Small scale effects in the observable power spectrum at large angular scales

TL;DR

This paper demonstrates that small-scale effects can influence large-scale angular power spectrum measurements in spectroscopic surveys, emphasizing the need to account for non-linearities even at low multipoles.

Contribution

It provides a detailed analysis of how small-scale non-linearities impact large-scale angular power spectrum measurements in spectroscopic surveys.

Findings

Small-scale effects influence large angular scales in spectroscopic surveys.

Non-linearities on small scales must be considered at low multipoles.

Using the correlation function in wide redshift bins can mitigate small-scale effects.

Abstract

In this paper we show how effects from small scales can enter the angular-redshift power spectrum $C_\ell(z,z')$. In particular, we show that spectroscopic surveys with high redshift resolution are already affected on large angular scales, i.e. at low multipoles, by features from small scales. When considering the angular power spectrum with spectroscopic redshift resolution, it is therefore important to account for non-linearities relevant on small scales, even at low multipoles. This may also motivate the use of the correlation function in relatively wide redshift bins, which is not affected by non-linearities on large scales, instead of the angular power spectrum. The extent to which small-scale effects become visible on large scales, which is more relevant for bin auto-correlations than for cross-correlations, is quantified in detail.