Initial Conditions For Bubble Universes

The “bubble universes” of Coleman and De Luccia play a crucial role in string cosmology. Since our own Universe is supposed to be of this kind, bubble cosmology should supply definite answers to the long-standing questions regarding cosmological initial conditions. In particular, it must explain how an initial singularity is avoided, and also how the initial conditions for Inflation were established. We argue that the simplest non-anthropic approach to these problems involves a requirement that the spatial sections defined by distinguished bubble observers should not be allowed to have arbitrarily small volumes. Casimir energy is a popular candidate for a quantum effect which can ensure this, but [because it violates energy conditions] there is a danger that it could lead to non-perturbative instabilities in string theory. We make a simple proposal for the initial conditions of a bubble universe, and show that our proposal ensures that the system is non-perturbatively stable. Thus, low-entropy conditions can be established at the beginning of a bubble universe without violating the Second Law of thermodynamics and without leading to instability in string theory. These conditions are inherited from the ambient spacetime. 1. Getting Inflation Started in a Bubble In string theory, the leading approach to the problem of the cosmological constant is given by the Landscape [1]. String theory gives a consistent account of a set of possible universes which are so numerous — 10 is the standard estimate — and have values of the cosmological constant spaced in such a way, that the value we actually observe ceases to seem surprising. Instead we conclude that our Universe corresponds to a point in the Landscape. The mathematical consistency of Landscape universes does not suffice to solve the cosmological constant problem: one needs to explain how such a vast array of possible worlds actually comes into existence. This is achieved by means of the nucleation of Coleman-De Luccia bubbles [2][3][4]. These are bubbles of “true” vacuum which spontaneously arise within a larger spacetime containing a scalar field which is initially in a “false” vacuum state. With a suitable potential for the scalar, and with the usual assumptions [“potential domination”] regarding the initial conditions for the inflaton, such bubbles can be made compatible with the standard inflationary account of the evolution of a universe like ours. This is the “open Inflation” scenario [5], which works quite well in bubble universes — provided, of course, that Inflation can actually begin inside a bubble: something which is by no means obvious, since the precise nature of inflationary initial conditions remains to be fully understood. Indeed, if bubble nucleation is to be taken seriously as an account of the origin of our Universe, then it must be expected to answer all of the long-standing questions regarding cosmological initial conditions. In particular, it should supply answers to the following fundamental questions: • Was the beginning singular? If not, how are the singularity theorems evaded? • The Second Law of thermodynamics dictates that the Universe began in an extremely low-entropy state. How was that arranged? Particularly: how does one enforce the very special conditions needed for Inflation to start [6][7][8]? The first of these questions requires no elaboration. The second question concerns the “specialness” of the initial conditions of our Universe. This specialness [or “nongenericity”] is still manifested, even after the passage of more than 13 billion years, as an Arrow of time [9][10][11][12]. The point is that a truly generic initial state would be dominated by black holes [16]. But such an initial state would not evolve to a Universe like ours, with its extremely strong past/future asymmetry. A crucial instance of this is that Inflation cannot begin with such initial conditions; in fact, as Albrecht [7] and others have stressed, Inflation can only begin if the inflaton is itself initially in a very specific state, in which extremely few of the scalar field degrees of freedom have yet been excited. If we cannot produce a theory which necessarily entails such extraordinarily non-generic initial conditions for at least some universes, then we will not be able to find a universe, It has been argued [13] that this is not true of a universe which begins along a non-compact spatial hypersurface. Here we shall avoid this controversial question by postulating that the original universe was created from “nothing” [14][15] along a compact hypersurface. In this case, a singularity-dominated beginning would indeed have been generic.