Non-Gaussian estimates of tensions in cosmological parameters

Abstract Upon embedding the axion-inflation in the minimal left-right symmetric gauge extension of the SM with gauge group SU(2)L × SU(2)R × U(1)B−L, [1] proposed a new particle physics model for inflation. In this work, we present a more detailed analysis. As a compelling consequence, this setup provides a new mechanism for simultaneous baryogenesis and right-handed neutrino creation by the chiral anomaly of WR in inflation. The lightest right-handed neutrino is the dark matter candidate. This setup has two unknown fundamental scales, i.e., the scale of inflation and left-right symmetry breaking SU(2)R × U(1)B−L→ U(1)Y. Sufficient matter creation demands the left-right symmetry breaking scale happens shortly after the end of inflation. Interestingly, it prefers left-right symmetry breaking scales above 1010 GeV, which is in the range suggested by the non-supersymmetric SO(10) Grand Unified Theory with an intermediate left-right symmetry scale. Although WR gauge field generates equal amounts of right-handed baryons and leptons in inflation, i.e. B − L = 0, in the Standard Model sub-sector B − LSM ≠ 0. A key aspect of this setup is that SU(2)R sphalerons are never in equilibrium, and the primordial B − LSM is conserved by the Standard Model interactions. This setup yields a deep connection between CP violation in physics of inflation and matter creation (visible and dark); hence it can naturally explain the observed coincidences among cosmological parameters, i.e., ηB ≃ 0.3Pζ and ΩDM ≃ 5ΩB. The new mechanism does not rely on the largeness of the unconstrained CP-violating phases in the neutrino sector nor fine-tuned masses for the heaviest right-handed neutrinos. The SU(2)R-axion inflation comes with a cosmological smoking gun; chiral, non-Gaussian, and blue-tilted gravitational wave background, which can be probed by future CMB missions and laser interferometer detectors.

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Fast and easy super-sample covariance of large-scale structure observables

Astronomy and Astrophysics ◽

10.1051/0004-6361/201834343 ◽

2019 ◽

Vol 624 ◽

pp. A61 ◽

Cited By ~ 7

Author(s):

Fabien Lacasa ◽

Julien Grain

Keyword(s):

Large Scale ◽

Signal To Noise Ratio ◽

Cosmological Parameters ◽

Power Spectra ◽

Large Scale Structure ◽

Scale Structure ◽

Numerical Application ◽

Sample Covariance ◽

Non Gaussian ◽

Fast Prediction

We present a numerically cheap approximation to super-sample covariance (SSC) of large-scale structure cosmological probes, first in the case of angular power spectra. No new elements are needed besides those used to predict the considered probes, thus relieving analysis pipelines from having to develop a full SSC modeling, and reducing the computational load. The approximation is asymptotically exact for fine redshift bins Δz → 0. We furthermore show how it can be implemented at the level of a Gaussian likelihood or a Fisher matrix forecast as a fast correction to the Gaussian case without needing to build large covariance matrices. Numerical application to a Euclid-like survey show that, compared to a full SSC computation, the approximation nicely recovers the signal-to-noise ratio and the Fisher forecasts on cosmological parameters of the wCDM cosmological model. Moreover, it allows for a fast prediction of which parameters are going to be the most affected by SSC and at what level. In the case of photometric galaxy clustering with Euclid-like specifications, we find that σ8, ns, and the dark energy equation of state w are particularly heavily affected. We finally show how to generalize the approximation for probes other than angular spectra (correlation functions, number counts, and bispectra) and at the likelihood level, allowing for the latter to be non-Gaussian if necessary. We release publicly a Python module allowing the implementation of the SSC approximation and a notebook reproducing the plots of the article.

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The impact of braiding covariance and in-survey covariance on next-generation galaxy surveys

Astronomy and Astrophysics ◽

10.1051/0004-6361/201936683 ◽

2020 ◽

Vol 634 ◽

pp. A74 ◽

Cited By ~ 2

Author(s):

Fabien Lacasa

Keyword(s):

