Assessing the Accuracy of Cosmological Parameters Estimated from Velocity – Density Comparisons

Abstract

A promising method for measuring the cosmological parameter combination fσ₈ is to compare observed peculiar velocities with peculiar velocities predicted from a galaxy density field using linear perturbation theory, known as velocity-velocity (velocity-density) comparisons. We use N-body simulations and semi-analytic models of galaxy formation to quantify the accuracy and precision of this method. Specifically, we examine a number of technical aspects, including the optimal smoothing length applied to the density field, the use of dark matter halos or galaxies as tracers of the density field, the effect of noise in the halo mass estimates or in the stellar-to-halo mass relation, and the effect of finite survey volumes. We find that for a Gaussian smoothing of 4 Mpc/h, the method has only small systematic biases at the level of 5%. We estimate that cosmic variance affects current measurements at the 5% level due to the volume of current redshift data sets.

Previous work has tested the accuracy of velocity-density comparisons with N-body simulations, but generally on idealised mock galaxy surveys. However, systematic biases may arise solely due to survey selection effects such as flux-limited samples, edge-effects and complications due to the obscuration of the Galactic plane. In this thesis, we explore the impact of each of these effects independently and simultaneously, using the semi-analytic models from numerical simulations to generate mock catalogues that mimic the 2M++ density field. We find the reconstruction and analysis methods used for our 2M++ mocks produce a value of fσ₈ that is biased high by a factor 1.04±0.01 compared to the true value. Moreover, a cosmic volume matching that of 2M++ has a cosmic variance uncertainty in fσ₈ of ∼5%. The systematic bias is a function of distance: it is unbiased close to the origin but is biased slightly high for distances in the range 100–180 Mpc/h. Correcting for this small bias, we find a linear fσ₈ = 0.362 ± 0.023. The predicted peculiar velocities from 2M++ have an error of 170 km/s that slowly increases with distance, exceeding 200 km/s only at distances of 180-200 Mpc/h. Finally, the residual bulk flow speeds found in previous work are shown to be not in conflict with those expected in the ΛCDM model.

Using these results we investigate the impact reconstructing cosmological redshifts, using peculiar velocities, has on measurements of the Hubble constant (H₀). Recent measurements of H₀ using type Ia supernovae explicitly correct for their estimated peculiar velocities using the 2M++ reconstruction of the local density field. The amount of uncertainty that is generated due to this reconstruction has thus far been unquantified. To rectify this we use our mock Universe realisations of 2M++ catalogues and peculiar velocities, that are generated using the same method as the predictions that are used to correct for the Pantheon+ catalogue. We find that the method is able to reproduce measurements to within ∼0.3 km/s/Mpc and hence is subdominant to the total uncertainty in H₀.