# The Newton constant and gravitational waves in some vector field adjusting mechanisms

## TL;DR

This paper investigates how certain Lorentz-breaking vector field models affect gravitational wave propagation and the Newton constant, confirming previous claims and proposing new models with similar desirable properties.

## Contribution

The paper explicitly verifies the behavior of the Newton constant and gravitational waves in specific Lorentz-breaking models, and introduces new models with similar features.

## Key findings

- Newton constant approaches correct asymptotic behavior
- Gravitational waves remain well-behaved at large times
- New models with similar adjustment mechanisms are proposed

## Abstract

As is well known, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant in the present era. An important aspect to analyze is the propagation of gravitational waves and the screening or enhancement of the Newton constant $G_N$ in these models. The problem is that the Lorentz symmetry breaking terms may induce an unacceptable value of the Newton constant $G_N$ or introduce longitudinal modes in the gravitational waves. Furthermore there may spoil the standard dispersion relation $\omega=ck$. In [21] the authors have presented a model for which they suggest that the behavior of the gravitational constant is the correct one for asymptotic times. In the present work, an explicit checking is made and we finally agree with these claims. Furthermore, it is suggested that the gravitational waves are also well behaved for large times. In the process, some new models with the same behavior are obtained, thus enlarging the list of possible adjustment mechanisms.