A reassessment of LVE method and hemispherical power asymmetry in CMB temperature data from Planck PR4

TL;DR

The paper addresses hemispherical power asymmetry (HPA) in CMB temperature data by reassessing the Local Variance Estimator (LVE) method using Planck PR4 SEVEM maps. It validates LVE with isotropic and dipole-modulated simulations, and then applies it to data across disc radii from 0.5° to 90° to probe scale dependence. The analysis finds a scale-dependent HPA with best-fit power-law parameters A_0 ≈ 0.054 and n ≈ 0.3, indicating stronger asymmetry at large angular scales and diminishing power at small scales, while dipole directions remain broadly consistent. These results reinforce HPA as a persistent anomaly challenging ΛCDM, while providing methodological refinements (grid matching, inverse-variance weighting, and bias correction) that improve reliability of the LVE-derived dipole measurements.

Abstract

We undertake a reassessment of one of the large angular scale anomalies observed in cosmic microwave background (CMB) temperature signal referred to as Hemispherical Power Asymmetry (HPA). For the present analysis we use \texttt{SEVEM} cleaned CMB maps from \emph{Planck}'s 2020 final data release (public release 4/PR4). To probe HPA, we employed the local variance estimator (LVE) method with different disc radii ranging from $0.5^\circ$ to $90^\circ$. Our emphasis here is to revalidate the LVE method in various ways for its optimal usage and probe the hemispherical power asymmetry in the form of a dipole modulation field underlying CMB sky. By and large, our results are in agreement with earlier reported ones with more detailed presentation of explicit and not-so-explicit assumptions involved in the estimation process. It is reaffirmed that HPA is confined to low multipoles or large angular scales of the CMB sky. A dipole like anisotropy was found in the LVE maps with anomalous power for disc radii of $2^\circ$ and upward up to $36^\circ$ at $\gtrsim2σ$ level. In the range $4^\circ$ to $10^\circ$ none of the 600 \sevem\ CMB simulations were found to have a dipole amplitude higher than the data when using LVE method as originally proposed. The above reported values fall in the reliability range of LVE method after this extensive re-evaluation. We also observe a scale dependence of the HPA dipole amplitude and model it as a power-law. We conclude that the hemispherical power asymmetry still remains as a challenge to the standard model.

Figures (12)

• Figure 1: Left : The SEVEM cleaned CMB map from Planck's PR4 data release. Right : Planck PR3 common mask recommended for use with PR4 cleaned CMB maps.
• Figure 2: Top: Covariance matrices $C_{pp'}$ as defined in Eq. (\ref{['eq:cov-mat']}) corresponding to normalized LVE maps generated at $N_{\rm side}$=2, 4, and 16 but for a particular disc radius $r=16^\circ$. Bottom: Correlation matrices, $\tilde{C}_{pp'}$, (normalized covariance matrices) as defined in Eq. (\ref{['eq:corr-mat']}) corresponding to the same disc radius but from LVE maps with different $N_{\rm side}$ as shown in the top panels.
• Figure 3: Top and Bottom panels depict the distribution of dipole amplitudes, $A_{\rm d}=A_{\rm LV}/2$, evaluated from normalized local variance maps obtained with varying $N_{\rm side}$ and fixed $N_{\rm side}$=16 schemes, respectively. Recovered dipole amplitudes from isotropic simulations are shown in gray, from low-$l$ dipole modulated maps in magenta and pure dipole modulated maps in black.
• Figure 4: Recovered dipole modulation directions in LVE maps for some select disc radii as indicated. The top, middle and bottom rows comparatively show the LVE maps' dipole directions from isotropic, pure-dm and low-$l$-dm simulation sets using fixed $N_{\rm side}$=16 (red dots) and varying $N_{\rm side}$ (black dots) schemes. These dipoles in LVE maps are fitted using inverse variance weighting with the functionality of HEALPix.
• Figure 7: Normalized LVE maps (per Eq. \ref{['eq:norm-lve']}) corresponding to SEVEM CMB solution from Planck PR4 for some select disc radii are shown here. In the top row, LVE maps obtained using varying $N_{\rm side}$ grid are shown, and in the bottom row the same are shown for fixed $N_{\rm side}$=16 grid in deriving LVE maps. From left to right the LVE maps shown correspond to disc radii $r=4^\circ$, $14^\circ$, and $50^\circ$.