4.3 The anthropic principle

The anthropic principle [171, 172] is essentially the idea that some of the parameters characterizing the universe we observe may not be determined directly by the fundamental laws of physics, but also by the truism that intelligent observers will only ever experience conditions which allow for the existence of intelligent observers. Many professional cosmologists view this principle in much the same way as many traditional literary critics view deconstruction - as somehow simultaneously empty of content and capable of working great evil. Anthropic arguments are easy to misuse, and can be invoked as a way out of doing the hard work of understanding the real reasons behind why we observe the universe we do. Furthermore, a sense of disappointment would inevitably accompany the realization that there were limits to our ability to unambiguously and directly explain the observed universe from first principles. It is nevertheless possible that some features of our world have at best an anthropic explanation, and the value of the cosmological constant is perhaps the most likely candidate.

In order for the tautology that ``observers will only observe conditions which allow for observers'' to have any force, it is necessary for there to be alternative conditions - parts of the universe, either in space, time, or branches of the wavefunction - where things are different. In such a case, our local conditions arise as some combination of the relative abundance of different environments and the likelihood that such environments would give rise to intelligence. Clearly, the current state of the art doesn't allow us to characterize the full set of conditions in the entire universe with any confidence, but modern theories of inflation and quantum cosmology do at least allow for the possibility of widely disparate parts of the universe in which the ``constants of nature'' take on very different values (for recent examples see [173, 174, 175, 176, 177, 178, 179]. We are therefore faced with the task of estimating quantitatively the likelihood of observing any specific value of within such a scenario.

The most straightforward anthropic constraint on the vacuum energy is that it must not be so high that galaxies never form [180]. From the discussion in Section (2.4), we know that overdense regions do not collapse once the cosmological constant begins to dominate the universe; if this happens before the epoch of galaxy formation, the universe will be devoid of galaxies, and thus of stars and planets, and thus (presumably) of intelligent life. The condition that (z_gal) _M(z_gal) implies

(60)

where we have taken the redshift of formation of the first galaxies to be z_gal ~ 4. Thus, the cosmological constant could be somewhat larger than observation allows and still be consistent with the existence of galaxies. (This estimate, like the ones below, holds parameters such as the amplitude of density fluctuations fixed while allowing to vary; depending on one's model of the universe of possibilities, it may be more defensible to vary a number of parameters at once. See for example [181, 182, 172].

However, it is better to ask what is most likely value of , i.e. what is the value that would be experienced by the largest number of observers [183, 184]? Since a universe with ₀ / _M0 ~ 1 will have many more galaxies than one with ₀ / _M0 ~ 100, it is quite conceivable that most observers will measure something close to the former value. The probability measure for observing a value of can be decomposed as

(61)

where P_*() d is the a priori probability measure (whatever that might mean) for , and () is the average number of galaxies which form at the specified value of . Martel, Shapiro and Weinberg [185] have presented a calculation of () using a spherical-collapse model. They argue that it is natural to take the a priori distribution to be a constant, since the allowed range of is very far from what we would expect from particle-physics scales. Garriga and Vilenkin [186] argue on the basis of quantum cosmology that there can be a significant departure from a constant a priori distribution. However, in either case the conclusion is that an observed ₀ of the same order of magnitude as _M0 is by no means extremely unlikely (which is probably the best one can hope to say given the uncertainties in the calculation).

Thus, if one is willing to make the leap of faith required to believe that the value of the cosmological constant is chosen from an ensemble of possibilities, it is possible to find an ``explanation'' for its current value (which, given its unnaturalness from a variety of perspectives, seems otherwise hard to understand). Perhaps the most significant weakness of this point of view is the assumption that there are a continuum of possibilities for the vacuum energy density. Such possibilities correspond to choices of vacuum states with arbitrarily similar energies. If these states were connected to each other, there would be local fluctuations which would appear to us as massless fields, which are not observed (see Section 4.5). If on the other hand the vacua are disconnected, it is hard to understand why all possible values of the vacuum energy are represented, rather than the differences in energies between different vacua being given by some characteristic particle-physics scale such as M_Pl or M_SUSY. (For one scenario featuring discrete vacua with densely spaced energies, see [187].) It will therefore (again) require advances in our understanding of fundamental physics before an anthropic explanation for the current value of the cosmological constant can be accepted.