Time delay and Doppler tests of the Lorentz symmetry of gravity

Modifications to the classic time-delay effect and Doppler shift in general relativity (GR) are studied in the context of the Lorentz-violating standard-model extension (SME). We derive the leading Lorentz-violating corrections to the time-delay and Doppler shift signals, for a light ray passing near a massive body. It is demonstrated that anisotropic coefficients for Lorentz violation control a time-dependent behavior of these signals that is qualitatively different from the conventional case in GR. Estimates of sensitivities to gravity-sector coefficients in the SME are given for current and future experiments, including the recent Cassini solar conjunction experiment.

Figure 1

Diagram illustrating the meaning of the position vectors ${\overrightarrow{r}}_p$, ${\overrightarrow{r}}_e$, $\overrightarrow{R}$, and the impact parameter $\overrightarrow{b}$, for the zeroth-order light trajectory passing a massive body from events $E$ to $P$.

Figure 2

The time-delay signals occurring in Eq. (38) near solar conjunction, plotted with the values for the Cassini experiment around June 21, 2002. The solid curve labeled GR gives the standard logarithmic dependence of GR, controlled by the combination $1+{\overline{s}}^{TT}$. The curves labeled lv1 and lv2 are the Lorentz-violating signals controlled by the combinations of coefficients ${\overline{s}}_1$ and ${\overline{s}}_2$, respectively.

Figure 3

The gravitational fractional frequency shift in Eq. (40) near solar conjunction, plotted with the values for the Cassini experiment around June 21, 2002. The solid curve labeled GR gives the standard $\dot{b}/b$ dependence of GR, controlled by the combination $1+{\overline{s}}^{TT}$. The curves labeled lv1 and lv2 are the Lorentz-violating signals controlled by the combinations of coefficients ${\overline{s}}_1$ and ${\overline{s}}_2$, respectively.

Figure 4

Diagram illustrating the conjunction configuration of a typical time-delay or Doppler experiment in the Solar System. The Sun-centered frame $Z$ axis is shown along with the ecliptic plane (dashed line).