Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background. (arXiv:1812.07678v1 [astro-ph.CO])
<a href="http://arxiv.org/find/astro-ph/1/au:+Pranav_P/0/1/0/all/0/1">Pratyush Pranav</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Adler_R/0/1/0/all/0/1">Robert J. Adler</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Buchert_T/0/1/0/all/0/1">Thomas Buchert</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Edelsbrunner_H/0/1/0/all/0/1">Herbert Edelsbrunner</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Jones_B/0/1/0/all/0/1">Bernard J.T. Jones</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Schwartzman_A/0/1/0/all/0/1">Armin Schwartzman</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Wagner_H/0/1/0/all/0/1">Hubert Wagner</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Weygaert_R/0/1/0/all/0/1">Rien van de Weygaert</a>
We study the topology generated by the temperature fluctuations of the Cosmic
Microwave Background (CMB) radiation, as quantified by the number of components
and holes, formally given by the Betti numbers, in the growing excursion sets.
We compare CMB maps observed by the Planck satellite with a thousand simulated
maps generated according to the LCDM paradigm with Gaussian distributed
fluctuations. The survey of the CMB over $mathbb{S}^2$ is incomplete due to
obfuscation effects by bright point sources and other extended foreground
objects like our own galaxy. To deal with such situations, where analysis in
the presence of “masks” is of importance, we introduce the concept of relative
homology.
The parametric $chi^2$-test shows differences between observations and
simulations, yielding $p$-values at per-cent to less than per-mil levels
roughly between 2 to 7 degrees. The highest observed deviation for $b_0$ and
$b_1$ is approximately between $3sigma$-4$sigma$ at scales of 3 to 7 degrees.
There are reports of mildly unusual behaviour of the Euler characteristic at
3.66 degrees in the literature, computed from independent measurements of the
CMB temperature fluctuations by Planck’s predecessor WMAP satellite. The mildly
anomalous behaviour of Euler characteristic is related to the strongly
anomalous behaviour of components and holes. These are also the scales at which
the observed maps exhibit low variance compared to the simulations.
Non-parametric tests show even stronger differences at almost all scales.
Regardless, beyond the trivial possibility that this may still be a
manifestation of an extreme Gaussian case, these observations, along with the
super-horizon scales involved, may motivate to look at primordial
non-Gaussianity. Alternative scenarios worth exploring may be models with
non-trivial topology.
We study the topology generated by the temperature fluctuations of the Cosmic
Microwave Background (CMB) radiation, as quantified by the number of components
and holes, formally given by the Betti numbers, in the growing excursion sets.
We compare CMB maps observed by the Planck satellite with a thousand simulated
maps generated according to the LCDM paradigm with Gaussian distributed
fluctuations. The survey of the CMB over $mathbb{S}^2$ is incomplete due to
obfuscation effects by bright point sources and other extended foreground
objects like our own galaxy. To deal with such situations, where analysis in
the presence of “masks” is of importance, we introduce the concept of relative
homology.
The parametric $chi^2$-test shows differences between observations and
simulations, yielding $p$-values at per-cent to less than per-mil levels
roughly between 2 to 7 degrees. The highest observed deviation for $b_0$ and
$b_1$ is approximately between $3sigma$-4$sigma$ at scales of 3 to 7 degrees.
There are reports of mildly unusual behaviour of the Euler characteristic at
3.66 degrees in the literature, computed from independent measurements of the
CMB temperature fluctuations by Planck’s predecessor WMAP satellite. The mildly
anomalous behaviour of Euler characteristic is related to the strongly
anomalous behaviour of components and holes. These are also the scales at which
the observed maps exhibit low variance compared to the simulations.
Non-parametric tests show even stronger differences at almost all scales.
Regardless, beyond the trivial possibility that this may still be a
manifestation of an extreme Gaussian case, these observations, along with the
super-horizon scales involved, may motivate to look at primordial
non-Gaussianity. Alternative scenarios worth exploring may be models with
non-trivial topology.
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