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

Abstract

At the present, there exist some Lorentz breaking scenarios which explain the smallness of the cosmological constant at the present era [1]-[2]. 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 wave propagation. Furthermore this breaking may spoil the standard dispersion relation ω=ck. In [3] the authors have presented a model suggesting that the behavior of the gravitational constant is correct 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.