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

Abstract

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 dynamics of the universe. Type I Shapovalov spaces are the most general form of gravitational-wave Shapovalov spacetimes, whose metric in privileged coordinate systems depends on three variables, including the wave variable. For Einstein vacuum spacetimes, these wave models degenerate into simpler types. The obtained exact models of gravitational waves in the quadratic theory of gravity can be used to test the realism of such theories of gravity.

16 pages

References in corpus (15)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models
• Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests
• Gauss-Bonnet term corrections in scalar field cosmology
• Reconstruction of GR cosmological solutions in modified gravity theories
• Pure radiation in space-time models that admit integration of the eikonal equation by the separation of variables method
• Shapovalov wave-like spacetimes
• Algebra of the symmetry operators of the Klein-Gordon-Fock equation for the case when groups of motions $G_3$ act transitively on null subsurfaces of spacetime
• Algebras of integrals of motion for the Hamilton-Jacobi and Klein-Gordon-Fock equations in spacetime with a four-parameter groups of motions in the presence of an external electromagnetic field
• Canonical Scalar Field Inflation with String and $R^2$-Corrections
• Early universe in view of a modified theory of gravity
• Wave-like spatially homogeneous models of Stackel spacetimes (2.1) type in the scalar-tensor theory of gravity
• Horndeski theories and beyond from higher dimensions
• Wave-like spatially homogeneous models of Stackel spacetimes (3.1) type in the scalar-tensor theory of gravity
• Exact models of pure radiation in R^2 gravity for spatially homogeneous Shapovalov spacetimes type II

Cited by in corpus (1)

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