---
_id: '6756'
abstract:
- lang: eng
  text: "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."
article_number: A163
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pratyush
  full_name: Pranav, Pratyush
  last_name: Pranav
- first_name: Robert J.
  full_name: Adler, Robert J.
  last_name: Adler
- first_name: Thomas
  full_name: Buchert, Thomas
  last_name: Buchert
- first_name: Herbert
  full_name: Edelsbrunner, Herbert
  id: 3FB178DA-F248-11E8-B48F-1D18A9856A87
  last_name: Edelsbrunner
  orcid: 0000-0002-9823-6833
- first_name: Bernard J.T.
  full_name: Jones, Bernard J.T.
  last_name: Jones
- first_name: Armin
  full_name: Schwartzman, Armin
  last_name: Schwartzman
- first_name: Hubert
  full_name: Wagner, Hubert
  id: 379CA8B8-F248-11E8-B48F-1D18A9856A87
  last_name: Wagner
- first_name: Rien
  full_name: Van De Weygaert, Rien
  last_name: Van De Weygaert
citation:
  ama: Pranav P, Adler RJ, Buchert T, et al. Unexpected topology of the temperature
    fluctuations in the cosmic microwave background. <i>Astronomy and Astrophysics</i>.
    2019;627. doi:<a href="https://doi.org/10.1051/0004-6361/201834916">10.1051/0004-6361/201834916</a>
  apa: Pranav, P., Adler, R. J., Buchert, T., Edelsbrunner, H., Jones, B. J. T., Schwartzman,
    A., … Van De Weygaert, R. (2019). Unexpected topology of the temperature fluctuations
    in the cosmic microwave background. <i>Astronomy and Astrophysics</i>. EDP Sciences.
    <a href="https://doi.org/10.1051/0004-6361/201834916">https://doi.org/10.1051/0004-6361/201834916</a>
  chicago: Pranav, Pratyush, Robert J. Adler, Thomas Buchert, Herbert Edelsbrunner,
    Bernard J.T. Jones, Armin Schwartzman, Hubert Wagner, and Rien Van De Weygaert.
    “Unexpected Topology of the Temperature Fluctuations in the Cosmic Microwave Background.”
    <i>Astronomy and Astrophysics</i>. EDP Sciences, 2019. <a href="https://doi.org/10.1051/0004-6361/201834916">https://doi.org/10.1051/0004-6361/201834916</a>.
  ieee: P. Pranav <i>et al.</i>, “Unexpected topology of the temperature fluctuations
    in the cosmic microwave background,” <i>Astronomy and Astrophysics</i>, vol. 627.
    EDP Sciences, 2019.
  ista: Pranav P, Adler RJ, Buchert T, Edelsbrunner H, Jones BJT, Schwartzman A, Wagner
    H, Van De Weygaert R. 2019. Unexpected topology of the temperature fluctuations
    in the cosmic microwave background. Astronomy and Astrophysics. 627, A163.
  mla: Pranav, Pratyush, et al. “Unexpected Topology of the Temperature Fluctuations
    in the Cosmic Microwave Background.” <i>Astronomy and Astrophysics</i>, vol. 627,
    A163, EDP Sciences, 2019, doi:<a href="https://doi.org/10.1051/0004-6361/201834916">10.1051/0004-6361/201834916</a>.
  short: P. Pranav, R.J. Adler, T. Buchert, H. Edelsbrunner, B.J.T. Jones, A. Schwartzman,
    H. Wagner, R. Van De Weygaert, Astronomy and Astrophysics 627 (2019).
date_created: 2019-08-04T21:59:18Z
date_published: 2019-07-17T00:00:00Z
date_updated: 2023-08-29T07:01:48Z
day: '17'
ddc:
- '520'
- '530'
department:
- _id: HeEd
doi: 10.1051/0004-6361/201834916
external_id:
  arxiv:
  - '1812.07678'
  isi:
  - '000475839300003'
file:
- access_level: open_access
  checksum: 83b9209ed9eefbdcefd89019c5a97805
  content_type: application/pdf
  creator: dernst
  date_created: 2019-08-05T08:08:59Z
  date_updated: 2020-07-14T12:47:39Z
  file_id: '6766'
  file_name: 2019_AstronomyAstrophysics_Pranav.pdf
  file_size: 14420451
  relation: main_file
file_date_updated: 2020-07-14T12:47:39Z
has_accepted_license: '1'
intvolume: '       627'
isi: 1
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '07'
oa: 1
oa_version: Published Version
project:
- _id: 265683E4-B435-11E9-9278-68D0E5697425
  grant_number: M62909-18-1-2038
  name: Toward Computational Information Topology
- _id: 2561EBF4-B435-11E9-9278-68D0E5697425
  call_identifier: FWF
  grant_number: I02979-N35
  name: Persistence and stability of geometric complexes
publication: Astronomy and Astrophysics
publication_identifier:
  eissn:
  - '14320746'
  issn:
  - '00046361'
publication_status: published
publisher: EDP Sciences
quality_controlled: '1'
scopus_import: '1'
status: public
title: Unexpected topology of the temperature fluctuations in the cosmic microwave
  background
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
  short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 627
year: '2019'
...