Primordial Non-Gaussianity in the Cosmic Microwave Background

TL;DR

The paper surveys primordial non-Gaussianity as a probe of early-universe physics, anchored by the amplitude parameter $f_{ m NL}$ and the CMB bispectrum. It reviews inflationary theory, shapes of non-Gaussianity (local, equilateral, folded), and the mapping from primordial perturbations to CMB observables via transfer functions, culminating in optimal estimators for $f_{ m NL}$ that leverage temperature and polarization data. Current constraints from WMAP are tightening but still consistent with Gaussian initial conditions, while Planck and future missions are forecast to achieve dramatic improvements, potentially reaching $\\\Delta f_{ m NL}^{\\rm local} \\\approx 2$ and $\\\Delta f_{ m NL}^{\\rm equil} \\\approx 13$ (1$\\sigma$). The paper also discusses secondary non-primordial bispectra, their contaminations, and complementary probes such as the trispectrum, Minkowski functionals, and wavelet-based methods. Overall, the CMB bispectrum stands as a powerful discriminator among inflationary models, with ongoing and upcoming data expected to sharpen our understanding of the earliest moments of the universe.

Abstract

In the last few decades, advances in observational cosmology have given us a standard model of cosmology. We know the content of the universe to within a few percent. With more ambitious experiments on the way, we hope to move beyond the knowledge of what the universe is made of, to why the universe is the way it is. In this review paper we focus on primordial non-Gaussianity as a probe of the physics of the dynamics of the universe at the very earliest moments. We discuss 1) theoretical predictions from inflationary models and their observational consequences in the cosmic microwave background (CMB) anisotropies; 2) CMB--based estimators for constraining primordial non-Gaussianity with an emphasis on bispectrum templates; 3) current constraints on non-Gaussianity and what we can hope to achieve in the near future; and 4) non-primordial sources of non-Gaussianities in the CMB such as bispectrum due to second order effects, three way cross-correlation between primary-lensing-secondary CMB, and possible instrumental effects.

Figures (8)

• Figure 1: A toy scenario for the dynamics of the scalar field during inflation. During the flat part of potential, universe expand exponentially. When field reaches near the minima of the potential, the field oscillates and the radiation is generated.
• Figure 2: Evolution of comoving horizon and generation of perturbations in the inflationary universe. Figure from Ref. 2009arXiv0907.5424B.
• Figure 3: Shapes of Non-Gaussianity. The shape function $F(k_1, k_2, k_3)$ forms a triangle in Fourier space. The triangles are parametrized by rescaled Fourier modes, $x_2=k_2/k_1$ and $x_3=k_3/k_1$. Figure from Ref. 2009arXiv0907.5424B
• Figure 4: Plot of the function $F (1, x_2 , x_3 ) x^2_2 x^2_3$ for the Slow-Roll inflation as given by Eq. (21) (left panel) and the local distribution as given by Eq. (19) (right panel). The figures are normalized to have value 1 for equilateral configurations x2 = x3 = 1 and set to zero outside the region $1 - x_2 \leq x_3 \leq x_2$. Here $x3 \equiv k3 /k1$, $x2 \equiv k2 /k1$ and $\epsilon =\eta =1/30$. The figures are taken from Babich et al. 2003 Babich_etal_04.
• Figure 5: Plot of the function $F (1, x_2 , x_3 ) x^2_2 x^2_3$ for the inflation with higher derivatives as given by Eq. (23) (left panel) and the ghost inflation as given by Eq. (24) (right panel). The figures are normalized to have value 1 for equilateral configurations x2 = x3 = 1 and set to zero outside the region $1 - x_2 \leq x_3 \leq x_2$. Here $x3 \equiv k3 /k1$ and $x2 \equiv k2 /k1$. The figures are taken from Babich et al. 2003 Babich_etal_04