# Constraining graviton non-Gaussianity through the CMB bispectra

## TL;DR

This paper investigates how future CMB experiments can detect or constrain tensor non-Gaussianities from the (Weyl)^3 term during inflation, providing bounds on the strength of higher derivative gravitational interactions.

## Contribution

It provides forecasts for detecting the (Weyl)^3 tensor non-Gaussianity using upcoming CMB bispectrum measurements, linking theoretical parameters to observational sensitivities.

## Key findings

- Forthcoming experiments could detect the (Weyl)^3 term if L > 3.2 x 10^5 M_p^{-1}.
- Current bounds set the upper limit at M_p^4 L^4 ≈ 1.1 x 10^{19} r^{-4}.
- Detection would confirm higher derivative corrections in inflationary gravity.

## Abstract

Tensor non-Gaussianities are a key ingredient to test the symmetries and the presence of higher spin fields during the inflationary epoch. Indeed, the shape of the three point correlator of the graviton is totally fixed by the symmetries of the de Sitter stage and, in the case of parity conservation, gets contributions only from the ordinary gravity action plus a higher derivative term called the (Weyl)$^3$ action. We discuss current and future bounds on the three point tensor contribution from the (Weyl)$^3$ term using cosmic microwave background (CMB) bispectra. Our results indicate that forthcoming experiments, such as LiteBIRD, CMB-S4 and CORE, will detect the presence of the (Weyl)$^3$ term if $M_p^4 L^4 \sim 10^{17} r^{-4}$, where $L$ parametrizes the strength of the (Weyl)$^3$ term and $r$ is the tensor-to-scalar ratio, which corresponds to $L\gtrsim 3.2 \times 10^5 M_p^{-1}$, while the current upper limit is $M_p^4 L^4 = (1.1 \pm 4.0) \times 10^{19} r^{-4}$ (68%CL).