Hawking's Anthropic Principle

From: Michael Ragland (ragland66_at_webtv.net)
Date: 10/26/04 

Date: Tue, 26 Oct 2004 15:36:30 +0000 (UTC)

Hawking's brain is like a wet slippery eel in its complexity. On more
than one occasion I've seen him make statements which were wrong, or he
changed his mind or he made contradictory statements. It will be
interesting to see how history evaluates him if the human species
doesn't destroy itself. In this particular lecture which was very
technical I think he summed up his support for the anthropic principle
best by stating, "The fact that we exist shows that there must be a
solution to the anthropic constraints." This statement was made in 1998.
But Wikipedia citing Stephen Hawking's Anthropic Reasoning states,
"Recent publications (2004) by Stephen Hawking suggest that our universe
is much less 'special' than the proponents of the anthropic
principle claim it is. According to Hawking, there is a 98% chance that
a universe of a type as ours will come from a Big Bang. Further, using
the basic wavefunction of the universe as basis, Hawking's equations
indicate that such a universe can come into existence without relation
to anything prior to it, meaning that it could come out of nothing. In
2004, these publications and the theories in them are still subject to
scientific debate." What is interesting is that neither of Hawking's
positions necessarily contradict each other.

Michael Ragland

Anthropic principle

>>From Wikipedia, the free encyclopedia.
The anthropic principle in its most basic form states a truism: that any
valid theory of the universe must be consistent with our existence as
carbon-based human beings at this particular time and place in the
universe. Attempts to apply this principle to develop scientific
explanations in cosmology have led to some confusion and much
controversy.
Table of contents [showhide]
1 Origin
2 Proponents and versions
3 The Anthropic Cosmological Principle
4 Anthropic bias and anthropic reasoning
5 See also
6 External links
7 Footnote
[edit]
Origin

The term "anthropic principle" was first proposed in 1973 by Brandon
Carter during the celebration of Copernicus' 500th birthday, as if to
proclaim that humanity does hold a special place in the universe after
all.1
[edit]
Proponents and versions

Proponents of the anthropic principle suggest that we live in a
fine-tuned universe, i.e. a universe that appears to be "fine-tuned" to
allow the existence of life as we know it. If any of the basic physical
constants were different, then life as we know it would not be possible.
Papers have been written arguing that the anthropic principle would
explain the physical constants such as the fine structure constant, the
number of dimensions in the universe, and the cosmological constant.

The three primary versions of the principle, as stated by Barrow and
Tipler (1986), are:
Weak Anthropic Principle (WAP): "The observed values of all physical and
cosmological quantities are not equally probable but they take on values
restricted by the requirement that there exist sites where carbon-based
life can evolve and by the requirements that the Universe be old enough
for it to have already done so."

Strong Anthropic Principle (SAP): "The Universe must have those
properties which allow life to develop within it at some stage in its
history."

Final Anthropic Principle (FAP): "Intelligent information-processing
must come into existence in the Universe, and, once it comes into
existence, it will never die out."

The weak version has been criticized as an argument by lack of
imagination for assuming no other forms of life are possible (see also
carbon chauvinism). Furthermore, the range of constants allowing
evolution of carbon-based life may be much less restricted than proposed
(Stenger, "Timeless Reality"). The strong version is also criticized as
being neither testable nor falsifiable, and unnecessary. The final
version is discussed in more detail under Final Anthropic Principle;
Barrow and Tipler state that, although it is a physical statement, it is
nevertheless "closely connected with moral values".

Proponents of the intelligent design conjecture assert support from the
anthropic principle. On the other hand, the existence of alternate
universes is suggested for other reasons and the anthropic principle
provides additional support for their existence. Assuming some possible
universe would be capable of supporting intelligent life, some actual
universes must do so, and ours clearly is one of those.
[edit]

The Anthropic Cosmological Principle
In 1986, the controversial book The Anthropic Cosmological Principle by
John D. Barrow and Frank J. Tipler (Oxford University Press) was
published. In this book Barrow, a cosmological scientist, pioneered what
he called the anthropic principle in order to deal with the seemingly
incredible coincidences that allow for our presence in a universe that
appears to be perfectly set up for our existence. Everything from the
particular energy state of the electron to the exact level of the weak
nuclear force seems to be tailored for us to exist. We appear to live in
a universe dependent on several independent variables where only a
slight change would render it inhospitable for any form of life. And
yet, here we are. The anthropic principle states that the reason we are
here to ponder this question at all, is due to the fact that all the
correct variables are in place.

