The Quantum Structure of Space and Time (293 pages)

248 The Quantum Structure of Space and Time

It has been recognized recently that cosmic strings give a potentially large win-

dow into the string theory [3]. CMB observations put a stringent constraint on

cosmic strings produced at the end of inflation: only very light cosmic strings with

the tension (Gp),bs < 5. lo-' are consistent with the data. The KKLMMT model
[4] of stringy inflation is based on the throat geometry with the highly warped
region and therefore can easily explain the existence of light cosmic strings. At
present, however, no evidence is available for such cosmic strings, see [5] for the
recent Hubble Space Telescope observation which proved that the object CSL-1 is

not a lensing of a galaxy by a cosmic strings, contrary to previous expectations.

Inflationary models in string theory have few clear predictions for the primordial
spectral index and for the tensor to scalar ratio. A significant amount of gravita-
tional waves is expected to take place in chaotic models of inflation [6]. However,
most models of modular and brane inflation in string theory known at present do
not predict any significant amount of gravitational waves. Still there are models,
like [7] where in the context of string theory there is a possibility to explain the
primordial gravitational waves in case they will be actually detected.
With regard to the spectral index n, the situation is developing in a rather
interesting way. The 1st year WMAP data alone suggest

ns = 0.99 f 0.04 ,

the combination of the data from WMAP+CBI+ACBAR+2dFGRS gives

n, = 0.97 f 0.03.

Moreover, there is an indication from the most recent release of the Boomerang
data [l] that the central value of n, may be moving downwards towards
n, M 0.96
and it will most interesting to know what emerges from the new WMAP data".

The inflationary models in string theory in some cases have a clear computable

prediction for n,. For example, a racetrack model of modular inflation [8] predicts

n, = 0.95. This is a model with one Kahler modulus where the system has a saddle

point and inflates due to axion-inflaton into a stabilized KKLT string flux vacua

with de Sitter minimum [9] to account of the current acceleration of the universe.

Another model of hybrid inflation, the so-called D3/D7 brane inflation [lo], predicts

n, = 0.98 under a condition of the softly broken shift symmetry protecting the near-

flat inflationary potential in this model.

Planck satellite (2008?) is expected to provide the precision data on spectral

index n, at the level of 0.5%! This will help to focus on those models of inflation

loon March 16 2006, the WMAP three year data release took place at

http://lambda.gsfc.nasa.gov/.

The new data strongly support the standard cosmological model and favor an inflationary model

of [6]. The new value of the spectral index is ng = 0.95 f 0.02 in agreement with [l]. Fkom

all known at present models of stringy inflation with a clear prediction for the spectral index, the

racetrack model [8] seems to give the best fit to the data.