Geodesic deviation and tidal acceleration in the gravitational wave of the Bianchi type IV universe

For models of gravitational waves in the Bianchi type IV universe, an exact solution of geodesic deviation equations is obtained. The spacetime models under consideration refer to the Shapovalov wave spaces of type III and type N according to Petrov's classification. The form of test particle trajectories, the geodesic deviation vector, and tidal acceleration in a gravitational wave are found. The results are presented both in the privileged coordinate system and in the laboratory synchronous coordinate system, where the freely falling observer is at rest. The resulting exact models describe primordial gravitational waves. The presented approach can be applied both to Einstein's classical theory of gravity and to modified theories of gravity

Quadratic theory of gravity with a scalar field and type I Shapovalov wave spacetimes

For the quadratic theory of gravity with a scalar field, exact solutions are found for gravitational-wave models in Shapovalov I-type spacetimes, which do not arise in models of the general theory of relativity. The theory of gravity under consideration can effectively describe the early stages of the universe. Type I Shapovalov spaces are the most general forms of gravitational-wave Shapovalov spacetimes, whose metrics in privileged coordinate systems depend on three variables, including the wave variable. For Einstein vacuum spacetimes, these wave models degenerate into simpler types. The exact models of gravitational waves in the quadratic theory of gravity can be used to test the realism of such theories of gravity