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?
3. What can string theory tell us about quantum gravity and cosmology?
Low energy string cosmology
Most of the mass in our Universe appears to occur in the
form of dark matter. One leading candidate for the composition of this
dark matter is something called a WIMP,
a Weakly Interacting Massive Particle. One strong candidate for the
WIMP comes from supersymmetry.
The Minimal Supersymmetric Standard
Model (MSSM) predicts the existence of spin 1/2 fermions called neutralinos that are the fermionic superpartners
of the neutral gauge bosons and Higgs scalars. Neutralinos would have
a high mass but interact very weakly with other particles. They could
make up a significant portion of the mass density of the Universe without
emitting light, so that makes them good candidates for the mysterious
source of dark matter in the Universe.
String theories require supersymmetry, so in principle,
if neutralinos were discovered to make up cosmic dark matter, that would
be good. But if supersymmetry were unbroken, fermions and bosons would
be exactly matched in the Universe, and that's not the way things are.
The really hard part of any supersymmetric theory is to break the supersymmetry
without losing all the advantages of having had the supersymmetry to
begin with. (It's very much one of those proverbial cake situations.)
One of the reasons particle and string physicists have
liked supersymmetric theories is that they predict zero total vacuum
energy, because the fermion and boson vacuum energies cancel each other
out. When supersymmetry is broken, the fermions and bosons don't exactly
match any more, the cancellation doesn't occur any more.
There seems to be pretty good evidence from the red shifts
of distant supernovae that the expansion of our Universe is accelerating
due to something like a vacuum energy or a cosmological constant. So
whatever path by which supersymmetry is broken in string theory needs
to lead at the end to the right amount of vacuum energy to account for
this observed acceleration. This is a theoretical challenge, because
supersymmetry breaking seems to give too large a contribution.
Cosmology and extra dimensions
Superstring cosmology is enormously complicated by the
presence of those pesky six (or seven in the case of M theory) extra
space dimensions that are required for quantum consistency of the theory.
Extra dimensions
that just sit there are challenging enough to deal with in
string theory, but in the framework of cosmology, the extra dimensions
are evolving in time according to the physics of the Big Bang and whatever
happened before it. So what keeps the extra dimensions from expanding
to get as big as the three space dimensions that we observe and measure
in our Universe?
But wait  there's a complicating factor to the complicating
factor: a superstring duality symmetry known as T duality. When a space
dimension is rolled up in a circle of radius R, the resulting string
theory ends up being equivalent to another string theory with a space
dimension rolled up in a circle of radius L_{st}^{2}/R,
where L_{st} is the string length scale. For many of these theories,
when the extra dimension radius R satisfies the condition R = L_{st},
the string theory has an enhanced symmetry with some massive particles
becoming massless. This is called the self
dual point and has special significance for many reasons.
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.
Inflation vs. the giant brane collision
What does string theory predict for the source of the
vacuum energy and pressure necessary to drive the inflationary period
of accelerating expansion? Scalar fields that could inflate Universe
at GUT scale could also be involved in breaking supersymmetry at just
above electroweak scale, determining coupling strengths of gauge fields,
and maybe even providing the vacuum energy for a cosmological constant.
String theory contains the ingredients to build models with supersymmetry
breaking and inflation or quintessence, but the trick is to get all
the ingredients to work together, and that is still, as they say, an
active area of research.
A current alternative model to inflation is the giant
brain collision model, also known as the Ekpyrotic
Universe, or the Big Splat. This
intriguing model starts out with a cold, static fivedimensional spacetime
that is close to being perfectly supersymmetric. The four space dimensions
are bounded by two threedimensional walls or three
branes, and one of those threedimensional walls makes up the
space that we live on. The other brane is hidden from our perception.
According to this theory, there is a third three brane
loose between the two bounding branes of the four dimensional bulk,
and when this brane hits the brane we live on, the energy from the collision
heats up our brane and the Big Bang occurs in our visible Universe as
described elsewhere in this site.
This proposal is quite new, and it remains to be seen whether
it will survive careful scrutiny.
The problem with acceleration
There is a problem with an accelerating Universe that
is fundamentally challenging to string theory, and even to traditional
particle theory. In eternal inflation models and most quintessence models,
the expansion of the Universe accelerates indefinitely. This indefinite
acceleration leads to situation where a hypothetical observer traveling
forever through the Universe will be eternally blocked from seeing any
evidence of most of the Universe.
The boundary of the region beyond which an observer can
never see is called that observer's event horizon.
In cosmology, the event horizon is like the particle
horizon, except that it is in the future and not in the past.
From the point of view of human philosophy or the internal
consistency of Einstein's theory of relativity, there is no problem
with a cosmological event horizon. So what if we can't ever see some
parts of the Universe, even if we were to live forever?
But a cosmological event horizon is a major technical problem
in high energy physics, because of the definition of relativistic quantum
theory in terms of the collection of scattering amplitudes called the
S Matrix. One of the fundamental assumptions
of quantum relativistic theories of particles and strings is that when
incoming and outgoing states are infinitely separated in time, they
behave as free noninteracting states.
But the presence of an event horizon implies a finite Hawking
temperature and the conditions for defining the S Matrix cannot be fulfilled.
This lack of an S Matrix is a formal mathematical problem not only in
string theory but also in particle theories.
One recent attempt to address this problem invokes quantum
geometry and a varying speed of light.
This remains, as they say, an active area of research. But most experts
doubt that anything so radical is required.
