Planck 2015 results
Free Access

Fig. 1

image

KL divergence of slab (T1) topologies relative to an infinite Universe as a function of max with sizes and (top), and as a function of size L of the fundamental domain for various max (bottom). A torus with , corresponding to (H0L)-1< 0.154, has a fundamental domain that is larger than the distance to the last-scattering surface and leaves only a small trace in the CMB. This is why the KL divergence drops rapidly at this point. Note that the information for continues to rise with max whereas it levels off for the slightly larger case. In the lower panel we see that there is a slight feature in dKL at about half the horizon distance, which is probably due to harmonic effects. The corresponding figures for cubic (T3) topologies look qualitatively similar except that all dKL values are three times larger.

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