Determining the motion of the Solar system relative to the cosmic microwave background using Type Ia supernovae

We estimate the Solar system motion relative to the cosmic microwave background using Type Ia supernovae (SNe) measurements. We take into account the correlations in the error bars of the SNe measurements arising from correlated peculiar velocities. Without accounting for correlations in the peculiar velocities, the SNe data we use appear to detect the peculiar velocity of the Solar system at about the 3.5 sigma level. However, when the correlations are correctly accounted for, the SNe data only detect the Solar system peculiar velocity at about the 2.5 sigma level. We forecast that the Solar system peculiar velocity will be detected at the 9 sigma level by GAIA and the 11 sigma level by the Large Synoptic Survey Telescope. For these surveys, we find the correlations are much less important as most of the signal comes from higher redshifts where the number density of SNe is insufficient for the correlations to be important.