The redshift-space momentum power spectrum – I. Optimal estimation from peculiar velocity surveys

Abstract

Low redshift surveys of galaxy peculiar velocities provide a wealth of cosmological information. We revisit the idea of extracting this information by directly measuring the redshift-space momentum power spectrum from such surveys. We provide a comprehensive theoretical and practical framework for estimating and fitting this from data, analogous to well understood techniques used to measure the galaxy density power spectrum from redshift surveys. We formally derive a new estimator, which includes the effects of shot noise and survey geometry; we evaluate the variance of the estimator in the Gaussian regime; we compute the optimal weights for the estimator; we demonstrate that the measurements are Gaussian distributed, allowing for easy extraction of cosmological parameters; and we explore the effects of peculiar velocity measurement errors. We finish with a proof-of-concept using realistic mock galaxy catalogues, which demonstrates that we can measure and fit both the redshift-space galaxy density and momentum power spectra from peculiar velocity surveys and that including the latter substantially improves our constraints on the growth rate of structure. We also provide theoretical descriptions for modelling the non-linear redshift-space density and momentum power spectrum multipoles, and forecasting the constraints on cosmological parameters using the Fisher information contained in these measurements for arbitrary weights. These may be useful for measurements of the galaxy density power spectrum even in the absence of peculiar velocities.

Peculiar velocity cosmology with type Ia supernovae

“…Different approaches exist to model the velocity-velocity and velocity-density correlations (e.g., Lavaux 2016;Graziani et al 2019;Howlett 2019), and we adopt here a model-independant approach by focusing on Fisher-Matrix estimations. The precision in measuring f D can be projected for different peculiar velocity surveys.…”

WALLABY -- An SKA Pathfinder HI Survey

“…These can also be used to test ΛCDM and General Relativity by constraining to growth factor f σ 8 at low redshifts (Springob et al 2016). Furthermore, the velocity or momentum auto power and their cross-power spectrum with the density field can be used to accurately measure f σ 8 (Koda et al 2014;Howlett 2019;Qin et al 2019b).…”

Constraining the growth rate of structure with phase correlations

“…For the redshift-space power spectrum, we use a variant of the model from Vlah et al (2013), as implemented in Howlett (2019). To summarise, the model accounts for the large-scale coherent motions of galaxies towards overdensities (the Kaiser effect), random non-linear motions of these galaxies within virialised halos, and the non-linear and non-local bias of galaxies with respect to the underlying matter field.…”

“…In deriving the power spectrum model, the above bias expansion is renormalised following Saito et al (2014) and from which we also adopt b s = −4/7(b 1 − 1) and b 3nl = 32/315(b 1 − 1). The terms I i j , J i j , K i j and σ 3 are integrals over the matter power spectrum P m and are presented in the appendices of Vlah et al (2012) and Howlett (2019). s(x) is the Fourier transform of s(k), which is also presented in Vlah et al (2013).…”