1. Some Problems in String Cosmology Miao Li Institute of Theoretical Physics Academia Sinica

2. The Challenges from Observational Cosmology 1. Cosmological constant or dark energy Strong indication from the Hubble diagram of type Ia supernovae

4. Supported by other experiments such as Boomerang, Maxima and WMAP

5. 2. WMAP Results on CMB

6. Universe is flat (total density = critical density) Atoms 4% Dark Matter 23% Dark Energy (cosmological constant?) 72% Adiabatic, scale invariant, Gaussian Fluctuations (Harrison-Zeldovich-Peebles, Inflation)

7. Best fit model cosmic variance Temperature Temperature- polarization 1 deg 85% of sky n=0.99  8 = 0.9  b h 2 = 0.024  x h 2 = 0.126 H 0 = 72  = 0.17

8. The most interesting, yet tentative result is the running the spectral index

9. There have been many proposals on the nature of the dark energy, but this is not a subject of the present talk. We concentrate on a couple of theoretical problem associated with the CMB power spectrum

10. Strictly, there has been no accurate definition of string theory in a time-dependent background when spacetime is not asymptotically Minkowskian, since in string theory the only physical observables are S-matrix elements. String cosmology studies cosmology using either low energy effective action or equations of motion with stringy corrections. Motivated by recent observations, string theorists are getting serious about possible physical effects of short distance physics.

11. There are at least two schemes which have attracted considerable attention. 1. Short distance physics set by “boundary conditions” at a cut-off 2. Noncommutative spacetime effects

13. 1. The boundary conditions This has been considered by many people including U. Danielsson, Eather, B. Greene, Kinney, Shiu, Martin, Brandenberger, Goldstein, Lowe. And is a controversial issue regarding whether the correction to CMP power spectrum is of order

17. 2. Noncommutative spacetime

18. A scheme incorporating noncommutativity of spacetime in the inflation scenario was proposed by Brandenberger and Ho, we should not write down the detailed formulas. The main idea is to modify the relation between the wave-length of the perturbation and the creation time of the perturbation. For the power-law inflation

21. In conclusion, the noncommutative inflation model can rather easily explain the WMAP CMB data, especially the running of the spectral index. As a comparison, people have tried to understand these data within the standard inflation scenario, and found that a rather contrived and ugly potential of the inflaton is needed.

22. Since the WMAP result on the running spectral index is of only 2-sigma, we still need to wait for the second year results to see whether there is indeed a large deviation from the scaling invariant spectrum. We are rather hopeful that the future cosmology experiments will bring about a lot of excitements, and possible signature of Planck scale physics!