Testing Local Lorentz Invariance with Laser Tracking of the LAGEOS and LAGEOS II Satellites

Abstract

Violations of Lorentz Invariance, a cornerstone of modern physics, are predicted by theories of quantum gravity and by extensions of General Relativity involving new vector or tensor fields. In the weak-field limit, such a violation would primarily manifest as a non-zero value for the post-Newtonian parameter $α_1$, which is identically zero in General Relativity. We present a new test of Local Lorentz Invariance by searching for this signature in the orbits of the LAGEOS and LAGEOS II satellites. By applying a Phase Sensitive Detection technique to the mean argument of latitude, derived from about 30 years of Satellite Laser Ranging data, we isolate the periodic signal potentially induced by a preferred reference frame aligned with the Cosmic Microwave Background. {Our analysis yields a new constraint $|α_1| \sim 2 \times 10^{-5}$. This result improves upon the previous best limit from Lunar Laser Ranging and provides the most stringent constraint to date on preferred-frame effects in Earth's gravity.}

Figures (4)

• Figure 1: LAGEOS 7-day residuals in the rate of the longitude ${\ell}_0={\omega}+{M}$ versus time (black-GEODYN II, red-SATAN).
• Figure 2: FFT of the residuals in the rate of the longitude ${\ell}_0={\omega}+{M}$ of LAGEOS over the timespan of the analysis. For ease of consultation, the plot is reversed, carrying in abscissa the periods, i.e. 1/frequency. A peak at annual periodicity is clearly visible.
• Figure 3: Time behavior of $A_1(t)$ after the PSD for the in-phase analysis: blue-GEODYN II and red-SATAN. In this specific case we used a 3rd-order low-pass filter, corresponding to an attenuation of about 60 dB per decade of the amplitude of the signal above the cutoff frequency. The low-pass filter removes the higher frequencies and leaves the long-term trend we are looking for. A value of 3000 days was assumed for the integration time of the low-pass filter.
• Figure 4: Behavior of $\alpha_1$ (solid line: blue-GEODYN II and red-SATAN) as the phase of the demodulation sinusoid varies. The frequency of the sinusoid is fixed at the annual value. The blue and red dashed lines represent the corresponding values for the standard deviation. The two circles, blue and red, correspond to the values of $\alpha_1$ obtained for GEODYN II and SATAN respectively, see Eq. (\ref{['risultato']}). The green continuous line shows the overall estimated systematic error to $\alpha_1$ due to both gravitational and non-gravitational perturbations, about $8\times10^{-6}$. The filter parameters are the same as those used in Figure \ref{['fig:residui3']}.