A big complicating factor in understanding string cosmology
is understanding string theories. String theories and M theory appear
to be limiting cases of some bigger, more fundamental theory. Until
that's sorted out, anything we think we know today is potentially up
for grabs.
That being said, there are some basic issues in string
theory cosmology:
1. Can string theory make any cosmological predictions relevant to
Big Bang physics?
2. What happens to the extra dimensions?
3. Is there Inflation in string theory?
Low energy string cosmology
The baryonic matter that makes up the nuclei of atoms
seems to provide only a small fraction of the total mass in the Universe.
Most of the mass in our Universe appears to occur in the form of dark
matter, which is most likely made up of some exotic particle or particles
that interact very weakly and have a very large mass.
String theories require supersymmetry for quantum consistency,
and supersymmetric theories require bosons and fermions to come in pairs,
because the supercharge operator turns bosons into fermions and vice
versa.
So supersymmetric theories are good places to look for
exotic matter in the form of fermionic superpartners of bosonic particles
that carry forces.
In the Standard Model of particle physics, recall there
is a spontaneously broken symmetry that gives mass to the weak interaction
gauge bosons through the Higgs potential. The Standard model contains
three massive gauge bosons, two charged and one neutral, and a massive
neutral Higgs field.
The Minimal Supersymmetric Standard
Model (MSSM) is a supersymmetric
version of the Standard Model. The weak interaction gauge bosons and
Higgs fields in the MSSM have fermionic superpartners, and the neutral
superpartners are called neutralinos.
A neutralino would make a good candidate for for dark matter, because
it couples with weak interaction strength but should have a high mass.
But this is true only as long as it is stable. A neutralino
would be stable if there were nothing of lower mass that it could decay
into, i.e. it is the Lightest Supersymmetric Particle (LSP), and if
something called Rparity is conserved.
The experimental limits on supersymmetric particle masses
say that any neutralino LSP out there must have a mass greater than
40 GeV. A neutralino of that mass could give
and that's already in the right ballpark for the observed amount of
dark matter out there.
But the success of such a model depends on whether supersymmetry
can be broken at the right scale. Supersymmetry breaking has other cosmological
implications, such as a cosmological constant with a value that can
run away from the very small, but nonzero, value that has recently been
observed in the redshifts of supernovae. So this is far from a settled
problem.
Cosmology and string duality
The standard Big Bang cosmology assumes that the Universe
began expanding from a state that was very hot, very small, and very
highly curved. The Big Bang model agrees so well with observation that
it is therefore commonly assumed that any cosmological era that preceded
the Big Bang must have involved a Universe that was even hotter and
even smaller and more highly curved, until we reach the Planck scale
and the Planck temperature, where our ability to describe geometry runs
into fundamental quantum limits where gravity is strongly coupled and
can no longer be treated as a fixed classical substrate in which particles
or strings interact.
But string theory complicates such a naive monotonic extrapolation
backwards through time, temperature and curvature, because in string
theory there are symmetries that can obscure the difference between
large and small distance, large and small curvature, and large and small
coupling strength.
One such symmetry is Tduality. Recall that with strings
quantized in a flat spacetime background, if one dimension is wrapped
into a circle of radius R, by identifying x^{i} with x^{i}
+ 2pR, there are two new kinds
of modes added to the spectrum: modes with quantized momentum going
around the circle with quantum number n, and modes that wrap around
the circle with winding number w. The total mass squared of the string
then depends on these two numbers
This formula has a symmetry under the exchange
This is Tduality. The self dual point
is where
At the selfdual point, extra massless fields enter the dynamics that
reflect an enhanced group of symmetries.
Tduality has been applied to preBig Bang cosmology to
build a model that is probably wrong, but interesting to study nonetheless.
A cosmological solution to the vacuum Einstein equations
that is homogeneous but not isotropic is the Kasner metric, which can
be written as
The set of exponents {p_{i}} as constrained above have the
properties that they are all smaller than one, and they can't all have
the same sign. If n of the exponents are positive so that the Universe
expands as time increases in those n directions, then the remaining
Dn exponents are negative, and the Universe shrinks in those directions
as time increases.
String theory has a scalar field called the dilaton, and
the Kasner metric in this case extends to
Again, directions with p_{i} positive expand as time increases,
and those with p_{i} negative contract as time increases. Notice
that in this case, isotropic solutions are allowed where p_{i}
= ± D^{1/2}.
For every solution with some set of exponents and dilaton
{pi, f(t)}, there is a dual solution
with {pi',f'(t)} given by
So expanding solutions and contracting solutions are dual to one another.
This duality symmetry has led to an interesting proposal
for preBig Bang cosmology where the stringy Universe starts out flat,
cold and very large instead of curved,
hot and very small. This early Universe is unstable and starts
to collapse and contract until it reaches the self dual point, where
it heats up and starts to expand to give the expanding Universe we observe
today.
One advantage to this model is that it incorporates the
very stringy behavior of T duality and the self dual point, so it is
a very inherently stringy cosmology. Unfortunately, the model has failings
in both the technical and observational categories, so it's no longer
considered a viable model for string cosmology.
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