Effect of gravitational redshift on space-based gravitational wave detection with clock comparison

Abstract With the rapid development of atomic clocks, the potential for gravitational-wave detection through clock comparisons emerges as a viable prospect for the future. Given the profound significance of gravitational redshift and time dilation in such comparisons, assessing its impact on gravitational wave detection with clock comparisons becomes imperative. We contemplate a two-satellite system tailored for gravitational wave detection via clock comparisons, and simulate the gravitational redshift and time dilation induced by major celestial bodies within the Solar System. Leveraging this satellite system, we conduct numerical simulations to dissect the influence of gravitational redshift and time dilation on detection sensitivity. Our analysis shows that the Sun dominates the gravitational redshift budget. In the band above 10 − 4 Hz, the resulting fractional frequency shift (and time dilation) spectral density is two to three orders of magnitude below 10 − 20 / Hz , which is the target sensitivity of clock-comparison searches for gravitational waves in the millihertz band. Therefore, gravitational redshift and time dilation does not pose a notable obstacle to clock-comparison-based gravitational wave detection in frequencies above 10 − 4 Hz. This conclusion is also directly applicable to the frequency shifts of laser links in laser interferometric gravitational wave detection like TianQin, Taiji, and LISA.