# Biases in velocity reconstruction: investigating the effects on growth rate and expansion measurements in the local universe

**Authors:** Ryan J. Turner, Chris Blake  
**arXiv:** [2306.16664](https://arxiv.org/abs/2306.16664)  
**Date:** 2023-06-29  
**Summary page:** https://www.summarizepaper.com/en/paper/2306.16664v1/

## Key points

- Authors explore the impact of stochasticity of velocity reconstructions on errors in cosmological inferences
- Focus on local galaxy peculiar velocity field and its role in calibrating cosmic growth and expansion measurements
- Stochastic nature introduces uncertainties that affect cosmological inferences
- Introduce a statistical model to relate measured velocities to theoretical velocities
- Calibrate the model using linear theory and derive biases in the model velocity
- Use lognormal realizations to examine how biases affect measurements of growth rate and expansion rate
- Corrections are significant under certain scenarios and lead to improvements in determinations of the Hubble constant
- Importance of considering biases from velocity reconstructions for accurate measurements of cosmic growth rates and expansion rates within our local universe.

## Summary

In their paper titled "Biases in Velocity Reconstruction: Investigating the Effects on Growth Rate and Expansion Measurements in the Local Universe," authors Ryan J. Turner and Chris Blake explore the impact of the stochasticity of velocity reconstructions on statistical and systematic errors in cosmological inferences. They focus specifically on the local galaxy peculiar velocity field, which can be reconstructed from the distribution of large-scale structure surrounding it. The local galaxy peculiar velocity field plays a crucial role in calibrating cosmic growth and expansion measurements. However, its stochastic nature introduces uncertainties that can affect cosmological inferences. To address this issue, Turner and Blake introduce a simple statistical model that relates measured velocities to theoretical velocities. They calibrate the terms of this model using linear theory and derive biases in the model velocity. To assess the potential impact of these biases, they use lognormal realizations to examine how they affect measurements of the growth rate of structure when using a cosmic flow model as well as expansion rate measurements from host galaxies for gravitational wave standard sirens with electromagnetic counterparts. The authors demonstrate that under certain scenarios, these corrections are significant and lead to measurable improvements in determinations of the Hubble constant compared to standard forecasts. This research highlights the importance of considering biases arising from velocity reconstructions when making cosmological inferences based on large-scale structure distributions. By understanding and accounting for these biases, scientists can enhance their accuracy in measuring cosmic growth rates and expansion rates within our local universe.