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 (though rotational invariance washes out the flat-sky limit) and adding polarization data.

Figure 1

Normalized parity-odd trispectrum, $\tau (\mathbf{b},B)$ measured from Planck data (blue), 300 FFP10 simulations (red), and 1000 GRF simulations (green) using the polybin code with ${\ell }_{\min }=3$, ${\ell }_{\max }=510$. The horizontal axis gives the bin index (with large-scale modes on the left, ordered with ${\ell }_1\le {\ell }_2$, ${\ell }_1\le {\ell }_3$, ${\ell }_3\le {\ell }_4$), and shaded regions show the $1\sigma$ variance from simulations (shown explicitly in the bottom panel). The variance is close to the Gaussian prediction (unity) but exhibits a slight enhancement due to the nontrivial mask and finite number of bias simulations, though the correlation matrix is consistent with the identity (see the Supplemental Material [47]).

Figure 2

Probability of parity violation in the Planck dataset. We plot the ${\chi }^2$ values (6) extracted from the Planck SMICA maps (blue), the FFP10 simulations (red), and GRF simulations (green), alongside the binned theoretical prediction (black). Deviation of the Planck results from the expected curves would give evidence for parity violation. Relative to the GRF simulations, the Planck data has a rank of $357/1000$ (i.e., a larger ${\chi }^2$ than that of 356 simulations), or $128/300$ with respect to FFP10, with the consistency of the two sets of simulations indicating that our pipeline is robust and not affected by residual foregrounds. For the theoretical distribution, we find a ${\chi }^2$ probability to exceed of 63%, though caution that the likelihood may be non-Gaussian. Overall, we find no evidence for parity violation in the Planck dataset.