According to critics, this is simply a very elaborate way of saying 'if
things were different, they would be different'.

Brandon Carter presented his ideas about the anthropic principle in a
1974 publication of the International Astronomical Union. Later, in
1983, he claimed that, in its original form, the principle was meant
only to caution astrophysicists and cosmologists of possible errors in
the interpretation of astronomical and cosmological data unless the
biological constraints of the observer were taken into account. In 1983
he also included the warning that the inverse was true for evolutionary
biologists; Carter claimed that in interpreting the evolutionary record,
one must take into account the astrophysical restraints of the process.

Working with this in mind, Carter concluded that the evolutionary chain
probably could include only one or two highly improbable links given the
available time interval. A. Feoli and S. Rampone ("Is the Strong
Anthropic Principle Too Weak," 1999) argued that the estimated size of
our universe and number of planets allows a higher bound, indicating no
evidence for intelligent design in evolution.

There was renewed scientific interest in the anthropic principle in the
late-1990s motivated by observational cosmology and theoretical work in
quantum gravity. The theoretical work involved attempting to unify
gravity with the other forces. While there were a number of promising
developments, they all seemed to suffer from the problem that the
fundamental physical constants seemed to be unconstrained. The
observational motivation came from cosmological observations which gave
firm values for quantities such as the matter density of the universe.
Contrary to expectations, the value was not zero, but 0.7, which is a
non-obvious value.

Recent publications (2004) by Stephen Hawking suggest that our universe
is much less 'special' than the proponents of the anthropic
principle claim it is. According to Hawking, there is a 98% chance that
a universe of a type as ours will come from a Big Bang. Further, using
the basic wavefunction of the universe as basis, Hawking's equations
indicate that such a universe can come into existence without relation
to anything prior to it, meaning that it could come out of nothing. In
2004, these publications and the theories in them are still subject to
scientific debate.
[edit]

Anthropic bias and anthropic reasoning
In 2002, Nick Bostrom asked "Is it possible to sum up the essence of
observation selection effects in a simple statement?" He concluded that
it might be, but that "Many 'anthropic principles' are simply confused.
Some, especially those drawing inspiration from Brandon Carter's seminal
papers, are sound, but... they are too weak to do any real scientific
work. In particular, I argue that existing methodology does not permit
any observational consequences to be derived from contemporary
cosmological theories, in spite of the fact that these theories quite
plainly can be and are being tested empirically by astronomers. What is
needed to bridge this methodological gap is a more adequate formulation
of how observation selection effects are to be taken into account." His
Self-Sampling Assumption is "that you should think of yourself as if you
were a random observer from a suitable reference class." This he expands
into a model of anthropic bias and anthropic reasoning under the
uncertainty introduced by not knowing your place in our universe - or
even who "we" are. This may also be a way to overcome various cognitive
bias limits inherent in the humans doing the observation and sharing
models of our universe using mathematics, as suggested in the cognitive
science of mathematics.

[edit]
See also
Fine-tuned universe
Doomsday argument
Inverse gambler's fallacy
Big Bounce
[edit]
External links
Kane, Gordon L., Malcolm J. Perry, and Anna N. Zytkow, "The Beginning of
the End of the Anthropic Principle
(http://www.arxiv.org/abs/astro-ph/0001197)". (arxiv.org)
debate among scientists on arxiv.org
all/0/1)Anthropic Reasoning, Stephen Hawking Kavli-CERCA Conference Video
Archive (http://www.phys.cwru.edu/events/cerca_video_archive.php)
[edit]
Footnote
¹ The principle had, however, been invoked before then, e.g. in 1957,
R.H. Dicke wrote: 'The age of the Universe "now" is not random but
conditioned by biological factors ... [changes in the values of the
fundamental constants of physics] would preclude the existence of man to
consider the problem.' (R.H. Dicke, Principle of Equivalence and Weak
Interactions, Rev.Mod.Phys. 29, 355 (1957).) Even earlier statements of
the principle may be found in Alfred Russel Wallace's book Man's Place
in the Universe, which was first published in 1903. For example: "such a
vast and complex universe as that which we know exists around us, may
have been absolutely required ... in order to produce a world that
should be precisely adapted in every detail for the orderly development
of life culminating in man." (pp. 256-7 in the 1912 edition).
Retrieved from "http://en.wikipedia.org/wiki/Anthropic_principl

Quantum Cosmology, M-theory and the Anthropic Principle (January '99)
Please note that bullet marks indicate progression of slide show. The
slide show is a PowerPoint97 file.
It is viewable on machines without PowerPoint97. You need to download
the zip file.
This lecture is also available for download as a postscript file.
To download the file, right click on the link and select 'Save Link
As...' from the menu.
This lecture is the intellectual property of Professor S.W. Hawking. You
may not reproduce, edit or distribute this document in anyway for
monetary advantage.

