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Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations
We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussian...
Autores principales: | , , , , |
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Lenguaje: | eng |
Publicado: |
2013
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1088/1475-7516/2013/06/023 http://cds.cern.ch/record/1510202 |
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author | Verde, Licia Jimenez, Raul Alvarez-Gaume, Luis Heavens, Alan F. Matarrese, Sabino |
author_facet | Verde, Licia Jimenez, Raul Alvarez-Gaume, Luis Heavens, Alan F. Matarrese, Sabino |
author_sort | Verde, Licia |
collection | CERN |
description | We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter. |
id | cern-1510202 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2013 |
record_format | invenio |
spelling | cern-15102022023-03-14T19:42:47Zdoi:10.1088/1475-7516/2013/06/023http://cds.cern.ch/record/1510202engVerde, LiciaJimenez, RaulAlvarez-Gaume, LuisHeavens, Alan F.Matarrese, SabinoMulti-variate joint PDF for non-Gaussianities: exact formulation and generic approximationsAstrophysics and AstronomyWe provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.We provide an exact expression for the multi-variate jointprobability distribution function of non-Gaussian fieldsprimordially arising from local transformations of a Gaussianfield. This kind of non-Gaussianity is generated in many models ofinflation. We apply our expression to the non-Gaussianity estimationfrom Cosmic Microwave Background maps and the halo mass functionwhere we obtain analytical expressions. We also provide analyticapproximations and their range of validity. For the Cosmic MicrowaveBackground we give a fast way to compute the PDF which is valid upto more than 7σ for fNL values (both true andsampled) not ruled out by current observations, which consists ofexpressing the PDF as a combination of bispectrum and trispectrum ofthe temperature maps. The resulting expression is valid for any kindof non-Gaussianity and is not limited to the local type. The aboveresults may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.We provide an exact expression for the multi-variate joint probability distribution function of non-Gaussian fields primordially arising from local transformations of a Gaussian field. This kind of non-Gaussianity is generated in many models of inflation. We apply our expression to the non- Gaussianity estimation from Cosmic Microwave Background maps and the halo mass function where we obtain analytical expressions. We also provide analytic approximations and their range of validity. For the Cosmic Microwave Background we give a fast way to compute the PDF which is valid up to 7{\sigma} for fNL values (both true and sampled) not ruled out by current observations, which consists of expressing the PDF as a combination of bispectrum and trispectrum of the temperature maps. The resulting expression is valid for any kind of non-Gaussianity and is not limited to the local type. The above results may serve as the basis for a fully Bayesian analysis of the non-Gaussianity parameter.arXiv:1301.6017oai:cds.cern.ch:15102022013-01-28 |
spellingShingle | Astrophysics and Astronomy Verde, Licia Jimenez, Raul Alvarez-Gaume, Luis Heavens, Alan F. Matarrese, Sabino Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations |
title | Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations |
title_full | Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations |
title_fullStr | Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations |
title_full_unstemmed | Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations |
title_short | Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations |
title_sort | multi-variate joint pdf for non-gaussianities: exact formulation and generic approximations |
topic | Astrophysics and Astronomy |
url | https://dx.doi.org/10.1088/1475-7516/2013/06/023 http://cds.cern.ch/record/1510202 |
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