Gravitational waves in the extended theory of gravity

TL;DR

This paper explores gravitational wave polarizations in extended $f(R)$ gravity theories, introducing new models with multiple polarization states and scalar degrees of freedom to test deviations from General Relativity.

Contribution

It develops new $f(R)$ gravity models capable of describing multiple polarization states of gravitational waves, expanding the theoretical framework for testing gravity.

Findings

Up to six polarization states in extended $f(R)$ models

Existence of scalar degrees of freedom in $f(R)$ gravity

New $f(R)$ models with enhanced parametric flexibility

Abstract

Extended Theories of Gravity are considered as a new approach for solving the infrared and ultraviolet scale problems of the Standard Theory of Gravity (General Relativity). Observational evidence of gravitational waves and subsequent identification of the number of existing polarizations are an effective tool for testing general relativity and extended theories of gravity. The Newman-Penrose method is used to characterize the polarization modes for specific forms of $ f(R) $ in the present study. Both the forms of the $ f(R) $ theory belong to a far more general variational class of gravitational waves, capable of presenting up to six separate polarizations states. We have introduced new $ f(R) $ gravity models as an attempt to have a theory with more parametric regulations so that the model can be used to describe existing issues and discover different directions in gravity physics. The primary goal of this research is to look into the properties of gravitational waves with new cases. The model shows the existence of scalar degrees of freedom in $ f(R) $ gravity metric notation.