On Holography and Cosmology

TL;DR

This paper examines holographic bounds in inhomogeneous universes, highlighting their complexity and proposing a simplified version that avoids caustics, thereby clarifying the practical and theoretical challenges of applying holography to cosmology.

Contribution

It introduces a modified holographic proposal that simplifies light sheets by ending them on the past boundary, addressing issues of complexity and invariance in inhomogeneous universes.

Findings

Holographic bounds involve complex, possibly fractal light sheets in inhomogeneous universes.

The proposed modification simplifies light sheets by ending on the past boundary.

Practical application of holography to the cosmos faces significant theoretical and operational challenges.

Abstract

We consider a recent generalisation by Bousso of an earlier holography proposal by Fischler and Susskind. We demonstrate that in general inhomogeneous universes such a proposal would involve extremely complicated - possibly fractal - light sheets. Furthermore, in general such a light sheet cannot be known a priori on the basis of theory and moreover, the evolution of the universe makes it clear that in general such bounds cannot remain invariant under time reversal and will change with epoch. We propose a modified version of this proposal in which the light sheets end on the boundary of the past, and hence avoid contact with the caustics. In this way the resulting light sheets and projections can be made much simpler. We discuss the question of operational definability of these sheets within the context of both proposals and conclude that in both cases the theoretical existence of such sheets must be clearly distinguished from their complexity and the difficulty of their construction in practice. This puts into perspective the likely practical difficulties one would face in applying the holographic principle to the real cosmos. These issues may also be of relevance in debates regarding the applications of the holographic principle to other settings such as string theory.