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The shapes of galaxy N-point correlation functions can be used as standardrulers to constrain the distance-redshift relationship and thence the expansionrate of the Universe. The cosmological density fields traced by late-timegalaxy formation are initially nearly Gaussian, and hence all the cosmologicalinformation can be extracted from their 2-Point Correlation Function (2PCF) orits Fourier-space analog the power spectrum. Subsequent nonlinear evolutionunder gravity, as well as halo and then galaxy formation, generate higher-ordercorrelation functions. Since the mapping of the initial to the final densityfield is, on large scales, invertible, it is often claimed that the informationcontent of the initial field's power spectrum is equal to that of all thehigher-order functions of the final, nonlinear field. This claim implies thatreconstruction of the initial density field from the nonlinear field rendersanalysis of higher-order correlation functions of the latter superfluous. Wehere show that this claim is false when the N-point functions are used asstandard rulers. Constraints available from joint analysis of the galaxy powerspectrum and bispectrum (Fourier-space analog of the 3-Point CorrelationFunction) can, in some cases, exceed those offered by the initial powerspectrum even when the reconstruction is perfect. We provide a mathematicaljustification for this claim and also demonstrate it using a large suite ofN-body simulations. In particular, we show that for the z = 0 real-space matterfield in the limit of vanishing shot noise, taking modes up to k_max = 0.2h/Mpc, using the bispectrum alone offers a factor of two reduction in thevariance on the cosmic distance scale relative to that available from the powerspectrum.

Information Content of Higher-Order Galaxy Correlation Functions