Correlation function of the luminosity distances
  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.
