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

TL;DR

This paper investigates how local Solar System acceleration affects the Sandage-Loeb test of cosmic expansion, providing calculations and all-sky maps to correct for local motion biases in redshift measurements.

Contribution

It quantifies the impact of Solar System acceleration on redshift measurements for the Sandage-Loeb test and offers correction maps based on recent mass estimates of the LMC.

Findings

Solar System acceleration causes a 7 cm/s redshift change over 10 years.

Acceleration towards the Galactic Center dominates the local motion effect.

All-sky maps of redshift change and uncertainty are provided for correction purposes.

Abstract

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.