Cosmological Parameter Constraints from the SDSS Density and Momentum Power Spectra

We extract the galaxy density and momentum power spectra from a subset of early-type galaxies in the Sloan Digital Sky Survey (SDSS) DR7 main galaxy catalog. Using galaxy distance information inferred from the improved fundamental plane described in Yoon and Park, we reconstruct the peculiar velocities of the galaxies and generate number density and density-weighted velocity fields, from which we extract the galaxy density and momentum power spectra. We compare the measured values to the theoretical expectation of the same statistics, assuming an input Λ cold dark matter (CDM) model and using a third-order perturbative expansion. After validating our analysis pipeline with a series of mock data sets, we apply our methodology to the SDSS data and arrive at constraints $f{\sigma }_{8}={0.471}_{-0.080}^{+0.077}$ and ${b}_{1}{\sigma }_{8}={0.920}_{-0.070}^{+0.070}$ at a mean redshift $\bar{z}=0.04$ . Our result is consistent with the Planck cosmological best-fit parameters for the ΛCDM model. The momentum power spectrum is found to be strongly contaminated by small-scale velocity dispersion, which suppresses power by $\sim { \mathcal O }(30 \% )$ on intermediate scales k ∼ 0.05 h Mpc ^−1 .