Discrete Spectrum of Inflationary Fluctuations

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  • 20 October 2003
Abstract
It is proposed that a holographic bound on entropy during inflation leads to a discrete spectrum of cosmological perturbations instead of the continuous Gaussian spectrum predicted by field theory. Discrete amplitude spectra of field fluctuation modes and their conversion to quasi-classical perturbations are studied using modifications of a simple quantum harmonic oscillator. The covariant entropy bound is applied to slow-roll inflation to show that the maximum ``frozen entropy'' of fluctuations per e-folding is about 1.0x10^9 in each Hubble volume. If this bound is interpreted in terms of gravitationally entangled spatial field modes, it implies a discrete spectrum of at most 10^9 spatial modes per mode volume, although far fewer (perhaps about 10^5) may participate in the eigenstates that span vacuum fluctuation states. It is suggested that the resulting discrete spectrum in the spatial structure of large-scale perturbations may account for statistical anomalies in the anisotropy measured by WMAP.

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