The DESI DR1 Peculiar Velocity Survey: Growth Rate Measurements from the Galaxy Power Spectrum

TL;DR

This study develops and applies a generalized cross-power spectrum framework to jointly analyze density and velocity fields derived from distinct surveys, here DESI DR1 BGS (density) and DESI-PV (momentum), to measure the growth rate of structure via $f\sigma_8$ and the growth index $\gamma$. It extends one-loop perturbation theory to the cross-power spectrum, includes window-function convolution, and validates the approach with 675 realistic mocks, achieving robust recovery up to $k_{\max}=0.3\,h\,\mathrm{Mpc}^{-1}$. Applying the method to DESI DR1 data yields $f\sigma_8(z_{\rm eff}=0.07)=0.440^{+0.080}_{-0.096}$, with a consensus value $f\sigma_8(z_{\rm eff}=0.07)=0.450^{+0.055}_{-0.055}$ when combined with other DESI PV analyses; the resulting $\gamma=0.580^{+0.110}_{-0.110}$ (and $\Omega_m=0.301^{+0.011}_{-0.011}$, $\sigma_8=0.834^{+0.032}_{-0.032}$) are consistent with $\Lambda$CDM and General Relativity within uncertainties. The work also identifies systematic biases in the FP component of DESI-PV at small scales, motivates a conservative momentum-cut, and discusses limitations such as Galilean non-invariance of the momentum statistics and prospects for future improvements with DESI DR2 and pairwise momentum analyses.

Abstract

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 where 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 $fσ_8$, is 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 have been tested using mocks, confirming their robustness and accuracy in retrieving the fiducial growth rate from simulation. These techniques are then applied to analyze the power spectrum of the DESI Bright Galaxy Survey and Peculiar Velocity Survey, and the fit result of the growth rate is $fσ_8=0.440^{+0.080}_{-0.096}$ at effective redshift $z_{\rm eff}=0.07$. By synthesizing the fitting outcomes from correlation functions, maximum likelihood estimation and power spectrum, yields a consensus value of $fσ_8(z_{\rm eff}=0.07) = 0.450 ^{+0.055}_{-0.055}$, and correspondingly we obtain $γ=0.580^{+0.110}_{-0.110}$, $Ω_\mathrm{m}=0.301^{+0.011}_{-0.011}$ and $σ_8=0.834^{+0.032}_{-0.032}$. The measured $fσ_8$ and $γ$ are consistent with the prediction of the $Λ$ Cold Dark Matter Model and General Relativity.

Figures (17)

• Figure 1: The sky coverage in equatorial coordinates of the galaxies analyzed within this study. The black dots delineate the sky distribution of BGS galaxies, the gray dots represent that of FP galaxies, and the blue dots illustrate the distribution of TF galaxies. The purple band signifies the galactic plane.
• Figure 2: The redshift distribution of the galaxies employed in this paper. The y-axis is presented on logarithmic scales to enhance the clarity of the data. The black bars depict the redshift distribution of the BGS galaxies, the gray bars delineate the redshift distribution of FP galaxies, and the blue bars illustrate the redshift distribution of TF galaxies. Additionally, the yellow bars represent the redshift distribution of the entire DESI-PV sample, which constitutes a combination of FP and TF galaxies.
• Figure 3: The galaxy mean number density, denoted as $\bar{n}({\bf r})$, as a function of redshift $z$, for both the BGS and DESI-PV data and their corresponding mocks. Notably, the data points are derived from their respective random catalogs to ensure a smooth representation. The gray square with error bar represents the mean value and standard deviation of the data points within each redshift bin.
• Figure 4: The window function convolution matrix. The horizontal-axis is presented on logarithmic scales to enhance the clarity of the data. The left panel displays the convolution matrix for the density power spectrum of the BGS data. The middle panel illustrates the convolution matrix for the momentum power spectrum of the DESI-PV data. The right panel exhibits the convolution matrix for the cross power spectrum between the BGS and DESI-PV data.
• Figure 5: The power spectrum and parameter fitting outcomes from the BGS and DESI-PV mocks are displayed. In the left panels, the filled circles represent the averaged measurements of the density monopole, density quadrupole, momentum monopole, and cross dipole power spectrum, respectively, across 675 mocks. The error bars reflect the uncertainty associated with a single realization. The fitted model power spectrum are overlaid as curves. On the right, the marginalized histograms and two-dimensional contours of the MCMC samples for the cosmological parameters are shown, with the MCMC fit results annotated at the top of each histogram (or see Table \ref{['tabs2last2']}). The 2D contours delineate the 1, 1.5, 2, and 2.5$\sigma$ confidence levels, while the shaded regions in the histograms indicate the $1\sigma$ confidence interval. The vertical dashed line marks the fiducial value $f\sigma_8 = 0.466$.