0 70 5 . 41 41 v 1 [ he p - th ] 2 9 M ay 2 00 7 Bad Babies or Vacuum Selection and The Arrow of Time Brett McInnes

Even if string theory has a landscape of internally consistent universes, and even if one has a mechanism for actually creating these universes [as “baby universes”], it may well prove to be the case that the babies will not resemble the Universe we observe. For they may not have an Arrow of time: even if some of them have basic physical laws essentially identical to those we have discovered, they may have the wrong initial conditions. We argue that it is extremely difficult, indeed probably impossible, for a baby universe to have an Arrow of time [of the kind we observe]. Therefore it cannot resemble our Universe. The only Universe[s] with an Arrow like ours may be the one[s] that was [were] “created from nothing”, in accordance with the Ooguri-Vafa-Verlinde “entropic principle”. 1. The Arrow of Time and its Uses One of the most basic observations about our Universe is also one of the most difficult to explain: the existence of an Arrow of time [1][2][3][4]. Whether one examines the entropy that the early Universe might have had due to black holes [1] or uses “holographic” estimates of that entropy [4], the conclusion is that the initial conditions must have been “non-generic” to an almost unimaginable degree. The difficulties involved in explaining this extraordinary feature of the Universe have recently attracted some attention, leading to a variety of proposed solutions [5][6][7][8]. In this challenge, however, there lies a great opportunity. For if an Arrow of time is something that is very difficult to establish, if in fact extremely few universes have an Arrow, then the Arrow becomes a powerful tool for selecting universes in any theory that presents us with a multitude of them. That is, demanding the existence of an Arrow may allow us to rule out large classes of universes which might have exactly the right gauge group, spectrum of particles, and so on — which might, in short, have everything except the right initial conditions. The importance of settling this question can hardly be overstated: in particular, it is clear that nothing meaningful can be said about populating the string landscape [9] until one has a good understanding of the Arrow. For whatever an “observer” may be, one can feel confident that such devices do not exist if there is no Arrow. A key point that is often neglected in discussions of the Arrow is that our Universe does not merely have an Arrow: it has an Arrow of a particular kind. A successful theory of the Arrow must account for the existence of at least one Universe with an Arrow of this particular kind. Having passed this test, that theory should then be able to tell us how many other universes have such an Arrow. This holds out the prospect of avoiding the apparently intractable problems [10] faced by other approaches to “universe selection”. The first peculiarity of “our” Arrow, stressed particularly by Penrose, is simply the sheer scale of the “specialness” we observe. Penrose computes that the fraction of the relevant phase space corresponding to the actual initial conditions of our Universe was no more than 10 123 . It is not enough for a theory of the Arrow to produce a “special” initial state — it has to entail “specialness” on this kind of scale. The second point is that this low entropy takes a specific form: by no means all forms of entropy were low in the early Universe; the low entropy was stored almost exclusively in the form of smoothness [3]. That is, the initial low entropy takes the specific form of extreme geometric regularity of the earliest spatial sections. Thus, again, it is not enough for a theory of the Arrow to generate “low entropy” initial conditions. The theory must explicitly give rise to low geometric entropy [whatever the latter’s precise definition may be — see [11][12]]. In practice this is a major technical difficulty, because it means that we cannot begin by assuming a FRW form for the metric, even approximately. That is, we must use methods that can deal with all possible initial geometries. Clearly, we can expect the methods of classical singularity theory to be relevant here. An important subtlety here is that our Arrow probably cannot be explained in terms of purely local geometry. It cannot, for example, simply be reduced to the fact that the For example, Boltzmann suggested that the Arrow might be the result of a “rare fluctuation”. This does lead to an Arrow, but, as is well known [3][5], not to a Universe that resembles the one we observe.