CMB Bispectrum from Primordial Scalar, Vector and Tensor non-Gaussianities

TL;DR

This paper develops a comprehensive formalism for analyzing the CMB bispectrum caused by primordial non-Gaussianities in scalar, vector, and tensor modes, providing a method to evaluate their observational signatures.

Contribution

It introduces an all-sky, invariant formalism for the CMB bispectrum including vector and tensor modes, and demonstrates its application with a specific scalar-graviton non-Gaussianity example.

Findings

The bispectrum depends on angular and polarization modes.

Estimated constraint on non-Gaussianity parameter g_tss from PLANCK.

The bispectrum scales as fectively with multipole actors.

Abstract

We present an all-sky formalism for the Cosmic Microwave Background (CMB) bispectrum induced by the primordial non-Gaussianities not only in scalar but also in vector and tensor fluctuations. We find that the bispectrum can be formed in an explicitly rationally invariant way by taking into account the angular and polarization dependences of the vector and tensor modes. To demonstrate this and present how to use our formalism, we consider a specific example of the correlation between two scalars and a graviton as the source of non-Gaussianity. As a result, we show that the CMB reduced bispectrum of the intensity anisotropies is evaluated as a function of the multipole and the coupling constant between two scalars and a graviton denoted by $g_{tss}$; $|b_{\ell \ell \ell}| \sim \ell^{-4} \times 8 \times 10^{-18} |g_{tss}|$. By estimating the signal-to-noise ratio, we find that the constraint as $|g_{tss}| < 6$ will be expected from the PLANCK experiment.