Correlation function of the luminosity distances

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.

18 pages, 8 figures

References in corpus (6)

• How accurate is Limber's equation?
• Relativistic Effect in Galaxy Clustering
• Backreaction on the luminosity-redshift relation from gauge invariant light-cone averaging
• On the perturbation of the luminosity distance by peculiar motions
• The effects of velocities and lensing on moments of the Hubble diagram
• Measuring weak lensing correlations of Type Ia Supernovae

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