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 years) 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 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 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 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
in 10 years, while the accelerations due to LMC and M31 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.