Cosmological Parameters ◽

Necessary Condition ◽

Angular Power Spectrum ◽

Galaxy Surveys ◽

Sample Covariance ◽

Error Bar ◽

Error Bars ◽

Non Gaussian ◽

The Impact ◽

Parameter Constraints

As galaxy surveys improve their precision thanks to lower levels of noise and the push toward small, non-linear scales, the need for accurate covariances beyond the classical Gaussian formula becomes more acute. Here I investigate the analytical implementation and impact of non-Gaussian covariance terms that I had previously derived for the galaxy angular power spectrum. Braiding covariance is such an interesting class of such terms and it gets contributions both from in-survey and super-survey modes, the latter proving difficult to calibrate through simulations. I present an approximation for braiding covariance which speeds up the process of numerical computation. I show that including braiding covariance is a necessary condition for including other non-Gaussian terms, namely the in-survey 2-, 3-, and 4-halo covariance. Indeed these terms yield incorrect covariance matrices with negative eigenvalues if considered on their own. I then move to quantify the impact on parameter constraints, with forecasts for a survey with Euclid-like galaxy density and angular scales. Compared with the Gaussian case, braiding and in-survey covariances significantly increase the error bars on cosmological parameters, in particular by 50% for the dark energy equation of state w. The error bars on the halo occupation distribution (HOD) parameters are also affected between 12% and 39%. Accounting for super-sample covariance (SSC) also increases parameter errors, by 90% for w and between 7% and 64% for HOD. In total, non-Gaussianity increases the error bar on w by 120% (between 15% and 80% for other cosmological parameters) and the error bars on HOD parameters between 17% and 85%. Accounting for the 1-halo trispectrum term on top of SSC, as has been done in some current analyses, is not sufficient for capturing the full non-Gaussian impact: braiding and the rest of in-survey covariance have to be accounted for. Finally, I discuss why the inclusion of non-Gaussianity generally eases up parameter degeneracies, making cosmological constraints more robust for astrophysical uncertainties. I released publicly the data and a Python notebook reproducing the results and plots of the article.

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Cosmological constraints with weak-lensing peak counts and second-order statistics in a large-field survey

Astronomy and Astrophysics ◽

10.1051/0004-6361/201629928 ◽

2017 ◽

Vol 599 ◽

pp. A79 ◽

Cited By ~ 20

Author(s):

Austin Peel ◽

Chieh-An Lin ◽

François Lanusse ◽

Adrienne Leonard ◽

Jean-Luc Starck ◽

...

Keyword(s):

Order Statistics ◽

Large Scale ◽

Signal To Noise Ratio ◽

Cosmological Parameters ◽

Stochastic Approach ◽

Large Field ◽

Weak Lensing ◽

Galaxy Surveys ◽

Non Gaussian ◽

Robust Likelihood

Peak statistics in weak-lensing maps access the non-Gaussian information contained in the large-scale distribution of matter in the Universe. They are therefore a promising complementary probe to two-point and higher-order statistics to constrain our cosmological models. Next-generation galaxy surveys, with their advanced optics and large areas, will measure the cosmic weak-lensing signal with unprecedented precision. To prepare for these anticipated data sets, we assess the constraining power of peak counts in a simulated Euclid-like survey on the cosmological parameters Ωm, σ8, and w0de. In particular, we study how Camelus, a fast stochastic model for predicting peaks, can be applied to such large surveys. The algorithm avoids the need for time-costly N-body simulations, and its stochastic approach provides full PDF information of observables. Considering peaks with a signal-to-noise ratio ≥ 1, we measure the abundance histogram in a mock shear catalogue of approximately 5000 deg2 using a multiscale mass-map filtering technique. We constrain the parameters of the mock survey using Camelus combined with approximate Bayesian computation, a robust likelihood-free inference algorithm. Peak statistics yield a tight but significantly biased constraint in the σ8–Ωm plane, as measured by the width ΔΣ8 of the 1σ contour. We find Σ8 = σ8(Ωm/ 0.27)α = 0.77-0.05+0.06 with α = 0.75 for a flat ΛCDM model. The strong bias indicates the need to better understand and control the model systematics before applying it to a real survey of this size or larger. We perform a calibration of the model and compare results to those from the two-point correlation functions ξ± measured on the same field. We calibrate the ξ± result as well, since its contours are also biased, although not as severely as for peaks. In this case, we find for peaks Σ8 = 0.76-0.03+0.02 with α = 0.65, while for the combined ξ+ and ξ− statistics the values are Σ8 = 0.76-0.01+0.02 and α = 0.70. We conclude that the constraining power can therefore be comparable between the two weak-lensing observables in large-field surveys. Furthermore, the tilt in the σ8–Ωm degeneracy direction for peaks with respect to that of ξ± suggests that a combined analysis would yield tighter constraints than either measure alone. As expected, w0de cannot be well constrained without a tomographic analysis, but its degeneracy directions with the other two varied parameters are still clear for both peaks and ξ±.

