Some Problems in String Cosmology

Miao Li

Institute 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

P

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 of

the present talk.

We concentrate on a couple of theoretical

problem associated with the CMB power

spectrum

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

isintuition her thischeck whetcan We

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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 .)(H/or H/ 2

0|a

, at time k/a

: off-cut a toequal is

mode thisof size physical when thevacuum

Sitter de ain be k to modegiven a of state

quantum theconsiders one specific, more be To

k

k

))2

sin(1()2

(P

be tomodified is )2

(P

spectrumpower original theThus,

2k

2k

H

HH

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2. Noncommutative spacetime

theory.string gfor testinmotion"Brownian "

of kind ofrelation that thisis hope best we The

cm.10 to

cm10 from ranging scale, string theis where

,XT

relationy uncertaint spacetime the

relation, universal a is there theory,stringIn

18-

33-s

2s

l

l

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

nltt )/()a(

dlnk

dn ,

dlnk

dlnP(k)1n

defined are running its andindex spectral The

length.-wave

cmacroscopi a is k n, largely sufficient aFor tivity.noncommuta spacetime

todue is termsecond The .on depends k andn on depends where

))/(1()/((k)

have We

ss

c

scn

)1/(4)1/(22s

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kkkkkl ncn

nc

cm1086.3 cm,1015.2 12,n

parameterswith

modelinflation tivenoncommuta theusing data theseallfit can We

077.0)0.002Mpck(dlnk

dn ,20.1)0.002Mpck(n

,031.0)0.05Mpck(dlnk

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are results WMAPThe

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1-s12.011.0

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sll

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.

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!