# Correlation function of the luminosity distances

## TL;DR

This paper analyzes the correlation function of luminosity distances in a flat DM universe, decomposing it into velocity, potential, and lensing effects, highlighting their scale-dependent importance for cosmological insights.

## Contribution

It provides a detailed decomposition of luminosity distance correlations, emphasizing the significance of lensing at high redshift and the subdominance of gravitational potential effects when using gauge-invariant expressions.

## Key findings

- Lensing dominates at high redshift and small angles.
- Velocity effects are dominant at low redshift and larger angles.
- Gravitational potential contribution is always subdominant.

## Abstract

We present the correlation function of the luminosity distances in a flat $\Lambda$CDM universe. Decomposing the luminosity distance fluctuation into the velocity, the gravitational potential, and the lensing contributions, we study their individual contributions to the correlation function. The lensing contribution is important at large redshift ($z\gtrsim 0.5$) but only for small angular separation ($\theta \lesssim 3^\circ$), while the velocity contribution dominates over the other contributions at low redshift or at larger separation. However, the gravitational potential contribution is always subdominant at all scale, if the correct gauge-invariant expression is used. The correlation function of the luminosity distances depends significantly on the matter content, especially for the lensing contribution, thus providing a novel tool of estimating cosmological parameters.