Cosmological constraints from the redshift dependence of the volume
  effect using the galaxy 2-point correlation function across the line-of-sight
  We develop a methodology to use the redshift dependence of the galaxy 2-point
correlation function (2pCF) across the line-of-sight, $\xi(r_{\bot})$, as a
probe of cosmological parameters. The positions of galaxies in comoving
Cartesian space varies under different cosmological parameter choices, inducing
a {\it redshift-dependent scaling} in the galaxy distribution. This geometrical
distortion can be observed as a redshift-dependent rescaling in the measured
$\xi(r_{\bot})$. We test this methodology using a sample of 1.75 billion mock
galaxies at redshifts 0, 0.5, 1, 1.5, 2, drawn from the Horizon Run 4 N-body
simulation. The shape of $\xi(r_{\bot})$ can exhibit a significant redshift
evolution when the galaxy sample is analyzed under a cosmology differing from
the true, simulated one. Other contributions, including the gravitational
growth of structure, galaxy bias, and the redshift space distortions, do not
produce large redshift evolution in the shape. We show that one can make use of
this geometrical distortion to constrain the values of cosmological parameters
governing the expansion history of the universe. This method could be
applicable to future large scale structure surveys, especially photometric
surveys such as DES, LSST, to derive tight cosmological constraints. This work
is a continuation of our previous works as a strategy to constrain cosmological
parameters using redshift-invariant physical quantities.
