On CMB B-Mode Non-Gaussianity

TL;DR

This paper demonstrates that the CMB $B$-mode, when cross-correlated with two temperature modes as the $\langle BTT \rangle$ bispectrum, yields a powerful probe of primordial non-Gaussianity involving one tensor and two scalar fluctuations. Building on Maldacena's tensor–scalar–scalar template, the authors derive the flat-sky form of $\langle BTT \rangle$, connect it to transfer functions, and quantify its sensitivity via forecasts for Planck, current ground-based surveys, and future CMB-S4-like experiments. They show that for small tensor-to-scalar ratio $r$, $\sqrt{r}\,f_{\rm NL}^{h\zeta\zeta}$ can be constrained with roughly $\mathcal{O}(0.1)$ precision (per sky fraction), improving significantly over $TTT$-based bounds and opening a new window into early-universe physics. The work emphasizes the complementary nature of tensor non-Gaussianity to scalar NG tests and suggests extensions to full-sky analyses and other $B$-involving bispectra, highlighting the potential of future satellites to exploit this channel.

Abstract

We study the degree to which the cosmic microwave background (CMB) can be used to constrain primordial non-Gaussianity involving one tensor and two scalar fluctuations, focusing on the correlation of one polarization $B$ mode with two temperature modes. In the simplest models of inflation, the tensor-scalar-scalar primordial bispectrum is non-vanishing and is of the same order in slow-roll parameters as the scalar-scalar-scalar bispectrum. We calculate the $\langle BTT\rangle$ correlation arising from a primordial tensor-scalar-scalar bispectrum, and show that constraints from an experiment like CMB-Stage IV using this observable are more than an order of magnitude better than those on the same primordial coupling obtained from temperature measurements alone. We argue that $B$-mode non-Gaussianity opens up an as-yet-unexplored window into the early Universe, demonstrating that significant information on primordial physics remains to be harvested from CMB anisotropies.

Figures (8)

• Figure 1: Two triangles in multipole space that are mirrored images of one another. The three-point function $\langle ETT \rangle$ takes the same value on both configuration, whereas $\langle BTT \rangle$ changes sign.
• Figure 2: Two unique slices showing the primordial tensor-scalar-scalar bispectrum from single-field slow-roll inflation with $k_3$ representing the wave vector of the tensor. Left: The bispectrum is enhanced when $k_3 \ll k_1 \sim k_2$ (top left corner). The enfolded limit, i.e. $k_1 + k_2 = k_3$ (bottom left edge), is suppressed, since then all momenta are aligned. Right: When one or both scalar momenta $k_1$ and $k_2$ are aligned with the tensor momentum $k_3$ (bottom left edge) the spectrum is suppressed as compared to the equilateral configuration (top right).
• Figure 3: The $\langle BTT \rangle$ bispectrum in the fly-sky limit computed from Eq. \ref{['eq:BTTbispectrum2']} normalized using the analytical form of the local $\langle TTT \rangle$ bispectrum. We see explicitly that the $\langle BTT \rangle$ bispectrum changes sign under the interchange of of the two $T$ multipoles $\ell_1$ and $\ell_2$ and vanishes when $\ell_1 = \ell_2$. The overall amplitude of $\langle BTT \rangle$ for our chosen template is almost three orders of magnitude smaller than the local template $\langle TTT \rangle$ bispectrum from scalars.
• Figure 4: Top: the B-mode power spectrum computed on the full sky and in the flat-sky, thin-shell, approximation. The flat-sky approximation holds all the way down to $\ell \simeq 10$. Bottom: the local-type temperature bispectrum in the full sky and flat sky (thin-shell) for $\ell_1 = \ell_2=\ell_3$. There are some differences on large scales, but for computing the signal-to-noise ratio we do not expect these to lead to significant deviations. Note that for purposes of presentation, the total spectrum is divided by the large scale analytical limit of the local bispectrum. FergussonBisShape2009MoritzEtAlResonantBispectrum.
• Figure 5: Density plot showing the CMB modes to be measured in order to obtain a detection of the $\langle BTT \rangle$ bispectrum, showing the contributions to the inverse noise or Fisher matrix element. The color map on the bottom left, which uses a linear scale, shows the contribution as a function of the $B$ multipole and one of the two $T$ multipoles for the CMB-S4 case. The other panels show the collapsed one-dimensional distributions for CMB-S4 as well as three other cases. The signal is concentrated in slices with small $\ell_B$ and a wide range of values of $\ell_T$. We show constraints from several experiments, assuming no sample variance in the $B$ modes, as well as with the cosmic variance limit for $r = 0.01$.