfect fluid by using gamma law equation of state. Pradhan and Pandey [11], Pradhan and Vishwakarma [12], Panigrahi and Sahu [13], Venkateshwarlu and Kumar [14], Singh and Kumar [15], Venkateswarluet al. [16], Reddy and Naidu [17] and Katoreet al. [18] are some of the authors who have studied various aspects of cosmological models in Barber’s second selfcreation theory. Katoreet al. [19] have studied accelerating and decelerating hypersurfacehomogeneous cosmological models in Barbers’s second selfcreation theory. Recently, Mahanta [20] have studied dark energy (DE) models with variable EoS parameter in selfcreation theory of gravitation. 
Bianchi typeIX cosmological models are very popular for relativistic studies. These models are also used to examine the role of certain anisotropic sources during the formation of large scale structures as we seen the universe today. Chakraborty [21], Raj Bali and Dave [22], Raj Bali and Yadav [23] have studied Bianchi typeIX string as well as viscous fluid models in general relativity. Pradhan [24] have studied some homogeneous Bianchi typeIX viscous fluid cosmological models with varying . Tyagiet al. [25] have obtained Bianchi typeIX string cosmological models for perfect fluid distribution in general relativity. Ghate and Sontakke [2627] have studied Bianchi typeIX cosmological models in different context. 
In this paper, Bianchi typeIX cosmological model has been investigated in the presence of perfect fluid with disordered radiation. The solution to the Einstein field equations are obtained using the condition that expansion scalar is proportional to the shear scalar given by Berman. The physical and geometrical properties of model are also discussed. 
II. METRIC AND FIELD EQUATIION 
which represents disordered radiation of matter distribution. The field equations (2) and (3), for the metric (1) with the help of equations (4)(6) in Barber’s second selfcreation theory can be explicitly written as 
whereoverdot (˙) denotes partial differentiation with respect to t. 
III. SOLUTIONS OF THE FIELD EQUATIONS 
Equations (9)(12) are four highly nonlinear equations in six unknowns a, b,& p,and T . We can introduce more conditions either by an assumption corresponding to some physical situation or an arbitrary mathematical supposition, however these procedures have some drawbacks. Physical situation may lead to differential equations which will be difficult to integrate and mathematical supposition may lead to a nonphysical situation. Two additional conditions relating these unknowns are required to obtain explicit solutions of the systems. 
(i) Firstly, we assume that the expansion in the model is proportional to the shear . This condition leads to 
(13) 
wherem is proportionality constant. 
The motive behind assuming condition is explained with reference to Thorne [28], the observations of the velocity redshift relation for extragalactic sources suggest that Hubble expansion of the universe is isotropic today within 30 percent (Kantowski and Sachs [29]; Kristian and Sachs [30]). To put more precisely, redshift studies place the limit 
(ii) Secondly, the law of variation of Hubble’s parameter yields a constant value of deceleration parameter. Such type of relations have already been considered by Berman [32] for solving FRW models. We consider the constant deceleration parameter model defined by 
IV. PHYSICAL PROPERTIES OF THE MODEL 
The model (20) represents Bianchi typeIX disordered radiating cosmological model which is physically significant for the study of early stages of evolution of the universe. 
V. RESULTS AND DISCUSSION 
VI. CONCLUSION 
In this paper, we have investigated radiating Bianchi typeIX cosmological model in Barbers second selfcreation theory of gravitation using the law of variation for the Hubbles parameter which yields a constant value of decelerating parameter stated by Berman. At initial epoch the model starts evolving with zero volume and expands for large time 
anisotropic and represents the early stages of the universe which matches the results of recent experiments which shows that there is certain amount of anisotropy in the universe. Hence the anisotropic models are important. It is well known that the scalar fields have considerable effects on cosmological scale. The radiating model obtained here, will help to study early era in selfcreation cosmology. Also, this study of cosmological models and understanding our universe through these models has astrophysical importance and relevance. 
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