Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?

Appleby, Stephen; Park, Changbom; Pranav, Pratyush; Hong, Sungwook E.; Hwang, Ho Seong; Kim, Juhan; Buchert, Thomas

doi:10.48550/arxiv.2110.06109

Cited by 6 publications

(5 citation statements)

References 78 publications

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“…Recently, attention has turned toward developing alternative tools beyond the correlation functions and multispectra, which may potentially encode information of all orders. The principal tools in this regard have arisen from integral geometry and involve computing the Minkowski functionals or the Lifshitz-Killing curvatures (Adler 1981;Mecke et al 1994;Kerscher et al 1996;Schmalzing & Gorski 1998;Sahni et al 1998;Codis et al 2013;Ducout et al 2013;Matsubara 2010;Chingangbam et al 2017;Pranav et al 2019b;Appleby et al 2021). The jth Minkowski functional and (D − j)-th Lifshitz-Killing curvature of a D-dimensional manifold M are related by Q j (M) = j!ω j L D− j (M), where j = 0, .…”

Section: Introductionmentioning

confidence: 99%

Unexpected topology of the temperature fluctuations in the cosmic microwave background

Pranav

Adler

Buchert

et al. 2019

A&A

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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 comparison is multi-scale, being performed on a sequence of degraded maps with mean pixel separation ranging from 0.05 to 7.33 degrees. The survey of the CMB over 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 χ 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, 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 b 0 and b 1 is approximately between 3σ-4σ 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 (Wilkinson Microwave Anisotropy Probe) satellite. The mildly anomalous behaviour of Euler characteristic is phenomenologically related to the strongly anomalous behaviour of components and holes, or the zeroth and the first Betti numbers, respectively. Further, since these topological descriptors show anomalous behaviour consistently over independent measurements of Planck and WMAP, instrumental errors and systematics 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 to look at primordial non-Gaussianity. Alternative scenarios worth exploring may be models with non-trivial topology.

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Section: Introductionmentioning

confidence: 99%

Unexpected topology of the temperature fluctuations in the cosmic microwave background

Pranav

Adler

Buchert

et al. 2019

A&A

Self Cite

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“…Besides the abovementioned systematics, when applying the MFs to real surveys, one has to take care of the irregular shapes of the masked regions and survey boundaries. However, the effects of these systematics plus varying radial and angular selection functions can be corrected, and the MFs for real galaxy catalogs can be unbiasedly reconstructed [86,91]. In future work, we plan to investigate all these systematic effects comprehensively, and extract the constraints on neutrino mass by measuring the MFs from real surveys.…”

Section: Discussionmentioning

confidence: 99%

Probing massive neutrinos with the Minkowski functionals of large-scale structure

Liu,

Jiang,

Fang

2022

Preprint

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Massive neutrinos suppress the growth of structure under their free-streaming scales. The effect is most prominent on small scales where the widely-used two-point statistics can no longer capture the full information. In this work, we study the signatures massive neutrinos leave on large-scale structure (LSS) as revealed by its morphological properties, which are fully described by 4 Minkowski functionals (MFs), and quantify the constraints on the summed neutrino mass M ν from the MFs, by using publicly available N-body simulations. We find the MFs provide important complementary information, and give tighter constraints on M ν than the power spectrum. Specifically, depending on whether massive neutrinos are included in the density field (the 'm' field) or not (the 'cb' field), we find the constraint on M ν from the MFs with a smoothing scale of R G = 5h −1 Mpc is 48 or 4 times better than that from the power spectrum. When the MFs are combined with the power spectrum, they can improve the constraint on M ν from the latter by a factor of 63 for the 'm' field and 5 for the 'cb' field. Notably, when the 'm' field is used, the constraint on M ν from the MFs can reach 0.0177eV with a volume of 1(h −1 Gpc) 3 , while the combination of the MFs and power spectrum can tighten this constraint to be 0.0133eV, a 4.5σ significance on detecting the minimum sum of the neutrino masses. For the 'm' field, we also find the σ 8 and M ν degeneracy is broken with the MFs, leading to stronger constraints on all 6 cosmological parameters considered in this work than the power spectrum.

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“…To quantify the shape of the superclusters we employ SURFGEN2, which is an advanced version of the SURFGEN algorithm originally developed by Sheth et al (2003); Sheth (2006). The details of the refinements in SURFGEN2 can be found in Bag et al (2019Bag et al ( , 2018. However, for completeness, here we also briefly discuss the SURFGEN2 code which constructs isodensity surfaces from a given density field and subsequently calculates their Minkowski functionals and Shapefinders.…”

Section: Surfgen2 Algorithmmentioning

confidence: 99%

The shape distribution of superclusters in SDSS DR 12

Bag¹,

Liivamägi²,

Einasto³

2021

Preprint

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Superclusters are the largest structures formed due to the gravitational collapse and thus their geometrical information can shed light on the structure formation process on cosmological scales, hence on the fundamental properties of gravity itself. In this work we study the distributions of the shape, topology and morphology of the superclusters, defined in two different ways -using constant and individual density threshold on a luminosity weighted density field constructed from SDSS DR 12 main galaxy sample. For this purpose, we employ Minkowski functionals and Shapefinders, precisely calculated by the shape diagnostic tool SURFGEN2. We notice a striking similarity in the shape distributions of the supercluster samples those are obtained following these two distinct techniques. Not surprisingly, most of them are spherical in shape with trivial topology. But there are a significant number of superclusters that are quite filamentary and statistically tend to be large in size with non-zero genus values. The shape distribution results (catalogues) along with the modified SURFGEN2 code have been made publicly available.

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Minkowski Functionals of SDSS-III BOSS : Hints of Possible Anisotropy in the Density Field?

Cited by 6 publications

References 78 publications

Unexpected topology of the temperature fluctuations in the cosmic microwave background

Unexpected topology of the temperature fluctuations in the cosmic microwave background

Probing massive neutrinos with the Minkowski functionals of large-scale structure

The shape distribution of superclusters in SDSS DR 12

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