This talk will be based on work with Neil Turok and Harvey Reall. I will
describe what I see as the framework for quantum cosmology, on the basis
of M theory. I shall adopt the no boundary proposal, and shall argue
that the Anthropic Principle is essentia l, if one is to pick out a
solution to represent our universe, from the whole zoo of solutions
allowed by M theory.
Cosmology used to be regarded as a pseudo science, an area where wild
speculation, was unconstrained by any reliable observations. We now have
lots and lots of observational data, and a generally agreed picture of
how the universe is evolving. But cosmolo gy is still not a proper
science, in the sense that as usually practiced, it has no predictive
power. Our observations tell us the present state of the universe, and
we can run the equations backward, to calculate what the universe was
like at earlier tim es. But all that tells us is that the universe is as
it is now, because it was as it was then. To go further, and be a real
science, cosmology would have to predict how the universe should be. We
could then test its predictions against observation, like i n any other
science. The task of making predictions in cosmology is made more
difficult by the singularity theorems, that Roger Penrose and I proved.
These showed that if General Relativity were correct, the universe would
have begun with a singularity. Of course, we would expect classical
General Relativity to break down near a singularity, when quantum
gravitational effects have to be taken into acco unt. So what the
singularity theorems are really telling us, is that the universe had a
quantum origin, and that we need a theory of quantum cosmology, if we
are to predict the present state of the universe.

A theory of quantum cosmology has three aspects. The first, is the local
theory that the fields in space-time obey. The second, is the boundary
conditions for the fields. And I shall argue that the anthropic
principle, is an essential third element. As far as the local theory is
concerned, the best, and indeed the only consistent way we know, to
describe gravitational forces, is curved space-time. And the theory has
to incorporate super symmetry, because otherwise the uncancelled vacuum
energies of all the modes would curl space-time into a tiny ball. T hese
two requirements, seemed to point to supergravity theories, at least
until 1985. But then the fashion changed suddenly. People declared that
supergravity was only a low energy effective theory, because the higher
loops probably diverged, though no on e was brave, or fool hardy enough
to calculate an eight-loop diagram. Instead, the fundamental theory was
claimed to be super strings, which were thought to be finite to all
loops. But it was discovered that strings were just one member, of a
wider class of extended objects, called p-branes. It seems natural to
adopt the principle of p-brane democracy. All p-branes are created
equal. Yet for p greater than one, the quantum theory of p-branes,
diverges for higher loops.
I think we should interpret these loop divergences, not as a break down
of the supergravity theories, but as a break down of naive perturbation
theory. In gauge theories, we know that perturbation theory breaks down
at strong coupling. In quantum gravity, the role of the gauge coupling,
is played by the energy of a particle. In a quantum loop one integrates
over… So one would expect perturbation theory, to break down.

In gauge theories, one can often use duality, to relate a strongly
coupled theory, where perturbation theory is bad, to a weakly coupled
one, in which it is good. The situation seems to be similar in gravity,
with the relation between ultra violet and inf ra red cut-offs, in the
anti de Sitter, conformal field theory, correspondence. I shall
therefore not worry about the higher loop divergences, and use
eleven-dimensional supergravity, as the local description of the
universe. This also goes under the name of M theory, for those that
rubbished supergravity in the 80s, and don't want to admit it was
basically correct. In fact, as I shall show, it seems the origin of the
universe, is in a regime in which first order perturbation theory, is a
good approximati on.

The second pillar of quantum cosmology, are boundary conditions for the
local theory. There are three candidates, the pre big bang scenario, the
tunneling hypothesis, and the no boundary proposal.

