Doppler term in the galaxy two-point correlation function: wide-angle, velocity, Doppler lensing and cosmic acceleration effects

TL;DR

This paper investigates the Doppler term in the galaxy two-point correlation function, emphasizing its significance for future wide-angle surveys and its potential to mimic primordial non-Gaussianity effects, impacting cosmological parameter estimates.

Contribution

The study highlights the importance of including the Doppler term in galaxy correlation analyses for upcoming surveys and quantifies its impact on primordial non-Gaussianity measurements.

Findings

Doppler term is significant at low redshift and large angles.

It can mimic local primordial non-Gaussianity with an effective f_NL of a few.

Future low-redshift surveys can detect the Doppler term with high confidence.

Abstract

We study the parity-odd part (that we shall call Doppler term) of the linear galaxy two-point correlation function that arises from wide-angle, velocity, Doppler lensing and cosmic acceleration effects. As it is important at low redshift and at large angular separations, the Doppler term is usually neglected in the current generation of galaxy surveys. For future wide-angle galaxy surveys such as Euclid, SPHEREx and SKA, however, we show that the Doppler term must be included. The effect of these terms is dominated by the magnification due to relativistic aberration effects and the slope of the galaxy redshift distribution and it generally mimics the effect of the local type primordial non-Gaussianity with the effective nonlinearity parameter $f_{\rm NL}^{\rm eff}$ of a few, we show that this would affect forecasts on measurements of $f_{\rm NL}$ at low-redshift. Our results show that a survey at low redshift with large number density over a wide area of the sky could detect the Doppler term with a signal-to-noise ratio of $\sim 1-20$, depending on survey specifications.