Tests for Non-Gaussian Statistics in the DMR Four-Year Sky Maps

Kogut, A.; Banday, A. J.; Bennett, C. L.; Górski, K. M.; Hinshaw, G.; Smoot, George F.; Wright, E. L.

doi:10.1086/310078

Cited by 134 publications

(134 citation statements)

References 16 publications

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“…Several techniques have been developed to test COBE and future datasets for deviations from gaussianity (e.g. Kogut et al, 1996b;. Most tests have proven negative, but a few claims of non-gaussianity have been made.…”

Section: Gaussianity Of the Cmb Anisotropiesmentioning

confidence: 99%

The cosmic microwave background radiation

Gawiser

Silk

2000

Physics Reports

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Section: Gaussianity Of the Cmb Anisotropiesmentioning

confidence: 99%

The cosmic microwave background radiation

Gawiser

Silk

2000

Physics Reports

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“…These predictions are: a) the multipole power spectrum of the fluctuations that is approximately flat for low multipoles (C l ∝ 1 l(l+1) for 2 ≤ l ≤ 30); b) the right location and amplitude of the first acoustic (or "Doppler") peak of ∆T T at l = 200−250; c) the Gaussian statistics of the fluctuations (see, e.g., the 4-year COBE results for the spectrum [1] and statistics [2] of the fluctuations with l ≤ 20, and the results of the Saskatoon-95 experiment for l = 80 − 350 [3] and the CAT experiment for l = 400−600 [4]). Of course, this does not exclude alternative theories of the early Universe (e.g., topological defects) provided they are able to produce approximately the same observational predictions.…”

Section: Introductionmentioning

confidence: 99%

Quantum-to-classical transition of cosmological perturbations for non-vacuum initial states

1997

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Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schrödinger representations, as well as using the Wigner function. We show explicitly that these three approaches lead to the same prediction in the limit of large squeezing (i.e. when the squeezing parameter |r k | → ∞): each two-modes quantum state (k, − k) of these perturbations is equivalent to a classical perturbation that has a stochastic amplitude, obeying a non-gaussian statistics which depends on the initial state, and that belongs to the quasi-isotropic mode (i.e. it possesses a fixed phase). The Wigner function is not everywhere positive for any finite r k , hence its interpretation as a classical distribution function in phase space is impossible without some coarse graining procedure. However, this does not affect the transition to semiclassical behaviour since the Wigner function becomes concentrated near a classical trajectory in phase space when |r k | → ∞ even without coarse graining. Deviations of the statistics of the perturbations in real space from a Gaussian one lie below the cosmic variance level for the N -particles initial states with N = N (|k|) but may be observable for other initial states without statistical isotropy or with correlations between different k modes. As a way to look for this effect, it is proposed to measure 0 the kurtosis of the angular fluctuations of the cosmic microwave background temperature.

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“…Many studies have aimed at characterising the statistical properties of the COBE/DMR data (Amendola 1996;Kogut et al 1996;Ferreira et al 1998;Heavens 1998;Pando et al 1998b;Schmalzing & Gorski 1998;Bromley & Tegmark 1999;Magueijo 2000;Mukherjee et al 2000). These investigations have relied on various statistical indicators both in the real space (e.g.…”

Section: Introductionmentioning

confidence: 99%

Using the COBE/DMR data as a test-bed for normality assessments

Aghanim¹,

Forni²,

Bouchet³

2001

A&A

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Abstract.A very important property of a statistical distribution is to know whether it obeys Gaussian statistics or not. On the one hand, it is of paramount importance in the context of CMB anisotropy studies, since deviations from a Gaussian distribution could indicate the presence of uncorrected measurement systematics, of remaining fluctuations contributed by foregrounds, of deviations from the simplest models of inflation or of topological defects. On the other hand, looking for a non-Gaussian signal is a very ill-defined task and performances of various assessment methods may differ widely when applied in different contexts. In previous studies, we introduced a sensitive wavelet-based method which we apply here to the COBE/DMR data set, already extensively studied, using different approaches. This provides an objective way to compare methods. It turns out that our multi-scale wavelet decomposition is a sensitive method. Yet, we show that the results are rather sensitive to the choice of both the decomposition scheme and the wavelet basis. We find that the detection of the non-Gaussian signature is "marginal" with a probability of at most 99%.

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Tests for Non-Gaussian Statistics in the DMR Four-Year Sky Maps

Cited by 134 publications

References 16 publications

The cosmic microwave background radiation

The cosmic microwave background radiation

Quantum-to-classical transition of cosmological perturbations for non-vacuum initial states

Using the COBE/DMR data as a test-bed for normality assessments

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