Bayesian Limits on Primordial Isotropy Breaking
C. Armendariz-Picon, Larne Pekowsky
TL;DR
The paper tests the assumption of statistical isotropy for primordial perturbations by expanding the primordial power spectrum with a spherical-harmonic basis $\mathcal{P}_{\mathcal{R}}(\mathbf{k})=\sqrt{4\pi}\sum_{\ell m}\mathcal{P}_{\ell m}(k) Y_{\ell m}(\hat{k})$ and modeling $\mathcal{P}_{\ell m}(k)=\mathcal{A}_{\ell m}(k/k_0)^{n_s-1}$. A Bayesian analysis is performed on masked, five-year WMAP CMB data to infer the amplitudes $\mathcal{A}_{\ell m}$, accounting for the mask, beams, and noise via a covariance $C=(MHW)A(MHW)^T+MNM^T$ and applying priors on $\mathcal{A}_{00}$ and the ratios $R_{2m}=\mathcal{A}_{2m}/\mathcal{A}_{00}$; Markov Chain Monte Carlo is used to sample the posterior. The results show that the quadrupole components are consistent with zero within uncertainties, with $||\mathcal{R}_2||<0.24$ (V2), $<0.22$ (W1), and $<0.19$ (W1|V2); although a nonzero quadrupole can improve the maximum likelihood, information criteria favor isotropy. The bounds are model-independent and transferable to isotropy-breaking theories, supporting standard inflationary predictions and providing a framework for tighter constraints with future data.
Abstract
It is often assumed that primordial perturbations are statistically isotropic, which implies, among other properties, that their power spectrum is invariant under rotations. In this article, we test this assumption by placing model-independent bounds on deviations from rotational invariance of the primordial spectrum. Using five-year WMAP cosmic microwave anisotropy maps, we set limits on the overall norm and the amplitude of individual components of the primordial spectrum quadrupole. We find that there is no significant evidence for primordial isotropy breaking, and that an eventually non-vanishing quadrupole has to be subdominant.