An exact model of a gravitational wave in the Bianchi III universe based on Shapovalov II wave spacetime and the quadratic theory of gravity

Exact models of primordial gravitational waves in the Bianchi type III universe are constructed on the basis of the quadratic theory of gravity with a scalar field and pure radiation in Shapovalov wave spacetimes of type II (subtype 2). Exact solutions of field equations and scalar equation are obtained. The characteristics of pure radiation are determined. An explicit form of the scalar field functions included in the Lagrangian of the considered quadratic theory of gravity is found. Trajectories of propagation of light rays in the considered gravitational-wave models are obtained.