Holographic Discreteness of Inflationary Perturbations

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  • 3 January 2002
Abstract
The cosmological holographic principle, which states that the total observable entropy of de Sitter space (including gravitational quanta) is bounded by S< pi/H^2, where H is the expansion rate, is used to estimate the magnitude of quantum-gravitational effects on inflationary perturbations. The constraint is shown to imply that the initial states of the vacua for perturbation modes are not independent, and that field theory is not a reliable tool to study transplanckian effects on mode amplitudes and phases. It is argued that holographic discreteness alters the continuous, random-phase gaussian distribution predicted by standard field theory for fluctuations in the inflaton field that lead to cosmic background anisotropy. A toy model, applied in the context of scalar inflaton perturbations produced during standard slow-roll inflation, and assuming that horizon-scale perturbations ``freeze out'' in discrete steps separated by one bit of observable information, predicts discrete steps in anisotropy separated by Delta T ~ 10^{-10} K. It is conjectured that the Hilbert space of a typical observable perturbation is equivalent to that of no more than about 10^5 binary spins (approximately the inverse of the final scalar metric perturbation amplitude, independent of H and other parameters), and that some manifestations of this discreteness may be observable.

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