Statistical tests for the Gaussian nature of primordial fluctuations through CBR experiments

Luo, Xiaochun

doi:10.1103/physrevd.49.3810

Cited by 25 publications

(21 citation statements)

References 67 publications

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“…(5,6). We also assume here that the evolution of scalar field fluctuations can be studied in a particular gauge where metric perturbations can be neglected compared with those of the scalar field itself.…”

Section: B the Warm Inflation Bispectrummentioning

confidence: 99%

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Non-Gaussian signatures in the cosmic background radiation from warm inflation

et al. 2002

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We calculate the bispectrum of the gravitational field fluctuations generated during warm inflation, where dissipation of the vacuum potential during inflation is the mechanism for structure formation. The bispectrum is non-zero because of the self-interaction of the scalar field. We compare the predictions with those of standard, or 'supercooled', inflationary models, and consider the detectability of these levels of non-Gaussianity in the bispectrum of the cosmic microwave background. We find that the levels of non-Gaussianity for warm and supercooled inflation are comparable, and over-ridden by the contribution to the bispectrum due to other physical effects. We also conclude that the resulting bispectrum values will be undetectable in the cosmic microwave background for both the MAP and Planck Surveyor satellites. PACS number(s): 98.80. Cq, 98.70.Vc, 98.80.Es

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Section: B the Warm Inflation Bispectrummentioning

confidence: 99%

“…There are many ways of testing the Gaussian hypothesis, such as the genus and EulerPoincaré statistic [4][5][6][7], studies of tensor modes in the CMB [8], excursion set properties [9,10], peak statistics [11][12][13][14] and wavelet analyses (e.g. [15][16][17]).…”

mentioning

confidence: 99%

Non-Gaussian signatures in the cosmic background radiation from warm inflation

et al. 2002

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“…But many models of the early universe, like inflation (e.g. Bernardeau & Uzan 2002 and references therein), super strings or topological defects, predict non-Gaussian contributions to the initial fluctuations (Luo 1994b;Jaffe 1994;Gangui et al 1994). Furthermore, any nonlinearity in their evolution introduces additional non-Gaussian signatures.…”

Section: Introductionmentioning

confidence: 99%

Non-Gaussianity: Comparing wavelet and Fourier based methods

Aghanim

Kunz

Castro

et al. 2003

A&A

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Abstract. In the context of the present and future Cosmic Microwave Background (CMB) experiments, going beyond the information provided by the power spectrum has become necessary in order to tightly constrain the cosmological model. The non-Gaussian signatures in the CMB represent a very promising tool to probe the early universe and the structure formation epoch. We present the results of a comparison between two families of non-Gaussian estimators: The first act on the wavelet space (skewness and excess kurtosis of the wavelet coefficients) and the second group on the Fourier space (bi-and trispectrum). We compare the relative sensitivities of these estimators by applying them to three different data sets meant to reproduce the majority of possible non-Gaussian contributions to the CMB. We find that the skewness in the wavelet space is slightly more sensitive than the bispectrum. For the four point estimators, we find that the excess kurtosis of the wavelet coefficients has very similar capabilities than the diagonal trispectrum while a near-diagonal trispectrum seems to be less sensitive to non-Gaussian signatures.

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“…M(k, y) = exp(−ik · y), and j labels the wavevector k. Several physically-motivated models for primordial non-Gaussianity are expressed as local transformations of an underlying Gaussian field. For example, the non-Gaussianity of the so-called local type [5,7,30] is given by…”

Section: Set-upmentioning

confidence: 99%

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

Verde¹,

Jiménez²,

Álvarez‐Gaumé³

et al. 2013

J. Cosmol. Astropart. Phys.

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Abstract. 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 nonGaussianity 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 more than 7σ for f NL 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.

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Statistical tests for the Gaussian nature of primordial fluctuations through CBR experiments

Cited by 25 publications

References 67 publications

Non-Gaussian signatures in the cosmic background radiation from warm inflation

Non-Gaussian signatures in the cosmic background radiation from warm inflation

Non-Gaussianity: Comparing wavelet and Fourier based methods

Multi-variate joint PDF for non-Gaussianities: exact formulation and generic approximations

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