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2D-FFTLog: efficient computation of real-space covariance matrices for galaxy clustering and weak lensing

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa1726 ◽

2020 ◽

Vol 497 (3) ◽

pp. 2699-2714

Author(s):

Xiao Fang (方啸) ◽

Tim Eifler ◽

Elisabeth Krause

Keyword(s):

Large Scale ◽

Cosmological Parameters ◽

Real Space ◽

Covariance Matrices ◽

Weak Lensing ◽

Efficient Computation ◽

Galaxy Clustering ◽

Dark Energy Survey ◽

Stable Computation ◽

Non Gaussian

ABSTRACT Accurate covariance matrices for two-point functions are critical for inferring cosmological parameters in likelihood analyses of large-scale structure surveys. Among various approaches to obtaining the covariance, analytic computation is much faster and less noisy than estimation from data or simulations. However, the transform of covariances from Fourier space to real space involves integrals with two Bessel integrals, which are numerically slow and easily affected by numerical uncertainties. Inaccurate covariances may lead to significant errors in the inference of the cosmological parameters. In this paper, we introduce a 2D-FFTLog algorithm for efficient, accurate, and numerically stable computation of non-Gaussian real-space covariances for both 3D and projected statistics. The 2D-FFTLog algorithm is easily extended to perform real-space bin-averaging. We apply the algorithm to the covariances for galaxy clustering and weak lensing for a Dark Energy Survey Year 3-like and a Rubin Observatory’s Legacy Survey of Space and Time Year 1-like survey, and demonstrate that for both surveys, our algorithm can produce numerically stable angular bin-averaged covariances with the flat sky approximation, which are sufficiently accurate for inferring cosmological parameters. The code CosmoCov for computing the real-space covariances with or without the flat-sky approximation is released along with this paper.

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Gaussian and non-Gaussian estimates for heat kernels on the Sierpinski gasket

Dirichlet Forms and Stochastic Processes ◽

10.1515/9783110880052.283 ◽

2012 ◽

Cited By ~ 1

Author(s):

V. Metz ◽

K.-T. Sturm

Keyword(s):

Sierpinski Gasket ◽

Heat Kernels ◽

Sierpiński Gasket ◽

Non Gaussian ◽

Gaussian Estimates

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Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps – validation on simulations

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa2680 ◽

2020 ◽

Vol 498 (3) ◽

pp. 4060-4087

Author(s):

M Gatti ◽

C Chang ◽

O Friedrich ◽

B Jain ◽

D Bacon ◽

...

Keyword(s):

Dark Energy ◽

Cosmological Parameters ◽

Weak Lensing ◽

Subsequent Paper ◽

The Third ◽

Dark Energy Survey ◽

Simulated Likelihood ◽

Modelling Uncertainties ◽

Non Gaussian ◽

Energy Survey

ABSTRACT We present a simulated cosmology analysis using the second and third moments of the weak lensing mass (convergence) maps. The second moment, or variances, of the convergence as a function of smoothing scale contains information similar to standard shear two-point statistics. The third moment, or the skewness, contains additional non-Gaussian information. The analysis is geared towards the third year (Y3) data from the Dark Energy Survey (DES), but the methodology can be applied to other weak lensing data sets. We present the formalism for obtaining the convergence maps from the measured shear and for obtaining the second and third moments of these maps given partial sky coverage. We estimate the covariance matrix from a large suite of numerical simulations. We test our pipeline through a simulated likelihood analyses varying 5 cosmological parameters and 10 nuisance parameters and identify the scales where systematic or modelling uncertainties are not expected to affect the cosmological analysis. Our simulated likelihood analysis shows that the combination of second and third moments provides a 1.5 per cent constraint on S8 ≡ σ8(Ωm/0.3)0.5 for DES Year 3 data. This is 20 per cent better than an analysis using a simulated DES Y3 shear two-point statistics, owing to the non-Gaussian information captured by the inclusion of higher order statistics. This paper validates our methodology for constraining cosmology with DES Year 3 data, which will be presented in a subsequent paper.

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