The effect of our local motion on the Sandage–Loeb test of the cosmic expansion

Redshifts of an astronomical body measured at multiple epochs (e.g., separated by 10 yr) are different due to the cosmic expansion. This so-called Sandage–Loeb test offers a direct measurement of the expansion rate of the Universe. However, acceleration in the motion of the Solar System with respect to the cosmic microwave background also changes redshifts measured at multiple epochs. If not accounted for, it yields a biased cosmological inference. To address this, we calculate the acceleration of the Solar System with respect to the Local Group of galaxies to quantify the change in the measured redshift due to local motion. Our study is motivated by the recent determination of the mass of the Large Magellanic Cloud (LMC), which indicates a significant fraction of the Milky Way mass. We find that the acceleration towards the Galactic Center dominates, which gives a redshift change of 7 cm s−1 in 10 yr, while the accelerations due to the LMC and M 31 cannot be ignored, depending on lines of sight. We create all-sky maps of the expected change in redshift and the corresponding uncertainty, which can be used to correct for this effect.