Go to previous page Go up Go to next page

7.1 Gravitational waves

In the presence of dynamical Lorentz violation, where the entire action is diffeomorphism invariant, one generically expects new gravitational wave polarizations.31 The reason is simple. Any dynamical Lorentz violating tensor field must have kinetic terms involving derivatives of the form ab... \~/ mU, where ab... U is the Lorentz violating tensor. Furthermore, U must take a non-zero vacuum expectation value if it violates Lorentz invariance. At linear order in the perturbations hab, uab... (where gab = jab + hab,U ab...= <U ab...> + uab...), the connection terms in the covariant derivative are also first order, for example @ahbg <U bd...>. Upon varying the linearized metric, these terms contribute to the graviton equations of motion. The extra terms in the graviton equations give rise to new solutions. Since the potential that forces U to take a non-zero vacuum expectation value must involve the metric, variations in U are usually coupled to metric variations, implying that the new graviton modes mix with excitations of the Lorentz violating tensor fields. There is a large literature on gravitational wave polarizations in theories of gravity other than general relativity. For a thorough discussion, see [277Jump To The Next Citation Point] and references therein. Many of the models with preferred frame effects are similar to the types of theories that give rise to dynamical Lorentz violation. For example, the vector-tensor theories of Will, Hellings, and Nordtvedt [278237145Jump To The Next Citation Point] have many similarities to the aether theory of Section 4.4. The aether model’s wave spectrum has been calculated in [158136Jump To The Next Citation Point] and limits from the absence of ńĆerenkov emission of these modes by cosmic rays has been studied in [105] (see Section 6.5.7). Other consequences of dynamical Lorentz violation in Riemann-Cartan spacetimes have been examined in [57].

Unfortunately, few constraints currently exist on dynamical Lorentz violation from gravitational wave observations as the spectrum is only part of the story. Currently, the expected rate of production of these modes from astrophysical sources as a function of the coefficients in the Lagrangian is unknown. However, both the energy loss from inspiral systems due to gravitational radiation and gravitational wave observatories such as LIGO and LISA should produce strict bounds on the possibility of dynamical Lorentz violating fields.32 We note that aether type theories seem to be free of certain obvious problems such as a van Dam-Veltman-Zakharov type discontinuity [136]. The theories can therefore be made arbitrarily close to GR by tuning the coefficients to be near zero.


  Go to previous page Go up Go to next page