Violation of the Rotational Invariance in the CMB Bispectrum

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Abstract

We investigate a statistical anisotropy on the Cosmic Microwave Background (CMB) bispectrum, which can be generated from the primordial non-Gaussianity induced by quantum fluctuations of a vector field. We find new configurations in the multipole space of the CMB bispectrum given by \(\ell_1 = \ell_2 + \ell_3 + 2, |\ell_2 - \ell_3| - 2\) and their permutations, which violate the rotational invariance, such as an off-diagonal configuration in the CMB power spectrum. We also find that in a model presented by Yokoyama and Soda (2008), the amplitude of the statistically anisotropic bispectrum in the above configurations becomes as large as that in other configurations such as \(\ell_1 = \ell_2 + \ell_3\). As a result, it might be possible to detect these contributions in future experiments, which would give us novel information about the physics of the early Universe.

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Acoustic Signatures in the Primary Microwave Background Bispectrum

David Spergel, Eiichiro Komatsu (2000)

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 large angular scale, there is a simple relationship between the CMB temperature and the primordial curvature perturbation. 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. We find that the detection of the primary bispectrum by any kind of experiments should be problematic for the simple slow-roll inflationary 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 much more powerful tool than the 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.

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The inflationary prediction for primordial non-gaussianity

David H. Lyth, Yeinzon Rodríguez (2005)

We extend the \delta N formalism so that it gives all of the stochastic properties of the primordial curvature perturbation \zeta if the initial field perturbations are gaussian. The calculation requires only the knowledge of some family of unperturbed universes. A formula is given for the normalisation \fnl of the bispectrum of \zeta, which is the main signal of non-gaussianity. Examples of the use of the formula are given, and its relation to cosmological perturbation theory is explained.

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An All-Sky Analysis of Polarization in the Microwave Background

Uros Seljak, Matias Zaldarriaga (1996)

Using the formalism of spin-weighted functions we present an all-sky analysis of polarization in the Cosmic Microwave Background (CMB). Linear polarization is a second-rank symmetric and traceless tensor, which can be decomposed on a sphere into spin \(\pm 2\) spherical harmonics. These are the analog of the spherical harmonics used in the temperature maps and obey the same completeness and orthogonality relations. We show that there exist two linear combinations of spin \(\pm 2\) multipole moments which have opposite parities and can be used to fully characterize the statistical properties of polarization in the CMB. Magnetic-type parity combination does not receieve contributions from scalar modes and does not cross-correlate with either temperature or electric-type parity combination, so there are four different power spectra that fully characterize statistical properties of CMB. We present their explicit expressions for scalar and tensor modes in the form of line of sight integral solution and numerically evaluate them for a representative set of models. These general solutions differ from the expressions obtained previously in the small scale limit both for scalar and tensor modes. A method to generate and analyze all sky maps of temperature and polarization is given and the optimal estimators for various power spectra and their corresponding variances are discussed.

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Publication date Created: 04 July 2011

Publication date Updated: 2011-11-22

Article

DOI: 10.1143/PTP.126.923

ArXiV ID: 1107.0682

SO-VID: ca2e35f7-2446-4c74-832e-4ed11ab9f32e

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http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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Journal reference Prog. Theor. Phys. 126 (2011), 923-935

Comments 13 pages, 2 figures. Accepted for publication in PTP

Categories astro-ph.CO gr-qc hep-ph hep-th

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Violation of the Rotational Invariance in the CMB Bispectrum

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Core Readings in Statistical Mediation Analysis

Most cited references 10

Acoustic Signatures in the Primary Microwave Background Bispectrum

The inflationary prediction for primordial non-gaussianity

An All-Sky Analysis of Polarization in the Microwave Background

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