Superoscillatory initial states during inflation: theory, CMB constraints, and prospects for galaxy clustering

We construct an explicit boundary-action realization of superoscillatory initial states (SIS) for inflation, in which quantum interference within a band-limited initial wavefunctional generates a spectrally localized Bogoliubov excitation with a rapidly winding phase. Starting from a quadratic boundary term on the initial time surface, we derive the Bogoliubov coefficients and the resulting primordial curvature spectrum, obtaining a localized oscillatory feature fixed by the superoscillatory parameters $(a,N)$ rather than imposed phenomenologically. We compute the projection of this feature onto CMB angular power spectra and show that transfer-function smearing strongly suppresses the oscillatory component; full CAMB calculations confirm the qualitative effect and show that a simple Gaussian approximation overestimates the peak signal by about a factor of three. Using Planck 2018 TT data, we obtain an indicative matched-filter bound $\lambda \lesssim 0.05$ for a representative feature centered near the first acoustic peak, $\Delta k/k_* = 0.05$ at $k_* = 1.45\times 10^{-2}\,\mathrm{Mpc}^{-1}$. We further derive correlated predictions for polarization and the bispectrum, identify structural constraints that distinguish SIS from generic excited-state models, and show that galaxy clustering provides a qualitatively more powerful probe because it preserves the full oscillatory structure that CMB projection suppresses. This framework provides a concrete and testable realization of how initial-state quantum interference can imprint itself on cosmological observables.