Unless the positive contribution from symmetry breaking cancels almost exactly with the negative four form, galaxies wouldn’t form, and again, intelligent life wouldn’t develop. I very much doubt we will nd a non anthropic explanation for the cosmological constant.
In the eleven dimensional geometry, the integral of the four form over any four cycle, or its dual over any seven cycle, have to be integers.
This means that the four form is quantized, and can not be adjusted to cancel the symmetry breaking exactly. In fact, for reasonable sizes of the internal dimensions, the quantum steps in the cosmological constant would be much larger than the observational limits. At rst, I thought this was a set back for the idea there was an anthropically controlled cancellation of the cosmological constant.
But then, I realized that it was positively in favour. The fact that we exist, shows that there must be a solution to the anthropic constraints.
But the fact that the quantum steps in the cosmological constant, are so large, means that this solution, is probably unique. This helps with the problems of low , or exactly one, I described earlier. If there were a continuous family of solutions, the strong dependence of the Euclidean action, and the amount of ination, on the size of the instanton, would bias the probability, either to the lowest
, or = 1. This would give either a single galaxy in an otherwise empty universe, or a universe with
exactly one.
But if there is only one instanton in the anthropically allowed range, the biasing towards large instantons has no e ect. Thus matter and could be somewhere in the anthropically allowed region,
though it would be below the matter + = 1 line, if the universe is one of these open analytical continuations. This is consistent with the observations.
The red eliptic region is the three sigma limits of the supernova observations. The blue region is from clustering observations, and the purple is from the Doppler peak in the microwave. They seem to have a common intersection, on or below the total = 1 line.
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Comparison of Supernova, Microwave Background and Clustering regions
Galaxies
Anthropic
cannot
line
form in
this
Supernova
region
yger
en
um
cu
Va
Microwave background
Clustering
Matter density
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Assuming that one can nd a model that predicts a reasonable , how can we test it by observation.
The best way is by observing the spectrum of uctuations in the microwave background. This is a very clean measurement of the quantum uctuations, about the initial instanton. However, there is an important di erence between the non-singular Coleman De Lucia instantons, and the singular
instantons I have described.
As I said, quantum uctuations around the instanton are well dened, despite the singularity.
Perturbations of the Euclidean instanton have nite action, if and only they obey a Dirichelet boundary condition at the singularity. Perturbation modes that don’t obey this boundary condition, will have innite action, and will be suppressed. The Dirichelet boundary condition also arises, if the singularity is resolved in higher dimensions.
When one analytically continues to Lorentzian spacetime, the Dirichelet boundary condition implies that perturbations reect at the time like singularity.
This has an e ect on the two point correlation function of the perturbations. It is very small for the density perturbations, but calculations by Hertog and Turok, indicate a signicant di erence for
gravitational waves, if is less than one.
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The present observations of the microwave uctuations, are certainly not sensitive enough to detect this e ect. But it may be possible with the new observations that will be coming in from the map satellite in 2001, and the Planck satellite in 2006. Thus the no boundary proposal, and the singular instanton, are real science. They can be falsied by observation.
I will nish on that note.