Holographic Principle and String Cosmology 1

String cosmology is revisited from cosmological viewpoint of holographic principle put forward by ‘t Hooft, and by Fischler and Susskind. It is shown that the holography requires existence of a ‘graceful exit’ mechanism, which renders the Universe nonsingular by connecting preand post-big bang phases smoothly. It is proven that flat Universe is consistent with the holography only if it starts with an absolutely cold and vacuous state and particle entropy is produced during the ‘graceful exit’ period. Open Universe can always satisfy the holography no matter what initial state of the Universe is. 1 Work supported in part by KOSEF Interdisciplinary Research Grant and SRC-Program, KRF International Collaboration Grant, Ministry of Education Grant BSRI 98-2418 and 98-2425, UOS Academic Research Program, SNU Faculty Research Grant, and The Korea Foundation for Advanced Studies Faculty Fellowship. An emerging new paradigm in quantum gravity is the holographic principle, first put forward by ‘t Hooft [1] in the context of black hole physics and more recently extended by Susskind [2] to string theory. The principle demands that the degrees of freedom of a spatial region reside not in the bulk but only at the boundary of the region and that the number of degrees of freedom per Planck area is no greater than unity. Actually, basic ingredients leading to the holographic behavior seem to be quite generic in any gravitational (or diffeomorphism invariant) system that the principle should be equally applicable to a cosmological context. In fact, recently, Fischler and Susskind [3] have put forward a cosmological version of the holographic principle: at any time during cosmological evolution, the gravitational entropy within a closed surface should be always larger than the particle entropy that passes through the past light-cone of that surface. Applied to the standard big-bang cosmology, Fischler and Susskind have found that only open or flat universe but not closed one is compatible with the cosmological holographic principle, provided one makes certain assumptions on the initial big-bang singularity. In string theory, as first shown by Veneziano [4], cosmological evolution of the Universe is drastically different from that in the standard big-bang cosmology. In addition to postbig bang phase with an initial singularity, in string theory, a super-inflationary pre-big bang phase with a final singularity is present. Most interestingly, the pre-big bang phase may be juxtaposed with the post-big bang branch smoothly (referred as ‘branch change’ via ‘graceful exit’ [5]) so that the singularities of both phases are simultaneously smoothened out. This opens up an exciting possibility in string theory of realizing an eternally evolving, non-singular and inflationary universe. While physical detail of the ‘branch change’, where curvature and quantum effects are most pronounced, is yet to be understood thoroughly, recent studies have indicated that the ‘branch change’ could be triggered by higher-curvature [6], massive string state [7], and quantum [8] back reactions. In this paper, we put the string cosmology to a test of the cosmological holographic principle, assuming homogeneity and isotropy and applying the holography in string frame to the Friedmann-Robertson-Walker (FRW) Universe with flat or open spatial curvature . Summarizing the results, we find that flat Universe is ruled out by the principle unless the Universe is absolutely cold and vacuous throughout the pre-big bang phase. We also find that open universe can be consistent with the holographic principle, provided there exists a suitable mechanism of the ‘graceful exit’. While admittedly preliminary, the most compatible string cosmology with the holographic principle singles out the open Universe. Intriguingly, such an open Universe appears to be favored by recent measurement of the redshift-to-distance relation and theory of the large-scale structure formation [9]. Closed Universe will not be considered here since, as Veneziano [4] has emphasized, the very presence of initial and final singularities contradicts with the basic postulates of the non-singular string cosmology.