Qin F., Blake Gilks C, Howlett C., Turner J, Lodha K., Bautista J., Lai Y., Amsellem A. J., Aguilar J, Ahlen S, Bianchi D, Brooks Cash D, BenZvi S., Carr A., Chaussidon E, Claybaugh T, Cuceu A., de la Macorra A, Douglass K., Doel P, Ferraro S, Font-Ribera A, Forero-Romero J. E., Gaztanaga E, Gontcho A Gontcho S, Gutierrez G, Guy J., Herrera-Alcantar H. K., Honscheid K, Huterer D., Ishak M, J. A. R., Kim G, Kirkby D, Kisner T, Kremin A, Lahav O, Lamman C., Landriau M, Le Guillou L., Levi Maulana Nim. E, Manera M, M. A., Miquel R, Moustakas J, Munoz-Gutierrez A, Nadathur S, Palanque-Delabrouille N, Percival W. J., Poppett C, Prada F, Perez-Rafols I, Ross Andrew C., Rossi G, Sanchez E, Schlegel D, Said K., Schubnell M, Seo H, Silber J, Sprayberry D, Tarle G, Weaver B. A., Zarrouk P., Zhou R, Zou H
The large-scale structure of the Universe and its evolution encapsulate a wealth of cosmological information. A powerful means of unlocking this knowledge lies in measuring the auto-power spectrum and/or the cross-power spectrum of the galaxy density and momentum fields, followed by the estimation of cosmological parameters based on these spectrum measurements. In this study, we generalize the cross-power spectrum model to accommodate scenarios in which the density and momentum fields are derived from distinct galaxy surveys. The growth rate of the large-scale structures of the Universe, commonly represented as fσ8, was extracted by jointly fitting the monopole and quadrupole moments of the auto-density power spectrum, the monopole of the auto-momentum power spectrum, and the dipole of the cross-power spectrum. Our estimators, theoretical models, and parameter-fitting framework were tested using mocks, confirming their robustness and accuracy in retrieving the fiducial growth rate from simulation. These techniques were then applied to analyse the power spectrum of the DESI Bright Galaxy Survey and Peculiar Velocity Survey. The fit result of the growth rate is fσ8 = 0.440+0.080−0.096 f σ 8 = 0 . 440 − 0.096 + 0.080 $ f\sigma_8 = 0.440^{+0.080}_{-0.096} $ at effective redshift zeff = 0.07. By synthesizing the fitting outcomes from correlation functions, maximum likelihood estimation, and the power spectrum, a consensus value is yielded of fσ8(zeff = 0.07) = 0.450+0.055−0.055 f σ 8 ( z eff = 0.07 ) = 0 . 450 − 0.055 + 0.055 $ f\sigma_8(z_\mathrm{{eff}} = 0.07) = 0.450 ^{+0.055}_{-0.055} $ , and correspondingly we obtain γ = 0.580+0.110−0.110 γ = 0 . 580 − 0.110 + 0.110 $ \gamma = 0.580^{+0.110}_{-0.110} $ , Ωm = 0.301+0.011−0.011 Ω m = 0 . 301 − 0.011 + 0.011 $ \Omega_{\mathrm{m}} = 0.301^{+0.011}_{-0.011} $ , and σ8 = 0.834+0.032−0.032 σ 8 = 0 . 834 − 0.032 + 0.032 $ \sigma_8 = 0.834^{+0.032}_{-0.032} $ . The measured fσ8 and γ are consistent with the prediction of the Λ cold dark matter model and general relativity.