Generalized framework for likelihood-based field-level inference of growth rate from velocity and density fields

TL;DR

This work develops a generalized, likelihood-based field-level framework for inferring the growth rate of structure from velocity and density fields, implemented in the flip software. It unifies covariance modeling across wide-angle and plane-parallel regimes, introduces a new RC25 covariance model that extends to higher $k$ with robust numerical stability, and demonstrates substantial gains in inference efficiency and accuracy via a survey-geometry-aware Fisher forecast. The framework supports fast, non-compressed field-level inference and can accommodate nonlinear extensions, redshift dependencies, and multiple velocity probes, validated against N-body simulations. The approach promises improved constraints on $f\sigma_8$ in current and upcoming surveys by leveraging full field-level information and optimized computational techniques.

Abstract

Measuring the growth rate of large-scale structures (f) as a function of redshift has the potential to break degeneracies between modified gravity and dark energy models, when combined with expansion-rate probes. Direct estimates of peculiar velocities of galaxies have attracted interest as a means of estimating $fσ_8$. In particular, field-level methods can be used to fit the field nuisance parameter along with cosmological parameters simultaneously. This article aims to provide the community with a unified framework for the theoretical modeling of the likelihood-based field-level inference by performing fast field covariance calculations for velocity and density fields. Our purpose is to lay the foundations for a nonlinear extension of the likelihood-based method at the field level. We have developed a generalized framework, implemented in the dedicated software flip to perform a likelihood-based inference of $fσ_8$. We derived a new field covariance model, which includes wide-angle corrections. We also included the models previously described in the literature inside our framework. We compared their performance against ours, and we validated our model by comparing it with the two-point statistics of a recent N-body simulation. The tests we performed have allowed us to validate our software and determine the appropriate wavenumber range to integrate our covariance model and its validity in terms of separation. Our framework allows for a wider wavenumber coverage to be used in our calculations than in previous works. Finally, our generalized framework allows us to efficiently perform a survey geometry-dependent Fisher forecast of the $fσ_8$ parameter. We show that the Fisher forecast method we developed gives an error bar that is 30 % closer to a full likelihood-based estimation than a standard volume Fisher forecast.

Figures (13)

• Figure 1: Schematic representation of the two field elements, $a_1$ and $b_2$, for which we want to compute the theoretical correlation. Those two fields can be the peculiar velocity of a considered galaxy or group of galaxies, or the galaxy density field itself. The definition of the vector, $\mathbf{d}$, and consequently the angle, $\phi$, depends on the chosen wide-angle definition.
• Figure 2: Schematical implementation of the different modules in the flip package. The arrow represents data flows between two modules. The link in gray between vector construction and the covariance calculation represents an alternative way to compute the covariance matrix directly from the data vector object.
• Figure 3: Ratio of $C_{vv}$ as calculated using the C23 model (equivalent to RC25 velocity) and the pairV for a mock set of 3D positions using the same cosmology. The agreement is on average very close, but there are regions with instabilities.
• Figure 4: Comparison of the linear power spectra generated using flip and pairV. Whereas flip makes use of the CLASS Boltzmann code, pairV uses a fitting formula from EH-transfer_1998. The differences at the $P_{\theta\theta}$ level cause similar differences at the covariance level.
• Figure 5: Parallel ($\Pi$, solid blue line) and perpendicular ($\Sigma$, solid orange line) correlation components as a function of physical separation. Since $\Pi(r)$ turns negative at around 150 Mpc, we plot $-\Pi(r)$ with a dashed blue line.