Holographic Discreteness of Inflationary Perturbations

Abstract

The holographic entropy bound is used to estimate the quantum-gravitational discreteness of inflationary perturbations. In the context of scalar inflaton perturbations produced during standard slow-roll inflation, but assuming that horizon-scale perturbations ``freeze out'' in discrete steps separated by one bit of total observable entropy, it is shown that the Hilbert space of a typical horizon-scale inflaton perturbation is equivalent to that of about 10^5 binary spins-- approximately the inverse of the final scalar metric perturbation amplitude, independent of other parameters. Holography thus suggests that in a broad class of fundamental theories, inflationary perturbations carry a limited amount of information (about 10^5 bits per mode) and should therefore display discreteness not predicted by the standard field theory. Some manifestations of this discreteness may be observable in cosmic background anisotropy.

13 pages, Latex, 4 figures, to appear in Phys. Rev. D. New figures and references added

References in corpus (3)

• The holographic principle
• Signatures of Short Distance Physics in the Cosmic Microwave Background
• Building blocks of a black hole

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