The peculiar velocity correlation function of the Cosmicflows-4 catalog

We present an analysis of the parallel peculiar velocity correlation function using data from the Cosmicflows-4 (CF4) survey. CF4 significantly extends the depth of the peculiar velocity measurements, mitigating the impact of observers on the cosmic variance. We examine the distribution of cosmic variance using different velocity correlation estimators. The combination of the large peculiar velocity uncertainties and the anisotropy distribution of the CF4 data across the northern and southern hemispheres results in substantial statistical uncertainties in the velocity correlation function. To address this, we test different weighing schemes in the velocity correlation function and implement a more accurate peculiar velocity estimator that reduces velocity uncertainties, consequently decreasing the statistical uncertainty. Using the CF4 group dataset, we derive a growth rate of $f\sigma_8=0.384^{+0.116}_{-0.194}$ and a local growth rate of $f\sigma_8=0.569^{+0.054}_{-0.06}$ through a Markov Chain Monte Carlo method.