The pre big bang scenario claims that the boundary condition, is some
vacuum state in the infinite past. But if this vacuum state develops
into the universe we have now, it must be unstable. And if it is
unstable, it wouldn't be a vacuum state, and it wou ldn't have lasted an
infinite time before becoming unstable.

The quantum-tunneling hypothesis, is not actually a boundary condition
on the space-time fields, but on the Wheeler Dewitt equation. However,
the Wheeler Dewitt equation, acts on the infinite dimensional space of
all fields on a hyper surface, and is not well defined. Also, the 3+1,
or 10+1 split, is putting apart that which God, or Einstein, has joined
together. In my opinion therefore, neither the pre bang scenario, nor
the quantum-tunneling hypothesis, are viable.

To determine what happens in the universe, we need to specify the
boundary conditions, on the field configurations, that are summed over
in the path integral. One natural choice, would be metrics that are
asymptotically Euclidean, or asymptotically anti d e Sitter. These would
be the relevant boundary conditions for scattering calculations, where
one sends particles in from infinity, and measures what comes back out.
However, they are not the appropriate boundary conditions for cosmology.

We have no reason to believe the universe is asymptotically Euclidean,
or anti de Sitter. Even if it were, we are not concerned about
measurements at infinity, but in a finite region in the interior. For
such measurements, there will be a contribution fro m metrics that are
compact, without boundary. The action of a compact metric is given by
integrating the Lagrangian. Thus its contribution to the path integral
is well defined. By contrast, the action of a non-compact or singular
metric involves a surface term at infinity, or at the singularity. One
can add an arbitrary quantity to this surface term. It therefore seems
more natural to adopt what Jim Hartle and I called the no boundary
proposal. The quantum state of the universe is defined by a Euclidean p
ath integral over compact metrics. In other words, the boundary
condition of the universe is that it has no boundary.

There are compact Reechi flat metrics of any dimension, many with high
dimensional modulie spaces. Thus eleven-dimensional supergravity, or M
theory, admits a very large number of solutions and compactifications.
There may be some principle that we haven' t yet thought of, that
restricts the possible models to a small sub class, but it seems
unlikely. Thus I believe that we have to invoke the Anthropic Principle.

Many physicists dislike the Anthropic Principle. They feel it is messy
and vague, it can be us ed to explain almost anything, and it has little
predictive power. I sympathize with these feelings, but the Anthropic
Principle seems essential in quantum cosmology. Otherwise, why should we
live in a four dimensional world, and not eleven, or some other number
of dimensions. The anthropic answer is that two spatial dimensions, are
not enough for complicated structures, like intelligent beings.

On the other hand, four or more spatial dimensions would mean that
gravitational and electric forces would fall off faster than the inverse
square law. In this situation, planets would not have stable orbits
around their star, nor electrons have stable orbits around the nucleus
of an atom. Thus intelligent life, at least as we know it, could exist
only in four dim ensions. I very much doubt we will find a non anthropic
explanation.

The Anthropic Principle is usually said to have weak and strong
versions. According to the strong Anthropic Principle, there are
millions of different universes, each with different values of the
physical constants. Only those universes with suitable phys ical
constants will contain intelligent life. With the weak Anthropic
Principle, there is only a single universe. But the effective couplings
are supposed to vary with position, and intelligent life occurs only in
those regions, in which the couplings hav e the right values. However,
quantum cosmology, and the no boundary proposal remove the distinction
between the weak and strong Anthropic Principles. The different physical
constants are just different modulie of the internal space, in the
compactification of M theory, or eleven-dimensional supergravity. All
possible modulie will occur in the path integral over compact metrics.
By contrast, if the path integral were over non compact metrics, one
would have to specify the values of the modulie at infinity. But why
should the modulie at infinity, have those particular values, like four
uncompactified dimensions, that allow intelligent life. In fact, the
Anthropic Principle, really requires the no boundary proposal, and
vice-versa.

One can make the Anthropic Principle precise, by using Bayes statistics.
One takes the a-priori probability of a class of histories, to be the e
to the minus the Euclidean action, given by the no boundary proposal.
One then weights this a-priori probability, with the probability that
the class of histories contain intelligent life. As physicists, we don't
want to be drawn into to the fine details of chemistry and biology, but
we can reckon certain features, as essential prerequisites of life as we
know it. Among these are the existence of galaxies and stars, and
physical const ants near what we observe. There may be some other region
of modulie space, that allows some different form of intelligent life,
but it is likely to be an isolated island. I shall therefore ignore this
possibility, and just weight the a-priori probability , with the
probability to contain galaxies.

