Some Problems in String Cosmology

Miao LiInstitute of Theoretical Physics

Academia Sinica

The Challenges from Observational Cosmology

1. Cosmological constant or dark energy

• Strong indication from the Hubble diagram of type Ia supernovae

•Supported by other experiments such as Boomerang, Maxima and WMA

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2. WMAP Results on CMB

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)

Best fit model

cosmic variance

Temperature

Temperature-polarization

1 deg

85% of sky

n=0.99

8 = 0.9

bh2 = 0.024

xh2 = 0.126

H0 = 72

= 0.17

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

There have been many proposals on the nature

of the dark energy, but this is not a subject ofthe present talk.We concentrate on a couple of theoreticalproblem associated with the CMB powerspectrum

Strictly, there has been no accurate definition of stringtheory in a time-dependent background when spacetimeis not asymptotically Minkowskian, since in stringtheory the only physical observables are S-matrixelements.String cosmology studies cosmology using either lowenergy effective action or equations of motion withstringy corrections.Motivated by recent observations, string theorists aregetting serious about possible physical effects of short distance physics.

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

CMB. of spectrumpower thegcalculatinby correct

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1. The boundary conditions

This has been considered by many peopleincluding U. Danielsson, Eather, B. Greene, Kinney,Shiu, Martin, Brandenberger, Goldstein, Lowe.And is a controversial issue regarding whetherthe correction to CMP power spectrum is of order .)(H/or H/ 2

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2. Noncommutative spacetime

theory.string gfor testinmotion"Brownian "of kind ofrelation that thisis hope best we The

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A scheme incorporating noncommutativity ofspacetime in the inflation scenario wasproposed by Brandenberger and Ho, weshould not write down the detailed formulas.The main idea is to modify the relationbetween the wave-length of the perturbationand the creation time of the perturbation.For the power-law inflation

nltt )/()a(

dlnkdn

,dlnk

dlnP(k)1n

defined are running its andindex spectral The length.-wave

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In conclusion, the noncommutative inflationmodel can rather easily explain the WMAPCMB data, especially the running of thespectral index. As a comparison, people havetried to understand these data within thestandard inflation scenario, and found that arather contrived and ugly potential of theinflaton is needed.

Since the WMAP result on the runningspectral index is of only 2-sigma, we still need to wait for the second year results to seewhether there is indeed a large deviation from the scaling invariant spectrum.

We are rather hopeful that the futurecosmology experiments will bring about a lot of excitements, and possible signature of Planck scale physics!