Peculiar velocity measurement in a clumpy universe

TL;DR

This paper investigates how gravitational lensing and relativistic effects influence peculiar velocity measurements using supernova data, highlighting the importance of these factors at different redshifts and their impact on measurement accuracy.

Contribution

It quantifies the impact of lensing and relativistic corrections on peculiar velocity estimates in a clumpy universe, emphasizing their significance at intermediate redshifts.

Findings

Lensing effects cause overestimation of peculiar velocities at intermediate redshifts.

Relativistic corrections are crucial for accurate velocity measurements across all redshifts.

Current SNe Ia data uncertainties limit precise peculiar velocity measurements at low redshifts.

Abstract

In this work we address the issue of peculiar velocity measurement in a perturbed Friedmann universe using the deviations from measured luminosity distances of standard candles from background FRW universe. We want to show and quantify the statement that in intermediate redshifts ($0.5< z < 2$), deviations from the background FRW model are not uniquely governed by peculiar velocities. Luminosity distances are modified by gravitational lensing. We also want to indicate the importance of relativistic calculations for peculiar velocity measurement at all redshifts. For this task we discuss the relativistic correction on luminosity distance and redshift measurement and show the contribution of each of the corrections as lensing term, peculiar velocity of the source and Sachs-Wolfe effect. Then we use the SNe Ia sample of Union 2, to investigate the relativistic effects we consider. We show that, using the conventional peculiar velocity method, that ignores the lensing effect, will result in an overestimate of the measured peculiar velocities at intermediate redshifts. Here we quantify this effect. We show that at low redshifts the lensing effect is negligible compare to the effect of peculiar velocity. From the observational point of view, we show that the uncertainties on luminosity of the present SNe Ia data prevent us from precise measuring the peculiar velocities even at low redshifts ($z<0.2$).