Quantum Cosmology and the Constants of Nature

In models where the constants of Nature can take more than one set of values, the cosmological wave function ψ describes an ensemble of universes with different values of the constants. The probability distribution for the constants can be determined with the aid of the ‘principle of mediocrity’ which asserts that we are a ‘typical’ civilization in this ensemble. I discuss the implications of this approach for inflationary scenarios, the origin of density fluctuations, and the cosmological constant. Talk given at the RESCEU International Symposium “The Cosmological Constant and the Evolution of the Universe” 1. Variable Constants The observed values of the constants of Nature are conspicuously non-random (‘finetuned’). If particle masses are bounded by the Planck mass mp and the coupling constants by 1, then a random selection would give all masses ∼ mp and all couplings ∼ 1. The vacuum energy would then be ρv ∼ m 4 p. In contrast, some of the particle masses are more than 20 orders of magnitude below mp, and ρv ∼ 10mp. There is a popular view that all constants will in the end be determined from a unique logically consistent theory of everything. However, the constants we observe depend not only on the fundamental Lagrangian, but also on the vacuum state, which is likely not to be unique. For example, in higher-dimensional theories, the constants of the four-dimensional world depend on the way in which the extra dimensions are compactified. The number of different compactifications in superstring theories is believed to be > ∼10. Moreover, Coleman (1988a) suggested that all constants appearing in sub-Planckian physics may become totally undetermined due to Planck-scale wormholes connecting distant regions of spacetime. It has been argued (Carter 1974; Carr & Rees 1979; Barrow & Tipler 1986) that the values of the constants are, to a large degree, determined by anthropic considerations: these values should be consistent with the existence of conscious observers who can wonder about them. This ‘anthropic principle’ has not been particularly popular among cosmologists, since it appears to require the existence of an ensemble of universes with different values of the constants of Nature. It should be pointed out, however, that one is lead to the concept of such an ensemble if one adopts the view that the universe should be described quantummechanically. The approach I am going to describe here combines anthropic considerations with quantum cosmology and inflationary scenario. 2. Creation of Universes from Nothing The world view suggested by quantum cosmology is that small closed universes, with all possible values of the constants of Nature, spontaneously nucleate out of nothing. Here, ‘nothing’ refers to the absence of not only matter, but also of space and time (Vilenkin 1982, 1986; Hartle & Hawking 1983; Linde 1984). After nucleation, the universes enter a state of