The Covariance of Squeezed Bispectrum Configurations

Biagetti, Matteo; Castiblanco, Lina; Noreña, Jorge; Sefusatti, Emiliano

doi:10.48550/arxiv.2111.05887

Cited by 9 publications

(16 citation statements)

References 105 publications

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“…These results show a strong potential for primordial non-Gaussianity as compared to recent analyses. For instance, a Fisher forecast using the halo power spectrum and bispectrum in real space on the Eos simulations considered in this work gave ∆f loc NL ∼ 20 using full boxes of 8 (Gpc/h) 3 volume with a realistic theoretical covariance [79]. As for real data constraints, the power spectrum and bispectrum as measured from the BOSS survey was recently analyzed in the context of primordial non-Gaussianity and gave constraints of the order of ∆f loc NL ∼ 50 and ∆f equi NL ∼ 200 at 68% confidence on a volume of 2.4 (Gpc/h) 3 [4].…”

Section: Discussionmentioning

confidence: 92%

Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

Biagetti¹,

Calles²,

Castiblanco³

et al. 2022

Preprint

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We study the information content of summary statistics built from the multi-scale topology of large-scale structures on primordial non-Gaussianity of the local and equilateral type. We use halo catalogs generated from numerical N-body simulations of the Universe on large scales as a proxy for observed galaxies. Besides calculating the Fisher matrix for halos in real space, we also check more realistic scenarios in redshift space. Without needing to take a distant observer approximation, we place the observer on a corner of the box. We also add redshift errors mimicking spectroscopic and photometric samples. We perform several tests to assess the reliability of our Fisher matrix, including the Gaussianity of our summary statistics and convergence. We find that the marginalized 1-σ uncertainties in redshift space are ∆f loc NL ∼ 16 and ∆f equi NL ∼ 41 on a survey volume of 1 (Gpc/h) 3 . These constraints are weakly affected by redshift errors. We close by speculating as to how this approach can be made robust against small-scale uncertainties by exploiting (non)locality.

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Section: Discussionmentioning

confidence: 92%

Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

Biagetti¹,

Calles²,

Castiblanco³

et al. 2022

Preprint

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“…The comparison between the numerical estimate and analytic prediction for these quantities is shown in figure 3. One can see how the Gaussian prediction for C 00 , C 22 and C 44 is able to describe the measured ones at the level of 5%, with a slight deficit noticeable in the monopole and quadrupole case for squeezed triangles, due to the missing non-Gaussian contribution [52,53]. The agreement in the case of the cross-covariance C 1 2 (t i , t i ) is also rather good, with the theory underestimating the measurements by an overall 10%.…”

Section: Theoretical Gaussian Covariancementioning

confidence: 92%

“…The mass threshold for the mocks is chosen to reproduce (below percent level) the amplitude of the large-scale halo power spectrum (including shotnoise) of the numerical simulations (see Paper I for details). This quantity, in fact, accounts for the Gaussian contribution to the bispectrum covariance, the leading one for most triangular configurations (see also [52,53]). The covariance matrix for each bispectrum multipole and their cross-covariance is defined as…”

Section: Numerical Estimatementioning

confidence: 99%

The Halo Bispectrum Multipoles in Redshift Space

Rizzo¹,

Moretti²,

Pardede³

et al. 2022

Preprint

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We present the analysis of the halo bispectrum in redshift-space in terms of its multipoles, monopole, quadrupole and hexadecapole, measured from a large set of simulations. We fit such measurements with a tree-level model in perturbation theory that depends on linear and nonlinear bias parameters as well as on the growth rate f of density fluctuations. The likelihood analysis takes advantage of a very large set of mock catalogs, enabling a robust estimation of the covariance properties for all multipoles. We compare the numerical estimate of the covariance matrix to its Gaussian prediction finding discrepancies of 10% or less for all configurations with the sole exception of the squeezed triangles in the monopole case. We find the range of validity of the tree-level model, for the total simulation volume of about 1000 h −3 Gpc 3 , reaches a maximum wavenumber of 0.08 h Mpc −1 for the monopole, while it is limited to 0.06 and 0.045 h Mpc −1 respectively for quadrupole and hexadecapole. Despite this, the addition of the quadrupole to the analysis allows for significant improvements on the determination of the model parameters and specifically on f , similarly to the power spectrum case. Finally, we compare our numerical estimate for the full covariance with its theoretical prediction in the Gaussian approximation and find the latter to work remarkably well in the context of simulation boxes with periodic boundary condition.

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“…The 3pt correlation function and its Fourier transform -the bispectrum -have been widely studied in the literature as the lowest higher-order statistics able to lift parameters degeneracies present at the 2pt level [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] and therefore to capture additional information [26][27][28]. In particular, by employing the bispectrum in addition to the power spectrum, constraints on neutrino masses sum can be improved [29][30][31][32][33], together with baryonic acoustic oscillations (BAO) [34][35][36] and relativistic effects [37][38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Integrated trispectrum detection from BOSS DR12 NGC CMASS

Gualdi,

Verde

2022

Preprint

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We present the first detection of the integrated trispectrum (i-trispectrum) monopole and quadrupoles signal from BOSS CMASS NGC DR12. Extending the FKP estimators formalism to the Fourier transform of the four-point correlation function, we test shot-noise subtraction, Gaussianity of the i-trispectrum data-vector, significance of the detection and similarity between the signal from the data and from the galaxy mock catalogues used to numerically estimate the covariance matrix. Using scales corresponding to modes from minimum k min = 0.03 h/Mpc to maximum k min = 0.15 h/Mpc, we find a detection in terms of distance from the null hypothesis of (10.4, 5.2, 8.3, 1.1, 3.1) σ-intervals for the i-trispectrum monopole and quadrupoles respectively. This quantifies the presence of the physical signal of the four-points statistics on BOSS data. For completeness the same analysis is also performed for power spectrum and bispectrum, both monopoles and quadrupoles.

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The Covariance of Squeezed Bispectrum Configurations

Cited by 9 publications

References 105 publications

Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

Fisher Forecasts for Primordial non-Gaussianity from Persistent Homology

The Halo Bispectrum Multipoles in Redshift Space

Integrated trispectrum detection from BOSS DR12 NGC CMASS

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