Hawking.Stephen.W..The Future Of Quantum Cosmology

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exactly one.
But if there is only one instanton in the anthropically allowed range, the biasing towards large
instantons has no e ect. Thus and could be somewhere in the anthropically allowed region,
matter
though it would be below the + = 1 line, if the universe is one of these open analytical
matter
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 = 1 line.
total
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Comparison of Supernova, Microwave Background and Clustering regions
Galaxies
Anthropic
cannot
line
form in
this
Supernova
region
Microwave background
Clustering
Matter density
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Assuming that one can nd a model that predicts a reasonable , howcan 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 de ned, 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
in nite 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 re ect 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 signi cant di erence for
gravitational waves, if is less than one.
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Vacuum energy
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 falsi ed by observation.
I will nish on that note.
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