3.5. Are we witnessing environmental selection?
If the vacuum energy can in principle be calculated in terms of other measurable quantities, then we clearly don't yet know how to calculate it. Alternatively, however, it may be that the vacuum energy is not a fundamental quantity, but simply our feature of our local environment. We don't turn to fundamental theory for an explanation of the average temperature of the Earth's atmosphere, nor are we surprised that this temperature is noticeably larger than in most places in the universe; perhaps the cosmological constant is on the same footing.
To make this idea work, we need to imagine that there are many different regions of the universe in which the vacuum energy takes on different values; then we would expect to find ourselves in a region which was hospitable to our own existence. Although most humans don't think of the vacuum energy as playing any role in their lives, a substantially larger value than we presently observe would either have led to a rapid recollapse of the universe (if vac were negative) or an inability to form galaxies (if vac were positive). Depending on the distribution of possible values of vac, one can argue that the observed value is in excellent agreement with what we should expect (Weinberg 1987, Linde 1987, Vilenkin 1995, Efstathiou 1995, Martel, Shapiro & Weinberg 1998, Garriga & Vilenkin 2000, 2003).
The idea of understanding the vacuum energy as a consequence of environmental selection often goes under the name of the "anthropic principle," and has an unsavory reputation in some circles. There are many bad reasons to be skeptical of this approach, and at least one good reason. The bad reasons generally center around the idea that it is somehow an abrogation of our scientific responsibilities to give up on calculating something as fundamental as the vacuum energy, or that the existence of many unseen domains in the universe is a metaphysical construct without any testable consequences, and hence unscientific. The problem with these objections is that they say nothing about whether environmental selection actually happens; they are only declarations that we hope it doesn't happen, or it would be difficult for us to prove once and for all that it does. The good reason to be skeptical is that environmental selection only works under certain special circumstances, and we are far from understanding whether those conditions hold in our universe. In particular, we need to show that there can be a huge number of different domains with slightly different values of the vacuum energy, and that the domains can be big enough that our entire observable universe is a single domain, and that the possible variation of other physical quantities from domain to domain is consistent with what we observe in ours. (5)
Recent work in string theory has lent some support to the idea that there are a wide variety of possible vacuum states rather than a unique one (Dasgupta, Rajesh & Sethi 1999, Bousso & Polchinski 2000, Feng, March-Russell, Sethi & Wilczek 2001, Giddings, Kachru & Polchinski 2002, Kachru, Kallosh, Linde & Trivedi 2003, Susskind 2003, Douglas 2003, Ashok & Douglas 2003). String theorists have been investigating novel ways to compactify extra dimensions, in which crucial roles are played by branes and gauge fields. By taking different combinations of extra-dimensional geometries, brane configurations, and gauge-field fluxes, it seems plausible that a wide variety of states may be constructed, with different local values of the vacuum energy and other physical parameters. (The set of configurations is sometimes known as the "landscape," and the discrete set of vacuum configurations is unfortunately known as the "discretuum.") An obstacle to understanding these purported solutions is the role of supersymmetry, which is an important part of string theory but needs to be broken to obtain a realistic universe. From the point of view of a four-dimensional observer, the compactifications that have small values of the cosmological constant would appear to be exactly the states alluded to in the previous section, where one begins with a supersymmetric state with a negative vacuum energy, to which supersymmetry breaking adds just the right amount of positive vacuum energy to give a small overall value. The necessary fine-tuning is accomplished simply by imagining that there are many (more than 10100) such states, so that even very unlikely things will sometimes occur. We still have a long way to go before we understand this possibility; in particular, it is not clear that the many states obtained have all the desired properties (Banks, Dine & Motl 2001, Banks, Dine & Gorbatov 2003), or even if they are stable enough to last for the age of the universe (Hertog, Horowitz & Maeda, 2003).
Even if such states are allowed, it is necessary to imagine a universe in which a large number of them actually exist in local regions widely separated from each other. As is well known, inflation works to take a small region of space and expand it to a size larger than the observable universe; it is not much of a stretch to imagine that a multitude of different domains may be separately inflated, each with different vacuum energies. Indeed, models of inflation generally tend to be eternal, in the sense that the universe continues to inflate in some regions even after inflation has ended in others (Vilenkin 1983, Linde 1985, Goncharov, Linde & Mukhanov 1987). Thus, our observable universe may be separated by inflating regions from other "universes" which have landed in different vacuum states; this is precisely what is needed to empower the idea of environmental selection.
Nevertheless, it seems extravagant to imagine a fantastic number of separate regions of the universe, outside the boundary of what we can ever possibly observe, just so that we may understand the value of the vacuum energy in our region. But again, this doesn't mean it isn't true. To decide once and for all will be extremely difficult, and will at the least require a much better understanding of how both string theory (or some alternative) and inflation operate - an understanding that we will undoubtedly require a great deal of experimental input to achieve.
5 For example, if we have a theory that allows for any possible value of the vacuum energy, but insists that the vacuum energy scale be equal to the supersymmetry breaking scale in each separate domain, we haven't solved any problems. Back.