At linear order the only expected source of a curl-like, B mode, polarization pattern in the cosmic microwave background (CMB) is primordial gravitational waves. At second-order B modes are also produced from purely scalar, density, initial conditions. Unlike B modes from primordial gravitational waves, these B modes are expected to be non-Gaussian and not independent from the temperature and gradientlike polarization, E mode, CMB anisotropies. We find that the three point function between a second-order B mode and two first-order T/E modes is a powerful probe of second-order B modes. We focus on the contribution to the three point function arising from nonlinear evolution and scattering processes before the end of recombination as this provides new information on the universe at $z>1000$. We find that this contribution can be separated from the other contributions and is measurable at $\sim 2.5\sigma$ by CMB experiments with noise levels of $\sim 1\mu$ Karcmin and delensing efficiencies $\ge 90\%$, such as the proposed PICO satellite. We show that approximately half of the total signal arises from nonlinearly induced vector and tensor metric perturbations, as evaluated in the Newtonian gauge. This bispectrum is a unique probe of these perturbations in the CMB, as their contribution to the power spectrum is suppressed. An important feature of this bispectrum is that the detectability will increase with decreasing experimental noise, in the absence of primordial B modes, provided that delensing efficiencies improve in parallel.

• Received 22 March 2021
• Revised 30 June 2021
• Accepted 28 October 2021

DOI:https://doi.org/10.1103/PhysRevD.104.103527