Estimators for CMB Statistical Anisotropy (0908.0963v4)

Abstract: We use quadratic maximum-likelihood (QML) estimators to constrain models with Gaussian but statistically anisotropic Cosmic Microwave Background (CMB) fluctuations, using CMB maps with realistic sky-coverage and instrumental noise. This approach is optimal when the anisotropy is small, or when checking for consistency with isotropy. We demonstrate the power of the QML approach by applying it to the WMAP data to constrain several models which modulate the observed CMB fluctuations to produce a statistically anisotropic sky. We first constrain an empirically motivated spatial modulation of the observed CMB fluctuations, reproducing marginal evidence for a dipolar modulation pattern with amplitude 7% at L < 60, but demonstrate that the effect decreases at higher multipoles and is 1% at L~500. We also look for evidence of a direction-dependent primordial power spectrum, finding a very statistically significant quadrupole signal nearly aligned with the ecliptic plane; however we argue this anisotropy is largely contaminated by observational systematics. Finally, we constrain the anisotropy due to a spatial modulation of adiabatic and isocurvature primordial perturbations, and discuss the close relationship between anisotropy and non-Gaussianity estimators.

Anisotropy in Cosmic Microwave Background (CMB) Fluctuations

The paper of the Cosmic Microwave Background (CMB) provides invaluable insights into the early universe. The assumption that CMB fluctuations are statistically isotropic and Gaussian forms a foundational pillar in modern cosmology models, including the widely adopted $\Lambda$CDM model. This paper, authored by Hanson and Lewis, explores tools to rigorously test this isotropy assumption using quadratic maximum-likelihood (QML) estimators. The paper presents methodologies to detect and characterize statistical anisotropies in the CMB, particularly utilizing data from the Wilkinson Microwave Anisotropy Probe (WMAP).

Methods and Key Results

The authors employ QML estimators, an approach optimized for detecting small anisotropies and ensuring consistency with isotropy. The primary focus is on evaluating anisotropic modulations in over 400 modes of the CMB data. Key aspects of the methodology include:

• Quadratic Estimators for Modulation and Power Spectrum Anisotropy: The authors construct specific estimators tuned to capture anisotropic modulations of the CMB signal, particularly focusing on lower multipoles where potential anisotropies are expected to manifest clearly due to cosmic variance.
• Application to WMAP Data: By applying these estimators to WMAP data, they identify a marginally significant dipolar modulation in large-scale structures (multipoles $l \lesssim 60$), positing a 7% modulation amplitude at these scales. This modulation decreases at higher multipoles, indicating a decline in anisotropy magnitude.

Crucially, the paper also highlights detection of a statistically significant quadrupole anisotropy, almost aligned with the ecliptic plane, although heavily flagged by the authors as potentially contaminated by observational systematics.

Implications

The implications of these findings are multifaceted:

• Cosmological Models: Detection of anisotropy in the CMB challenges the assumption of statistical isotropy, prompting considerations for models that can accommodate such anisotropies. These might include models of anisotropic inflation or effects stemming from non-standard cosmological models and topological defects. The results broadly support the isotropic $\Lambda$CDM model but indicate possible areas for refinement or modification.
• Systematic Effects: The authors emphasize the entangled influence of systematic errors, particularly those arising from instrumental effects such as beam asymmetries. Such systematics could simulate anisotropy, necessitating clearer separation between cosmological signals and these artifacts in subsequent analyses.

Future Directions

Future developments in instrumentation, such as those envisioned for the Planck satellite, should improve anisotropy detection capabilities by offering higher sensitivity and resolution. In addition, polarization data can provide complementary constraints on anisotropy, potentially unraveling whether observed signals are cosmological or system-related.

The utilization of polarization alongside temperature estimates offers a robust test of the isotropy assumption. Upcoming data sets will facilitate more precise characterization of potential anisotropies, granting a clearer frontier over which theoretical models can be honed or expanded.

Conclusion

The paper by Hanson and Lewis represents a critical step in assessing one of modern cosmology's foundational conventions: the isotropy of the universe as evidenced in the CMB. While the research detects marginal anisotropy, the balance between detected signals and systematic effects highlights the intricate nature of CMB interpretation and the need for continued scientific inquiry.