Large-Scale Structure of the Universe as a Cosmic Standard Ruler
  We propose to use the large-scale structure of the universe as a cosmic
standard ruler, based on the fact that the pattern of galaxy distribution
should be maintained in the course of time on large scales. By examining the
scale-dependence of the pattern in different redshift intervals it is possible
to reconstruct the expansion history of the universe, and thus to measure the
cosmological parameters governing the expansion of the universe. The features
in the galaxy distribution that can be used as standard rulers include the
topology of large-scale structure and the overall shapes of galaxy power
spectrum and correlation function. The genus, being an intrinsic topology
measure, is resistant against the non-linear gravitational evolution, galaxy
biasing, and redshift-space distortion effects, and thus is ideal for
quantifying the primordial topology of the large-scale structure. The expansion
history of the universe can be constrained by comparing among the genus
measured at different redshifts. In the case of initially Gaussian fluctuations
the genus accurately recovers the slope of the primordial power spectrum near
the smoothing scale, and the expansion history can be constrained by comparing
between the predicted and measured genus.
