Do the CMB Temperature Fluctuations Conserve Parity?

Observations of the Cosmic Microwave Background (CMB) have cemented the notion that the large-scale Universe is both statistically homogeneous and isotropic. But is it invariant also under reflections? To probe this we require parity-sensitive statistics: for scalar observables, the simplest is the trispectrum. We make the first measurements of the parity-odd scalar CMB, focusing on the large-scale ($2<\ell<510$) temperature anisotropies measured by Planck. This is facilitated by new quasi-maximum-likelihood estimators for binned correlators, which account for mask convolution and leakage between even- and odd-parity components, and achieve ideal variances within $\approx 20\%$. We perform a blind test for parity violation by comparing a $\chi^2$ statistic from Planck to theoretical expectations, using two suites of simulations to account for the possible likelihood non-Gaussianity and residual foregrounds. We find consistency at the $\approx 0.4\sigma$ level, yielding no evidence for novel early-Universe phenomena. The measured trispectra allow for a wealth of new physics to be constrained; here, we use them to constrain eight primordial models, including Ghost Inflation, Cosmological Collider scenarios, and Chern-Simons gauge fields. We find no signatures of new physics, with a maximal detection significance of $2.0\sigma$. Our results also indicate that the recent parity excesses seen in the BOSS galaxy survey are not primordial in origin, given that the CMB dataset contains roughly $250\times$ more primordial modes, and is far easier to interpret, given the linear physics, Gaussian statistics, and accurate mocks. Tighter CMB constraints can be wrought by including smaller scales and adding polarization data.