Acoustic signatures in the primary microwave background bispectrum

By E. Komatsu, David N. Spergel. 2000

959 citations recorded by the source corpus.

If the primordial fluctuations are non-Gaussian, then this non-Gaussianity will be apparent in the cosmic microwave background (CMB) sky. With their sensitive all-sky observation, MAP and Planck satellites should be able to detect weak non-Gaussianity in the CMB sky. On a large angular scale, there is a simple relationship between the CMB temperature and the primordial curvature perturbation: $\ensuremath{\Delta}T/T=\ensuremath{-}\ensuremath{\Phi}/3.$ On smaller scales, however, the radiation transfer function becomes more complex. In this paper, we present the angular bispectrum of the primary CMB anisotropy that uses the full transfer function. We find that the bispectrum has a series of acoustic peaks that change a sign and a period of acoustic oscillations is twice as long as that of the angular power spectrum. Using a single non-linear coupling parameter to characterize the amplitude of the bispectrum, we estimate the expected signal-to-noise ratio for COBE, MAP, and Planck experiments. In order to detect the primary CMB bispectrum by each experiment, we find that the coupling parameter should be larger than 600, 20, and 5 for COBE, MAP, and Planck experiments, respectively. Even for the ideal noise-free and infinitesimal thin-beam experiment, the parameter should be larger than 3. We have included effects from the cosmic variance, detector noise, and foreground sources in the signal-to-noise estimation. Since the simple inflationary scenarios predict that the parameter is an order of 0.01, the detection of the primary bispectrum by any kind of experiments should be problematic for those scenarios. We compare the sensitivity of the primary bispectrum to the primary skewness and conclude that, when we can compute the predicted form of the bispectrum, it becomes a ``matched filter'' for detecting the non-Gaussianity in the data and a much more powerful tool than the skewness. For example, we need the coupling parameter of larger than 800, 80, 70, and 60 for each relevant experiment in order to detect the primary skewness. We also show that MAP and Planck can separate the primary bispectrum from various secondary bispectra on the basis of the shape difference. The primary CMB bispectrum is a test of the inflationary scenario and also a probe of the non-linear physics in the very early universe.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/fe529a44c5952f047941113d979d55f206f30b76

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Citations in the corpus

Inflationary trispectrum from graviton exchange (2008, background): “Occasionally, fNL is referred to as the non-linearity parameter [2, 3].”
The holographic universe (2010, result): “Our results indicate, however, that the non-Gaussianity parameter f local NL [30] is independent of N to leading order, consistent with current observational evidence [6].”
Rapidly-Varying Speed of Sound, Scale Invariance and Non-Gaussian Signatures (2008, background): “In the contracting case, however, the non-Gaussian signal peaks for squeezed triangles, corresponding to the so-called local form [27].”
Large-scale non-Gaussian mass function and halo bias: tests on N-body simulations (2009, background): “…from Gaussian initial conditions are commonly parametrized in terms of the dimensionless f NL parameter (Salopek & Bond 1990; Gangui et al. 1994; Verde et al. 2000; Komatsu & Spergel 2001): = φ + fNL(φ2 − 〈φ2〉) , (1) where denotes the gravitational potential and φ is a Gaussian random field.”
The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias (2007, background): “Local model The first one is described by the local expression for Bardeen’s curvature perturbations during the matter era, Φ(x), in position space (Gangui et al. 1994; Verde et al. 2000; Komatsu & Spergel 2001) Φ(x) = ΦG(x) + f loc.”
PRIMORDIAL NON-GAUSSIANITY, SCALE-DEPENDENT BIAS, AND THE BISPECTRUM OF GALAXIES (2009, background): “…a review), whereas the first term is the effect of the primordial non-Gaussianity of the “local type,” whose Bardeen’s curvature perturbation, Φ, is written as Φ(x) = φ(x) + fNLφ 2(x), where φ is a Gaussian field (Salopek & Bond 1990; Gangui et al. 1994; Verde et al. 2000; Komatsu & Spergel 2001).”
Planck 2018 results. IX. Constraints on primordial non-Gaussianity (2019, methodology): “In order to estimate the fNL value for a given primordial shape, we need to compute a theoretical prediction of the corresponding CMB bispectrum ansatz bth`1`2`3 and fit it to the observed 3-point function (see e.g., Komatsu & Spergel 2001).”
Planck 2015 results. XVII. Constraints on primordial non-Gaussianity (2015, positive): “(49) This constant is usually noted bPS or bsrc in the literature (e.g., Komatsu & Spergel 2001).”
Effects of scale-dependent non-Gaussianity on cosmological structures (2007, neutral): “Contents”