The simplest compact metric that could represent a four dimensional
universe, would be the product of a four sphere, with a compact internal
space. But the world we live in has a metric with Lorentzian signature,
rather than a positive definite Euclidean one. So one has to
analytically continue the four-sphere metric, to complex values of the
coordinates.
There are several ways of doing this.
One can analytically continue the coordinate, sigma, as sigma equator,
plus i t. One obtains a Lorentzian metric, which is a closed Friedmann
solution, with a scale factor that goes like cosh Ht. So this is a
closed universe that collapses to a minimum si ze, and then expands
exponentially again.

However, one can analytically continue the four-sphere in another way.
Define t = i sigma, and chi = i psi. This gives an open Friedmann
universe, with a scale factor like sinh Ht.
Thus one can get an apparently spatially infinite universe, from the no
boundary proposal. The reason is that one is using as a time coordinate,
the hyperboloids of constant distance, inside the light cone of a point
in de Sitter space. The point itself, and its light cone, are the big
bang of the Friedmann model, where the scale factor goes to zero. But
they are not singular. Instead, the spacetime continues through the
light cone to a region beyond. It is this region that deserves the name,
the pre big bang scenario, rather than the misguided model that commonly
bears that title.

If the Euclidean four-sphere were perfectly round, both the closed and
open analytical continuations, would inflate for ever. This would mean
they would never form galaxies. A perfect round four sphere has a lower
action, and hence a higher a-priori proba bility than any other four
metric of the same volume. However, one has to weight this probability,
with the probability of intelligent life, which is zero. Thus we can
forget about round 4 spheres.

On the other hand, if the four sphere is not perfectly round, the
analytical continuation will start out expanding exponentially, but it
can change over later to radiation or matter dominated, and can become
very large and flat. This provides a mechanism whereby all eleven
dimensions can have similar curvatures, in the compact Euclidean metric,
but four dimensions can be much flatter than the other seven, in the
Lorentzian analytical continuation. But the mechanism doesn't seem
specific to four large dime nsions. So we will still need the Anthropic
Principle, to explain why the world is four-dimensional.

In the semi classical approximation, which turns out to be very good,
the dominant contribution, comes from metrics near solutions of the
Euclidean field equations. So we need to study deformed four spheres, in
the effective theory obtained by dimensional reduction of eleven
dimensional supergravity, to four dimensions. These Kaluza Klein
theories, contain various scalar fields, that come from the three index
field, and the modulie of the internal space. For simplicity, I will
describe only the single sca lar field case.

The scalar field, phi, will have a potential, V of phi. In regions where
the gradients of phi are small, the energy momentum tensor will act like
a cosmological constant, Lambda =8 pi G V, where G is Newton's constant
in four dimensions. Thus it will curv e the Euclidean metric, like a
four-sphere.
However, if the field phi is not at a stationary point of V, it can not
have zero gradient everywhere. This means that the solution can not have
O5 symmetry, like the round four sphere. The most it can have, is O4
symmetry. In other words, the solution is a deformed four sphere.

One can write the metric of an O4 instanton, in terms of a function, b
of sigma. Here b is the radius of a three sphere of constant distance,
sigma, from the north pole of the instanton. If the instanton were a
perfectly round four-sphere, b would be a si ne function of sigma. It
would have one zero at the north pole, and a second at the south pole,
which would also be a regular point of the geometry. However, if the
scalar field at the north pole, is not at a stationary point of the
potential, it will var y over the four sphere. If the potential is
carefully adjusted, and has a false vacuum local minimum, it is possible
to obtain a solution that is non-singular over the whole four-sphere.
This is known as the Coleman De Lucia instanton.

However, for general potentials without a false vacuum, the behavior is
different. The scalar field will be almost constant over most of the
four-sphere, but will diverge near the south pole. This behavior is
independent of the precise shape of the potent ial, and holds for any
polynomial potential, and for any exponential potential, with an
exponent, a, less then 2. The scale factor, b, will go to zero at the
south pole, like distance to the third. This means the south pole is
actually a singularity of th e four dimensional geometry. However, it is
a very mild singularity, with a finite value of the trace K surface
term, on a boundary around the singularity at the south pole. This means
the actions of perturbations of the four dimensional geometry, are wel l
defined, despite the singularity. One can therefore calculate the
fluctuations in the microwave background, as I shall describe later.

