Wave-like exact models with symmetry of spatial homogeneity in the quadratic theory of gravity with a scalar field

TL;DR

This paper derives exact wave-like solutions in a quadratic gravity theory with a scalar field, revealing potential models for primary gravitational waves in the universe.

Contribution

It provides new exact solutions in quadratic gravity with scalar fields exhibiting spatial homogeneity and wave-like properties, expanding understanding of gravitational wave models.

Findings

Exact solutions for wave-like space-time models with scalar fields.

Scalar field forms and functions compatible with these solutions.

Potential description of primary gravitational wave disturbances.

Abstract

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space-time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton-Jacobi formalism by the method of separation of variables with separation of wave variables (Shapovalov spaces of type II). The form of the scalar field and the scalar field functions included in the Lagrangian of the theory is found. The obtained exact solutions can describe the primary gravitational wave disturbances in the Universe (primary gravitational waves).