---
res:
bibo_abstract:
- "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 ΛCDM paradigm with Gaussian distributed fluctuations.
The comparison is multi-scale, being performed on a sequence of degraded maps
with mean pixel separation ranging from 0.05 to 7.33°. The survey of the CMB over
\U0001D54A2 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 χ2-test shows differences between observations
and simulations, yielding p-values at percent to less than permil levels roughly
between 2 and 7°, with the difference in the number of components and holes peaking
at more than 3σ sporadically at these scales. The highest observed deviation between
the observations and simulations for b0 and b1 is approximately between 3σ and
4σ at scales of 3–7°. There are reports of mildly unusual behaviour of the Euler
characteristic at 3.66° in the literature, computed from independent measurements
of the CMB temperature fluctuations by Planck’s predecessor, the Wilkinson Microwave
Anisotropy Probe (WMAP) satellite. The mildly anomalous behaviour of the Euler
characteristic is phenomenologically related to the strongly anomalous behaviour
of components and holes, or the zeroth and first Betti numbers, respectively.
Further, since these topological descriptors show consistent anomalous behaviour
over independent measurements of Planck and WMAP, instrumental and systematic
errors may be an unlikely source. These are also the scales at which the observed
maps exhibit low variance compared to the simulations, and approximately the range
of scales at which the power spectrum exhibits a dip with respect to the theoretical
model. Non-parametric tests show even stronger differences at almost all scales.
Crucially, Gaussian simulations based on power-spectrum matching the characteristics
of the observed dipped power spectrum are not able to resolve the anomaly. Understanding
the origin of the anomalies in the CMB, whether cosmological in nature or arising
due to late-time effects, is an extremely challenging task. 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
the study of primordial non-Gaussianity. Alternative scenarios worth exploring
may be models with non-trivial topology, including topological defect models.@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Pratyush
foaf_name: Pranav, Pratyush
foaf_surname: Pranav
- foaf_Person:
foaf_givenName: Robert J.
foaf_name: Adler, Robert J.
foaf_surname: Adler
- foaf_Person:
foaf_givenName: Thomas
foaf_name: Buchert, Thomas
foaf_surname: Buchert
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Edelsbrunner, Herbert
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
- foaf_Person:
foaf_givenName: Bernard J.T.
foaf_name: Jones, Bernard J.T.
foaf_surname: Jones
- foaf_Person:
foaf_givenName: Armin
foaf_name: Schwartzman, Armin
foaf_surname: Schwartzman
- foaf_Person:
foaf_givenName: Hubert
foaf_name: Wagner, Hubert
foaf_surname: Wagner
foaf_workInfoHomepage: http://www.librecat.org/personId=379CA8B8-F248-11E8-B48F-1D18A9856A87
- foaf_Person:
foaf_givenName: Rien
foaf_name: Van De Weygaert, Rien
foaf_surname: Van De Weygaert
bibo_doi: 10.1051/0004-6361/201834916
bibo_volume: 627
dct_date: 2019^xs_gYear
dct_isPartOf:
- http://id.crossref.org/issn/00046361
- http://id.crossref.org/issn/14320746
dct_language: eng
dct_publisher: EDP Sciences@
dct_title: Unexpected topology of the temperature fluctuations in the cosmic microwave
background@
...