The deep reason, behind this good behavior of the singularity, was first
seen by Garriga. He pointed out that if one dimensionally reduced five
dimensional Euclidean Schwarzschild, along the tau direction, one would
get a four-dimensional geometry, and a scalar field. These were singular
at the horizon, in the same manner as at the south pole of the
instanton. In other words, the singularity at the south pole, can be
just an artifact of dimensional reduction, and the higher dimensional
space, can be non s ingular. This is true quite generally. The scale
factor, b, will go like distance to the third, when the internal space,
collapses to zero size in one direction.

When one analytically continues the deformed sphere to a Lorentzian
metric, one obtains an open universe, which is inflating initially.
One can think of this as a bubble in a closed de Sitter like universe.
In this way, it is similar to the single bubble inflationary universes
that one obtains from Coleman De Lucia instantons. The difference is
that the Coleman De Lucia instantons require d carefully adjusted
potentials, with false vacuum local minima. But the singular
Hawking-Turok instanton, will work for any reasonable potential. The
price one pays for a general potential, is a singularity at the south
pole. In the analytically continue d Lorentzian space-time, this
singularity would be time like, and naked. One might think that anything
could come out of this naked singularity, and propagate through the big
bang light cone, into the open inflating region. Thus one would not be
able to p redict what would happen. However, as I already said, the
singularity at the south pole of the four sphere, is so mild, that the
actions of the instanton, and of perturbations around it, are well
defined.
This behavior of the singularity means one can determine the relative
probabilities of the instanton, and of perturbations around it. The
action of the instanton itself is negative, but the effect of
perturbations around the instanton, is to increase the action, that is,
to make the action less negative. According to the no boundary proposal,
the probability of a field configuration, is e to minus its action. Thus
perturbations around the instanton have a lower probability, than the
unperturbed background . This means that quantum fluctuation are
suppressed, the bigger the fluctuation, as one would hope. This is not
the case with some versions of the tunneling boundary condition.
How well do these singular instantons, account for the universe we live
in? The hot big bang model seems to describe the universe very well, but
it leaves unexplained a number of features.

First is the isotropy. Why are different regions of the microwave sky,
at very nearly the same temperature, if those regions have not
communicated in the past? Second, despite this overall isotropy, why are
there fluctuations of order one part in 10 to th e minus 5, with a
fairly flat spectrum? Third, why is the density of matter, still so near
the critical value, when any departure would grow rapidly with time?
Fourth, why is the vacuum energy, or effective cosmological constant, so
small, when symmetry b reaking might lead one to expect a value ten to
the 80 higher?

In fact, the present matter and vacuum energy densities can be regarded
as two axes in a plane of possibilities. For some purposes, it is better
to deal with the linear combinations, matter plus vacuum energy, which
is related to the curvature of space. A nd matter minus twice vacuum
energy, which gives the deceleration of the universe.

Inflation was supposed to solve the problems of the hot big bang model.
It does a good job with problem one, the isotropy of the universe. If
the inflation continues for long enough, the universe would now be
spatially flat, which would imply that the sum of the matter and vacuum
energies had the critical value. But inflation by itself, places no
limits on the other linear combination of matter and vacuum energies,
and does not give an answer to problem two, the amplitude of the
fluctuations. These have t o be fed in, as fine tunings of the scalar
potential, V. Also, without a theory of initial conditions, it is not
clear why the universe should start out inflating in the first place.
The instantons I have described predict that the universe starts out in
an inflating, de Sitter like state. Thus they solve the first problem,
the fact that the universe is isotropic. However, there are difficulties
with the other three problems. Accordin g to the no boundary proposal,
the a-priori probability of an instanton, is e to the minus the
Euclidean action. But if the Reechi scalar is positive, as is likely for
a compact instanton with an isometry group, the Euclidean action will be
negative.

The larger the instanton, the more negative will be the action, and so
the higher the a-priori probability. Thus the no boundary proposal,
favors large instantons. In a way, this is a good thing, because it
means that the instantons are likely to be in th e regime, where the
semi classical approximation is good. However, a larger instanton, means
starting at the north pole, with a lower value of the scalar potential,
V. If the form of V is given, this in turn means a shorter period of
inflation. Thus the u niverse may not achieve the number of e-foldings,
needed to ensure omega matter, plus omega lambda, is near to one now. In
the case of the open Lorentzian analytical continuation considered here,
the no boundary a-priori probabilities, would be heavily we ighted
towards omega matter, plus omega lambda, equals zero. Obviously, in such
an empty universe, galaxies would not form, and intelligent life would
not develop. So one has to invoke the anthropic principle.

