Peculiar velocities in the local Universe and its role in observational cosmology

The study of peculiar velocity in the low redshift Universe plays an important role in observational cosmology in two main ways: i) It introduces correlated errors in the measurement of the redshifts, potentially making up a non-negligible fraction of the systematic error budget in the measurement of the expansion history, ii) Peculiar velocities are the only probe of growth of structure in the very low-redshift Universe. In this talk, I will present some recent results on both of these aspects. First, I will present some results from our investigation into the role of peculiar velocity corrections in the measurement of $H_0$. I will show that assumptions on the line-of-sight peculiar velocity can lead to significant differences in the measured value of $H_0$. Then, I will present results of constraints on cosmological parameters from velocity-velocity comparison. The constraints on $f\sigma_8$ from peculiar velocities are competitive and complementary to probes of structure growth at high redshifts.