Using Multipoles of the Correlation Function to Measure H(z), DA(z), and β(z) from Sloan Digital Sky Survey Luminous Red Galaxies
Abstract
Galaxy clustering data can be used to measure the cosmic expansion history H(z), the angular-diameter distance DA(z), and the linear redshift-space distortion parameter beta(z). Here we present a method for using effective multipoles of the galaxy two-point correlation function (0(s), 2(s), 4(s), and 6(s), with s denoting the comoving separation) to measure H(z), DA(z)$, and beta(z), and validate it using LasDamas mock galaxy catalogs. Our definition of effective multipoles explicitly incorporates the discreteness of measurements, and treats the measured correlation function and its theoretical model on the same footing. We find that for the mock data, 0+2+4 captures nearly all the information, and gives significantly stronger constraints on H(z), DA(z), and beta(z), compared to using only 0+2. We apply our method to the sample of luminous red galaxies (LRGs) from the Sloan Digital Sky Survey (SDSS) Data Release 7 (DR7) without assuming a dark energy model or a flat Universe. We find that 4(s) deviates on scales of s<60Mpc/h from the measurement from mock data (in contrast to 0(s), 2(s), and 6(s)), thus we only use 0+2 for our fiducial constraints. We obtain H(0.35), DA(0.35), Omegamh2, beta(z) = 79.6-8.7+8.3 km/s/Mpc, 1057-87+88Mpc, 0.1030.015, 0.440.15 using 0+2. We find that H(0.35)rs(zd)/c and DA(0.35)/rs(zd) (where rs(zd) is the sound horizon at the drag epoch) are more tightly constrained: H(0.35)rs(zd)/c, DA(0.35)/rs(zd) = 0.0437-0.0043+0.0041, 6.48-0.43+0.44\ using 0+2.
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.