Searching for unparticles with the cosmic microwave background

Multi-field models of inflation typically assume that interactions between particles are weak and can be treated perturbatively. Strongly-coupled models provide an intriguing alternative and may offer novel inflationary phenomenology. In this work, we study the ``unparticle'' scenario, where the inflaton is weakly mixed with a strongly-coupled sector, specified by a (gapless) conformal field theory. For certain choices of the conformal scaling dimension, $\Delta$, the exchange of unparticles leads to distinctive non-Gaussian features in the primordial curvature distribution, including bispectra with enhanced squeezed limits and oscillations close to the equilateral regime. Efficiently analyzing these models using Cosmic Microwave Background (CMB) data is a challenge since (a) they are defined over a wide range of $\Delta$, (b) the novel phenomenology is not restricted to squeezed limits, (c) the bispectra are non-factorizable in momenta, (d) the signatures are often highly degenerate with single-field self-interactions. Here, we overcome these limitations using a library of tools, including recently developed neural-network factorization schemes, principal component analyses (with carefully-chosen bases), and optimal CMB estimators. Our combined pipeline condenses 161 non-separable unparticle bispectra into just 7 factorizable forms, with negligible loss of signal-to-noise. We apply the model to the latest temperature and polarization data from \textit{Planck}, asking two key questions: (1) can we detect unparticles? (2) can we distinguish between unparticle bispectra and single-field self-interactions? Across $1\leq \Delta\leq 9$, we find a maximal signal-to-noise of $1.2\sigma$ (or $1.7\sigma$ in an analysis marginalized over self-interactions), implying no evidence for new physics. We also place the first CMB constraints on the modified consistency-condition-satisfying orthogonal bispectrum typically used in galaxy survey analyses with $f^{\rm orth^*}_{\rm NL} = -12\pm12$. While many unparticle models are very degenerate with the single-field shapes (and highly correlated amongst themselves), certain values of $\Delta$ (close to half-integers) have very different shapes, offering an intriguing discovery channel for future experiments. The methods developed herein can be directly applied to other classes of strongly-coupled sectors (and beyond), motivating the exploration of models beyond the standard weakly-coupled paradigm.