# Multipole moment data for PT challenges

## Overview

I provide multipole moments of the redshift-space power spectrum measured from mock galaxies created on this webpage.

• Simulations are done in periodic comoving cubes with the side length of 3840Mpc/h with 3072^3 particles.
• I assume a flat Lambda-CDM cosmology. Omega_nu is set to be zero.
• I do not tell you the 3 cosmological parameters Om, H0 and sigma8 (or As @ k0 = 0.05[1/Mpc]).
• These 3 parameters are drawn randomly around the Planck cosmology.
• Other parameters are set to Planck 2018 (fb = Ob/Om = 0.1571, ns=0.9649).
• To be precise, I provide the parameter file for CAMB which is used to compute the linear power spectrum, with the parameters relevant to the challenge erased. You can download it from here.
• I assume a flat Lambda-CDM cosmology with Om=0.3 to simulate the Alcock-Paczynski effect: the simulation cube is artificially distorted according to the ratio of the angular diameter distance (x and y direction) or the Hubble parameter (z direction) for the true and the assumed (Om=0.3) cosmology.
• The mock galaxies are created based on Rockstar (which detects both central and satellite halos) and a simple selection scheme is implemented to roughly match to the BOSS data (the monopole moment, especially. See below.).
• The HOD of the resultant galaxy catalog is also tested and found to be similar to what is usually assumed in the literature.
• The standard 1/n shot-noise contribution is already subtracted from the signal.
• Data is available at z=0.61 (CMASS2), z=0.51 (CMASS1) and z=0.38 (LOWZ). Other snapshots are also kept for testing purposes (at z=3, 2 and 1, but not analyzed yet.).
• I assume Gaussianity to estimate the covariance matrix; ignore the covariace between different k-bins, but different multipoles have covariance at the same k-bin.
• 2 types of covariance matrices are provided. One is for BOSS data (scaled according to the volume and the number density) and the other is for the simulation itself. The latter is extremely small because of the large box size.

## Properties of the catalog

• Halo mass function and HOD (average over the 10 realizations)

• Multipole moments (average over the 10 realizations)
The shaded region are the estimated 1-sigma regions assuming the BOSS parameters around the simulation data.
The triangle symbols are from Buetler et al. (arXiv:1607.03150) for the North and South Galactic Cap.

## Data

Data files are formatted as:

• column #1: k[h/Mpc]
• column #2: P0[(Mpc/h)^3] (monopole)
• column #3: P2[(Mpc/h)^3] (quadrupole)
• column #4: P4[(Mpc/h)^3] (hexadecapole)
• column #5: Cov_00 (scaled to BOSS parameters)
• column #6: Cov_22 (scaled to BOSS parameters)
• column #7: Cov_44 (scaled to BOSS parameters)
• column #8: Cov_02 (scaled to BOSS parameters)
• column #9: Cov_04 (scaled to BOSS parameters)
• column #10: Cov_24 (scaled to BOSS parameters)
• column #11: Cov_00 (from the simulation volume and number density)
• column #12: Cov_22 (from the simulation volume and number density)
• column #13: Cov_44 (from the simulation volume and number density)
• column #14: Cov_02 (from the simulation volume and number density)
• column #15: Cov_04 (from the simulation volume and number density)
• column #16: Cov_24 (from the simulation volume and number density)

## Challenge participants and results

Participants $\Delta \ln (10^{10}A_s) / \ln (10^{10}A_s)$ $\Delta \Omega_\mathrm{m}/\Omega_\mathrm{m}$ $\Delta H_0/H_0$ Model $k_\mathrm{max}\,[h\mathrm{Mpc}^{-1}]$ Reference Submitted on Blind analysis
Mikhail Ivanov, Marko Simonović, Matias Zaldarriaga $-0.0011 \pm 0.0069$ $0.012 \pm 0.009$ $-0.0059 \pm 0.0046$ EFT 1-loop (see the challenge paper for detail) 0.12 arXiv:2003.08277 (East Coast Team) May 24th 2019 Yes
Guido D'Amico, Leonardo Senatore and Pierre Zhang $0.001 \pm 0.007$ $0.012\pm 0.008$ $-0.006\pm 0.006$ EFT 1-loop (see the challenge paper for detail) 0.12 arXiv:2003.08277 (West Coast Team) Jun 4th 2019 Yes
Shi-Fan Chen, Zvonimir Vlah, Martin White $-0.0013 \pm 0.0054$ $0.0052 \pm 0.0050$ $-0.0088 \pm 0.0049$ MONE: Moment expansion using the first two pairwise-velocity moments at one-loop order + counterterm ansatz for the third moment. Non-cosmological parameters: bias (b1, b2, bs, third order set to zero), one counterterm per multipole, two stochastic terms (constant + k^2 mu^2). The counterterm ansatz set to zero because it is degenerate with the two multipole counterterms. 0.12 Model description in arXiv:2005.00523, challenge results in arXiv:2012.04636 July 11th 2020 Yes
$0.0009 \pm 0.0053$ $0.0039 \pm 0.0046$ $-0.0047 \pm 0.0051$ REPT: EPT with IR-resummation based on wiggle/no-wiggle split. Bias choice same as the above (third-order bias assumed to correspond to zero Lagrangian bias) 0.12
Shi-Fan Chen, Zvonimir Vlah, Emanuele Castorina, Martin White $-0.0004 \pm 0.0065$ $0.0037 \pm 0.0054$ $-0.0007 \pm 0.0056$ LPT 1-loop, full IR resummation of both displacements and velocities 0.12 arXiv:2012.04636 Dec 3rd 2020 No
Yosuke Kobayashi (w/ Takahiro Nishimichi and Masahiro Takada) $0.0139 \pm 0.0062$ $0.0157 \pm 0.0078$ $-0.0196 \pm 0.0051$ Halo-model based emulator with a HOD prescription to connect to galaxies 0.2 Model described in arXiv:2005.06122, challenge results to be described in a separate paper April 2nd 2021 Yes (Ground-truth values blinded only to Y. Kobayashi, who conducted all the analysis)

## Referece

Takahiro Nishimichi, Guido D'Amico, Mikhail M. Ivanov, Leonardo Senatore, Marko Simonović, Masahiro Takada, Matias Zaldarriaga, Pierre Zhang, "Blinded challenge for precision cosmology with large-scale structure: results from effective field theory for the redshift-space galaxy power spectrum"

arXiv:2003.08277

Physical Review D 102 123541 (2020)

last update: 27 September 2021 (Mon)