Discrete Quantum Spectrum of Observable Correlations from Inflation

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The decoherence of quantum fluctuations into classical perturbations during inflation is discussed. A simple quantum mechanical argument, using a spatial particle wavefunction rather than a field description, shows that observable correlations from inflation must have a discrete spectrum, since they originate and freeze into the metric within a compact region. The number of discrete modes is estimated using a holographic bound on the number of degrees of freedom. The discreteness may be detectable in some models; for example, if there is a fundamental universal frequency spectrum, the inflationary gravitational wave background may be resolvable into discrete emission lines.