If one is going to have to appeal to the anthropic principle, one may as
well use it also for the other fine tuning problems of the hot big bang.
These are the amplitude of the fluctuations, and the fact that the
vacuum energy now, is incredibly near zero . The amplitude of the scalar
perturbations depends on both the potential, and its derivative. But in
most potentials, the scalar perturbations are of the same form as the
tensor perturbations, but are larger by a factor of about ten. For
simplicity, I sh all consider just the tensor perturbations. They arise
from quantum fluctuations of the metric, which freeze in amplitude when
their co-moving wavelength, leaves the horizon during inflation.

Thus amplitude of the tensor perturbation, will thus be roughly one over
the horizon size, in Planck units. Longer co-moving wavelengths, leave
the horizon first during inflation. Thus the spectrum of the tensor
perturbations, at the time they re-enter th e horizon, will slowly
increase with wavelength, up to a maximum of one over the size of the
instanton.

The time, at which the maximum amplitude re-enters the horizon, is also
the time at which omega begins to drop below one. One has two competing
effects. The a-priori probability from the no boundary proposal wants to
make the instantons large, and probabi lity of the formation of
galaxies, which requires that both omega, and the amplitude of the
fluctuations, not be too small. This would give a sharp peak in the
probability distribution for omega, of about ten to the minus three. The
probability for the te nsor perturbations will peak at order ten to the
minus eight. Both these values, are much less than what is observed. So
what went wrong.

We haven't yet taken into account the anthropic requirement, that the
cosmological constant is very small now. Eleven dimensional supergravity
contains a three-form gauge field, with a four-form field strength. When
reduced to four dimensions, this acts a s a cosmological constant. For
real components in the Lorentzian four-dimensional space, this
cosmological constant is negative. Thus it can cancel the positive
cosmological constant, that arises from super symmetry breaking. Super
symmetry breaking is an anthropic requirement. One could not build
intelligent beings from mass less particles. They would fly apart.

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 find a non
anthropic explanation for the cosmologic al 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 f act, for reasonable sizes of
the internal dimensions, the quantum steps in the cosmological constant,
would be much larger than the observational limits. At first, I thought
this was a set back for the idea there was an anthropically controlled
cancellati on of the cosmological constant. But then, I realized that it
was positively in favor.

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
problem of low omega I described earlier. If there were several discrete
solutions, or a continuous family of t hem, the strong dependence of the
Euclidean action on the size of the instanton, would bias the
probability to the lowest omega and fluctuation amplitude possible. This
would give a single galaxy in an otherwise empty universe, not the
billions we observe . But if there is only one instanton in the
anthropically allowed range, the biasing towards large instantons, has
no effect. Thus omega matter and omega lambda, could be somewhere in the
anthropically allowed region, though it would be below the omega ma tter
plus omega lambda =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 omega tota l =1 line.
Assuming that one can find a model that predicts a reasonable omega, how
can we test it by observation? The best way is by observing the spectrum
of fluctuations, in the microwave background. This is a very clean
measurement of the quantum fluctuations, a bout the initial instanton.
However, there is an important difference between the non-singular
Coleman De Lucia instantons, and the singular instantons I have
described. As I said, quantum fluctuations around the instanton are well
defined, despite the singularity. Perturbations of the Euclidean
instanton, have finite action if and only, they obey a Dirichelet
boundary condition at the singularity. Perturbation modes that don't
obey this boundary condition, will have infinite 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 space-time, the Dirichelet
boundary condition implies that perturbations reflect at the time like
singularity.

This has an effect on the two-point correlation function of the
perturbations, but it seems to be quite small. The present observations
of the microwave fluctuations are certainly not sensitive enough to
detect this effect. But it may be possible with the new observations
that will be coming in, from the map satellite in two thousand and one,
and the Planck satellite in two thousand and six. Thus the no boundary
proposal, and the pea instanton, are real science. They can be falsified
by observation. I will finish on that note.

"It's uncertain whether intelligence has any long term survival value.
Bacteria do quite well without it."

Stephen Hawking