Weakly non-Gaussian formula for the Minkowski functionals in general dimensions

Matsubara, Takahiko; Kuriki, Shinya

doi:10.1103/physrevd.104.103522

Cited by 14 publications

(12 citation statements)

References 117 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analytical predictions for the MFs are known for Gaussian density fields [62] and weakly non-Gaussian fields [63,64]. They agree with measurements from N-body simulations when the smoothing scale is large enough [65,66].…”

Section: Jcap07(2022)045supporting

confidence: 61%

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

Liu

Jiang

Fang

2022

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

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 Mν from the MFs, by using publicly available N-body simulations. We find the MFs provide important complementary information, and give tighter constraints on Mν 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 Mν from the MFs with a smoothing scale of RG = 5h -1Mpc 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 Mν 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 Mν from the MFs can reach 0.0177eV with a volume of 1( -1Gpc)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 Mν degeneracy is broken with the MFs, leading to stronger constraints on all 6 cosmological parameters considered in this work than the power spectrum.

show abstract

Section: Jcap07(2022)045supporting

confidence: 61%

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

Liu

Jiang

Fang

2022

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

show abstract

“…In this study, we compare the measured statistics on t reion (r) mentioned above to GRF theory predictions. This theory allows us to compute statistics of Gaussian-distributed field (Rice 1944;Longuet-Higgins 1957;Doroshkevich 1970;Bardeen et al 1986;Hamilton et al 1986;Pogosyan et al 2009a,b;Pichon et al 2010;Gay et al 2012;Cadiou et al 2020) or weakly non-Gaussian fields (Matsubara 2003;Pogosyan et al 2011;Gay et al 2012;Cadiou et al 2020;Matsubara & Kuriki 2021). Rice (1944) first introduced the GRF theory to extract statistics from the 1D random noise of electronic devices.…”

Section: Gaussianity Of the Reionisation Time Fieldmentioning

confidence: 99%

“…More recently, Gay et al (2012) extracted many statistics of 2D and 3D cosmological fields thanks to this theory, for example counting the peaks on synthesised cosmic microwave background (CMB) maps to study their nongaussianities. Some widely used statistics in the context of the EoR can be analytically calculated thanks to the GRF theory, such as Minkowski functionals, the derived genus or Euler characteristics, and Betti numbers (Schmalzing & Gorski 1998;Matsubara 2003;Lee et al 2008;Gay et al 2012;Kapahtia et al 2019;Matsubara & Kuriki 2021). For example, Lee et al (2008) computed the genus of the neutral hydrogen field x HII to study the evolution of the EoR through many phases.…”

Section: Gaussianity Of the Reionisation Time Fieldmentioning

confidence: 99%

Topology of reionisation times: Concepts, measurements, and comparisons to Gaussian random field predictions

Thélie¹,

Aubert²,

Gillet³

et al. 2023

A&A

View full text Add to dashboard Cite

Context. In the next decade, radio telescopes, such as the Square Kilometer Array (SKA), will explore the Universe at high redshift, and particularly during the epoch of reionisation (EoR). The first structures emerged during this epoch, and their radiation reionised the previously cold and neutral gas of the Universe, creating ionised bubbles that percolate at the end of the EoR (z ∼ 6). SKA will produce 2D images of the distribution of the neutral gas at many redshifts, pushing us to develop tools and simulations to understand its properties. Aims. With this paper, we aim to measure topological statistics of the EoR in the so-called reionisation time fields from both cosmological and semi-analytical simulations. This field informs us about the time of reionisation of the gas at each position; it is used to probe the inhomogeneities of reionisation histories and can be extracted from 21 cm maps. We also compare these measurements with analytical predictions obtained within Gaussian random field (GRF) theory. Methods. The GRF theory allows us to compute many statistics of a field, namely the probability distribution functions (PDFs) of the field or its gradient, isocontour length, critical point distributions, and skeleton length. We compare these theoretical predictions to measurements made on reionisation time fields extracted from an EMMA simulation and a 21cmFAST simulation at 1 cMpc/h resolution. We also compared our results to GRFs generated from the fitted power spectra of the simulation maps. Results. Both EMMA and 21cmFAST reionisation time fields (t reion (r)) are close to being Gaussian fields, in contrast with the 21 cm, density, or ionisation fraction, which have all been shown to be non-Gaussian. Only accelerating ionisation fronts at the end of the EoR seem to be the cause of small non-gaussianities in t reion (r). Overall, this topological description of reionisation times provides a new quantitative and reproducible way to characterise the EoR scenario. Under the assumption of GRFs, it enables the generation of reionisation models with their propagation, percolation, or seed statistics simply from the reionisation time power spectrum. Conversely, these topological statistics provide a means to constrain the properties of the power spectrum and by extension the physics that drive the propagation of radiation.

show abstract

“…As of the important role of the large-scale structures and corresponding observational catalogs, there are many attempts to incorporate the geometrical and topological virtues of diverse relevant fields such as the genus statistic (Gott et al 1986;Hamilton et al 1986), contour statistics including one-, two-, and three-dimensional features (Ryden 1988;Ryden et al 1989), and Minkowski functionals (MFs) consisting of d + 1 scalar quantities that describe the morphology of isodensity contours of a d-dimensional field (Mecke et al 1994;Schmalzing & Buchert 1997; see also Kerscher et al 1997;Sahni et al 1998;Matsubara 2003;Hikage et al 2006;Pogosyan et al 2009;Einasto et al 2011;Gay et al 2012;Codis et al 2013;Liu et al 2020;Matsubara & Kuriki 2021;Liu et al 2022;Matsubara et al 2022, and references therein).…”

Section: Introductionmentioning

confidence: 99%

Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative

Kanafi,

Movahed

2024

ApJ

View full text Add to dashboard Cite

Focusing on the redshift space observations with plane-parallel approximation and relying on the rotational dependency of the general definition of excursion sets, we introduce the so-called conditional moments of the first derivative (cmd) measures for the smoothed matter density field in three dimensions. We derive the perturbative expansion of cmd for the real space and redshift space where peculiar velocity disturbs the galaxies’ observed locations. Our criteria can successfully recognize the contribution of linear Kaiser and Finger-of-God effects. Our results demonstrate that the cmd measure has significant sensitivity for pristine constraining the redshift space distortion parameter β = f/b and interestingly, the associated normalized quantity in the Gaussian linear Kaiser limit has only β dependency. Implementation of the synthetic anisotropic Gaussian field approves the consistency between the theoretical and numerical results. Including the first-order contribution of non-Gaussianity perturbatively in the cmd criterion implies that the N-body simulations for the Quijote suite in the redshift space have been mildly skewed with a higher value for the threshold greater than zero. The non-Gaussianity for the perpendicular direction to the line of sight in the redshift space for smoothing scales R ≳ 20 Mpc h −1 is almost the same as in the real space. In contrast, the non-Gaussianity along the line-of-sight direction in the redshift space is magnified. The Fisher forecasts indicate a significant enhancement in constraining the cosmological parameters Ω m , σ 8, and n s when using cmd + cr jointly.

show abstract

Weakly non-Gaussian formula for the Minkowski functionals in general dimensions

Cited by 14 publications

References 117 publications

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

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

Topology of reionisation times: Concepts, measurements, and comparisons to Gaussian random field predictions

Probing the Anisotropy and Non-Gaussianity in the Redshift Space through the Conditional Moments of the First Derivative

Contact Info

Product

Resources

About