Using peculiar velocity surveys to constrain the growth rate of structure with the wide-angle effect

Amongst the most popular explanations for dark energy are modified theories of gravity. The galaxy overdensity and peculiar velocity fields help us to constrain the growth rate of structure and distinguish different models of gravity. We introduce an improved method for constraining the growth rate of structure with the galaxy overdensity and peculiar velocity fields. This method reduces the modelling systematic error by accounting for the wide-angle effect and the zero-point calibration uncertainty during the modelling process. We also speed up the posterior sampling by around 30 times by first calculating the likelihood at a small number of fiducial points and then interpolating the likelihood values during MCMC sampling. We test the new method on mocks and we find it is able to recover the fiducial growth rate of structure. We applied our new method to the SDSS PV catalogue, which is the largest single peculiar velocity catalogue to date. Our constraint on the growth rate of structure is \(f\sigma_8 = 0.405_{-0.071}^{+0.076}\) (stat) \(\pm 0.009\) (sys) at the effective redshift of 0.073. Our constraint is consistent with a Planck 2018 cosmological model, \(f\sigma_8 = 0.448\), within one standard deviation. Our improved methodology will enable similar analysis on future data, with even larger sample sizes and covering larger angular areas on the sky.