Revitalizing the 3-Point Correlation Function of Galaxies to Sharpen the BAO Standard Ruler

Abstract

Though dark energy constitutes 72% of the Universe’s present-day energy density, its nature remains unknown. Precise measurements of the Universe’s expansion over cosmic time constrain dark energy’s ratio of pressure to energy density and allow model discrimination. One of the leading techniques for measuring the expansion rate is the Baryon Acoustic Oscillation (BAO) method, which uses the imprint on galaxy clustering today of relativistic waves in the ionized early Universe as a standard ruler. Thus far, the BAO method has used correlations of pairs of galaxies (the 2-point correlation function or 2PCF) to make 1% precision cosmic distance measurements. We present a derivation of the BAO’s late-time signature from first principles and then explore one of the few known possible sources of systematic error in the BAO method: a relative velocity between baryons and dark matter sourced by their different behaviors prior to redshift roughly 1000. We show how this systematic can shift the BAO scale measured from the 2PCF, and that it has a unique signature in correlations of galaxy triplets (the 3-point correlation function or 3PCF). We then present a reformulation of the 3PCF with several transformative advantages: speed comparable to the 2PCF calculation, a tractable covariance matrix, and the ability to exploit all triangles. Using an algorithm this reformulation enables, we report the first high-significance (4.5σ) detection of the BAO in the 3PCF, allowing us to measure the distance to redshift 0.57 with 1.7% precision from the 3PCF alone. This distance scale measurement is highly independent of that from the 2PCF. Using it in conjunction with the 2PCF is equivalent to extending the observing time of the Baryon Oscillation Spectroscopic Survey (BOSS) by roughly 30%. We also make highly precise measurements of the linear biasing of galaxy formation and a moderate-significance (2.5σ) detection of tidal tensor biasing of galaxy formation. Finally, we place a 1% precision constraint on the baryon-dark matter relative velocity bias. This constraint means that the possible shift in the BAO scale measured from the BOSS 2PCF is less than a quarter percent and thus greatly sub-dominant to the statistical errors.