# Scalar modes in extended hybrid metric-Palatini gravity: weak field phenomenology

## TL;DR

This paper explores the weak field phenomenology of extended hybrid metric-Palatini gravity, revealing scalar modes that influence gravitational potential corrections and wave polarizations, with implications for dark matter and gravitational wave observations.

## Contribution

It introduces and analyzes two coupled scalar modes in extended hybrid metric-Palatini gravity, detailing their effects on Newtonian potential and gravitational wave polarizations.

## Key findings

- Yukawa corrections to Newtonian potential from scalar fields
- Scalar modes can mimic dark matter effects
- Scalar gravitational waves exhibit breathing and longitudinal polarizations

## Abstract

We investigate the nature of additional scalar degrees of freedom contained in extended hybrid metric-Palatini gravity, outlining the emergence of two coupled dynamical scalar modes. In particular, we discuss the weak field limit of the theory, both in the static case and from a gravitational waves perspective. In the first case, performing an analysis at the lowest order of the post parameterized Newtonian (PPN) structure of the model, we stress the settling of Yukawa corrections to the Newtonian potential. In this respect, we show that one scalar field can have long range interactions and used in the principle for mimicking dark matter effects. Concerning the gravitational waves propagation, instead, we demonstrate that is possible to have well-defined physical degrees of freedom, provided by suitable constraints on model parameters. Moreover, the study of the geodesic deviation points out the presence of breathing and longitudinal polarizations due to these novel scalar waves, which on peculiar assumptions can give rise to beating phenomena during their propagation.