On Holography and Cosmology

Starting with the suggestion of Fischler and Susskind, various attempts have recently been made to apply the holographic principle to cosmology. Among these is a generalisation by Bousso which avoids the difficulties of the original proposal in the re-collapsing FLRW models. Here we take a closer look at the question of holography in cosmology with particular reference to this generalisation. We demonstrate that in general realistic inhomogeneous universes such a proposal would involve extremely complicated possibly fractal light sheets. Furthermore, in a real inhomogeneous universe with evolving degrees of lumpiness on a variety of scales, such a light sheet becomes time dependent and cannot be known a priori on the basis of theory. Its construction requires a detailed knowledge of the distribution and growth of inhomogeneities on all scales, and of the resulting caustics in null surfaces. 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.