An Investigation into LRS Bianchi I Universe in Brans-Dicke Theory

In this study, the homogenous and anisotropic locally rotationally symmetric (LRS) Bianchi type-I universe filled with the bulk viscous and the string cloud matter has been investigated in the Brans-Dicke (BD) scalar-tensor theory. The modified Einstein field equations of the constructed model have been solved by using the relation of the scale factors $A=B^m$ and considering the deceleration parameter to be $q=m-1$. It is found that the string does not survive for the model due to the obtained zero string energy density ($\rho_s=0$) and agrees with some studies in recent years. Moreover, it is possible to say that string matter may be turned into phantom energy over time, depending on the obtained negative rest energy density of the matter. When BD scalar field $\Phi$ is assumed constant, the attained solutions are reduced to General Relativity (GR) solutions for the static vacuum. Thus, the constructed model has not allowed the reduction of the BD solutions to GR solutions, including the matter distributions. In addition, some expansion models for choosing a value of constant $m$ have been obtained and provided. All the results have been analyzed in detail.