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

    Ali Nayeri*

    • *Contact author: nayeri@mit.edu

    Phys. Rev. D 114, 023508 – Published 7 July, 2026

    DOI: https://doi.org/10.1103/b4yl-qlxn

    Abstract

    We construct an explicit boundary-action realization of superoscillatory initial states (SIS) for inflation, in which quantum interference within a band-limited initial wave functional 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 λ≲0.05 for a representative feature centered near the first acoustic peak, Δk/k*=0.05 at k*=1.45×10−2  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.

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