Non-detection of a statistically anisotropic power spectrum in large-scale structure

TL;DR

This paper tests the hypothesis of statistical isotropy in the large-scale matter distribution by constraining a quadrupolar modulation of the primordial power spectrum using SDSS photometric LRGs. It develops a rigorous quadratic-estimator framework incorporating the direction-dependent power spectrum $P(k)=\bar{P}(k)[1+\sum_{M} g_{2M} R_{2M}(\hat{k})]$, projects 3D fluctuations onto 2D sky maps, and accounts for sky systematics with dedicated templates. Across eight redshift slices, the combined measurements of the quadrupole coefficients $g_{2M}$ are consistent with zero, and the axisymmetric constraint along the CMB-reported direction yields $g_*^{\mathrm{LRG}}=0.006\pm0.036$, indicating no detectable primordial quadrupole within the LSS data. A marginalized constraint on the amplitude $g_*$ gives $-0.41<g_*<0.38$ (95% CL), suggesting that the CMB-like quadrupole signal is not present in the LSS field at the probed scales, though future wide-volume surveys could greatly improve sensitivity. The work clarifies that the CMB quadrupole anomaly is unlikely to be primordial and demonstrates the value of LSS studies in testing SI with independent systematics.

Abstract

We search a sample of photometric luminous red galaxies (LRGs) measured by the Sloan Digital Sky Survey (SDSS) for a quadrupolar anisotropy in the primordial power spectrum, in which P(\vec{k}) is an isotropic power spectrum P(k) multiplied by a quadrupolar modulation pattern. We first place limits on the 5 coefficients of a general quadrupole anisotropy. We also consider axisymmetric quadrupoles of the form P(\vec{k}) = P(k){1 + g_*[(\hat{k}\cdot\hat{n})^2-1/3]} where \hat{n} is the axis of the anisotropy. When we force the symmetry axis \hat{n} to be in the direction (l,b)=(94 degrees,26 degrees) identified in the recent Groeneboom et al. analysis of the cosmic microwave background, we find g_*=0.006+/-0.036 (1 sigma). With uniform priors on \hat{n} and g_* we find that -0.41<g_*<+0.38 with 95% probability, with the wide range due mainly to the large uncertainty of asymmetries aligned with the Galactic Plane. In none of these three analyses do we detect evidence for quadrupolar power anisotropy in large scale structure.

Figures (10)

• Figure 1: The redshift distributions for the 8 photometric redshift slices.
• Figure 2: The LRG density in the 8 photometric redshift slices. The 45$^\circ$ radius caps are displayed in a Lambert Azimuthal Equal-Area Projection, with the North Galactic Pole at the centre, $l=0^\circ$ at right, and $l=90^\circ$ at bottom. The labels indicate the characteristic redshift of each slice.
• Figure 3: The predicted angular power spectra for each of the 8 redshift slices. The solid lines show nonlinear auto power spectra, while the dash-dotted lines show the cross power power spectra with the adjacent slice at higher redshift. The dashed lines show the predicted $[-F_{g,l(l+2)}]$. The dotted lines show the effect of redshift space distortions on all three spectra.
• Figure 4: The parameter values for the simulation test with no input anisotropy or modulation, including 1-sigma errors. The top left panel shows the $\tilde{C}_n$, the top right panel shows the $g_{2M}$s, and the bottom panel shows the $h_{2M}$s.
• Figure 5: The parameter values for the simulation test with input anisotropy and modulation, including 1-sigma errors. The top left panel shows the $\tilde{C}_n$, the top right panel shows the $g_{2M}$s, and the bottom panel shows the $h_{2M}$s. Note that the input values for $g_{20}$ and $h_{20}$ are 0.5.