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.

中文翻译：

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我们的局部运动对宇宙膨胀的 Sandage-Loeb 检验的影响

由于宇宙膨胀，在多个时代（例如，相隔 10 年）测量的天体的红移是不同的。这种所谓的 Sandage-Loeb 测试提供了对宇宙膨胀率的直接测量。然而，太阳系运动相对于宇宙微波背景的加速也会改变在多个时代测量的红移。如果不加以考虑，它会产生有偏见的宇宙学推断。为了解决这个问题，我们计算了太阳系相对于本地星系群的加速度，以量化由于本地运动而导致的测量红移的变化。我们的研究是由最近确定的大麦哲伦星云 (LMC) 的质量推动的，这表明银河系质量的很大一部分。我们发现朝向银河中心的加速度占主导地位，这给出了 10 年 7 cm/s 的红移变化，而 LMC 和 M31 引起的加速度根据视线不能忽略。我们创建了红移预期变化和相应不确定性的全天图，可用于校正这种影响。