B. Extra Dimensions and Cosmology
The flurry of interest in extra dimensional physics [Antoniadis(1990), Lykken(1996), Arkani-Hamed et al.(1998), Antoniadis et al.(1998), Randall and Sundrum(1999)] has led to a number of interesting proposals for modifying cosmology at early times. While one must be careful not to interfere with the successful predictions of the standard cosmology [Arkani-Hamed et al.(1999), Hall and Smith(1999), Cullen and Perelstein(1999)], the evolution of the universe at the earliest times must be very different in these models from that expected in the usual 3 + 1 dimensional framework [Arkani-Hamed et al.(2000a)]. When confronted with a new model for the early universe, cosmologists typically ask themselves the following three fundamental questions: 1) Is there a new way to address the horizon and flatness problems in this picture? 2) Is there a way to understand the observed size of the cosmological constant in this picture? 3) Is there a new mechanism for generating the density and temperature fluctuations seen in large scale structure and the CMB? As far as the first point goes, there have been several suggestions. In ref [Starkman et al.(2001a), Starkman et al.(2001b)] it was suggested that if the universe is the direct product of a (3+1)-dimensional FRW space and a compact hyperbolic manifold [Kaloper et al.(2000)], the decay of massive Kaluza-Klein modes leads to the injection of any initial bulk entropy into the observable (FRW) universe. This can act to smooth out any initial inhomogeneities in the distribution of matter and of 3-curvature sufficiently to account for the current homogeneity and flatness of the universe. In ref [Khoury et al.(2001b)] it has been suggested that the true vacuum of the universe is a BPS state in heterotic M-theory. The fields describing our universe live on a brane in this space and the hot expanding phase that we know as the big bang arises due to an instanton effect [Khoury et al.(2001c)] in which a new brane nucleates, travels across one of the extra dimensions and collides with our brane, depositing its energy there. The eternal nature of the cosmology and the special, flat nature of the BPS state lead to a flat and homogeneous FRW cosmology on our brane after the collision. While there may be existing fine-tunings in the above models, their feasibility and implications for cosmology are under investigation.
The cosmological constant problem remains unaddressed in the above scenarios. However, a particular scheme, the so-called self-tuning model [Arkani-Hamed et al.(2000b), Kachru et al.(2000)], has been proposed in the bane world context to address this issue. The cosmological constant problem arises in a simple sense because space-time is sensitive to the presence of vacuum energy. In the self-tuning picture, the effective theory of gravity on our brane is such that it does not respond to the presence of vacuum energy. This occurs because of a careful choice of coupling between the matter fields living on the brane and in the 5-dimensional bulk. As a result, whatever the value of the cosmological constant, or however it may change, the 3 + 1-dimensional metric remains unaffected by it. However, there are a number of unresolved questions regarding the self-tuning models. First, there seems to be a singularity in these models, the possible resolution of which is yet to be understood [Forste et al.(2000), Csaki et al.(2000), Horowitz et al.(2000), Grinstein et al.(2000), Zhu(2000), Barger et al.(2000), Binetruy et al.(2000a), Maeda and Wands(2000), Mendes and Mazumdar(2001), Kakushadze(2000), Kennedy and Prodanov(2000), Kim et al.(2001a), Kim et al.(2001b), Brax and Davis(2001)]. Second, it seems quite difficult to reconcile the self-tuning picture with what is known about the cosmology of our universe. In particular, it seems necessary to modify the Friedmann equation on our brane [Binetruy et al.(2000b), Csaki et al.(1999), Cline et al.(1999), Binetruy et al.(2000c), Shiromizu et al.(2000), Flanagan et al.(2000)] , which can lead to problems with big bang nucleosynthesis [Carroll and Mersini(2001)].
Finally, the issue of density and temperature perturbations is a highly quantitative challenge to any new theory of the early universe. The precision measurements of the temperature fluctuations in the CMB, and in particular the observation of the second (and perhaps third) acoustic peaks in the power spectrum now provide solid evidence for a scale-free adiabatic spectrum of initial fluctuations, consistent with that predicted by inflation. The question of whether any other mechanism could be responsible for these observations is a particularly pressing one for particle cosmology. Recently it was claimed that one of the scenarios mentioned above, the ekpyrotic scenario [Khoury et al.(2001b)], may be able to generate the necessary perturbations. However, at present this is a hotly debated topic [Lyth(2001a), Brandenberger and Finelli(2001), Hwang(2001), Lyth(2001b), Khoury et al.(2001a)], and the ultimate outcome is unclear. Certainly, if this claim is true, the ekpyrotic scenario will have earned further careful study.