Topology and the suppression of CMB large-angle correlations

Abstract

To date, no compelling evidence has been found that the universe has non-trivial spatial topology. Meanwhile, anomalies in the observed CMB temperature map, such as the lack of correlations at large angular separations, remain observationally robust. We show that if our universe is flat and has one compact dimension of appropriate size (slab topology), this would suppress large-angle temperature correlations while maintaining a low-$\ell$ angular power spectrum consistent with observations. The optimal length appears to be $1.4$ times the conformal radius of the CMB's last scattering surface (${\chi }_{rec}$). We construct the probability distribution function of the statistic $S_{1/2}$ using simulated Sachs-Wolf-only skies for each of several values of $L_z/{\chi }_{rec}$. For $L_z\simeq 1.4{\chi }_{rec}$ the $p$-value of four standard masked Planck maps is $p\simeq 0.15$, compared to $p\lesssim 0.003$ for the conventional topologically trivial space. The mean angular power spectrum $⟨C_{\ell }⟩$ of the $L_z=1.4{\chi }_{rec}$ slab space matches the observed power spectrum at $2\le \ell \lesssim 6$ -- including a substantially suppressed quadrupole $C_2$, a slightly suppressed octopole $C_3$, and unsuppressed higher multipoles. It does not predict other low-$\ell$ CMB anomalies, and does not take account of normally sub-dominant Integrated Sachs Wolfe contributions. An $L_z=1.4{\chi }_{rec}$ slab topology is consistent with published limits from the Planck maps ($L_z\gtrsim 1.12{\chi }_{rec}$). It is within the 95% confidence range $1.2\le L_z/{\chi }_{rec}\le 2.1$ inferred using the covariance-matrix of temperature fluctuations. However, it violates published circles-in-the-sky limits from WMAP and related unpublished limits from Planck ($L_z/{\chi }_{rec}\gtrsim 1.9$). We remark on the possibility to satisfy these limits, and "postdict" other large-angle anomalies, with closely related topologies.

arXiv comment5 pages, 2 figures

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