Lecture 4 on String Cosmology: Brane Inflation and Cosmic Superstrings

Transcription

1 Lecture 4 on String Cosmology: Brane Inflation and Cosmic Superstrings Henry Tye Cornell University and HKUST IAS-CERN School 20 January 2012

2 Brane world

3 Brane world in Type IIB r m " W + G µ!

4 Inflationary Scenario Quantum Fluctuations V(!) Slow!Roll Region Damped Oscillations, Reheating!

5 How is inflation realized in brane world? Brane inflation Dvali and H.T. hep-ph/ Inflaton is an open string mode Inflaton potential comes from the closed string exchange

6 D3-anti-D3 brane inflation D3 Relatively flat potential? anti-d3 C.P. Burgess, M. Majumdar, D. Nolte, F. Quevedo, G. Rajesh, R. Zhang, hep-th/ G. Dvali, Q. Shafi and S. Solganik, hep-th/

7 FIGURES V Inflaton potential RIEF ARTICLE THE AUTHOR e via quantum mechanihas been studied in the ]. Here we shall use ctive action to find the d check the validity of pproximation. V (') For 1/' fixed 4 ion (that is, constant ϕ, proximation in the slowing of V the (y), as inflationary shown Fig. epoch 1. iverse), Like P hybrid = e 3 /G we calculate inflation the π e aimimv to(y) do = Γ((p so includibution from all kinetic + 3)/2) open string Regge slope), 1/ y potential V (y) as a function of the separation y for the Dp Dp-brane pair for 1. The dashed curve is the imaginary part of V (y). The thick line is the real part ulombic potential (the thin red curve) is shown for comparison. string one-loop channel, since only the tachyon mode contribution has an at the one-loop level, the evaluation of Im V (y) is completely field theoretic eneralization from 4 spacetime dimensions to (p + 1) dimensions yields the ( ) m 2 (p+1)/2 tachyon 0.5 (1) 4π

8 Flux compactification where all moduli of the 6-dim. manifold are stabilized D7 branes D7 branes warped throat Giddings, Kachru, Polchinski Kachru, Kallosh, Linde, Trivedi and many others KKLT vacuum

9 The KKLMMT scenario D7 branes D7 branes D3-brane anti-d3-brane Kachru, Kallosh, Linde, Maldacena, MacAllister, Trivedi, hep-th/

10 Why brane inflation is so robust? S = d 4 x a 3 (t) T 1 2 /T + V ( ) T Dirac-Born-Infeld action yields Lorentz factor : = /T 2 < T ( ) T (φ) φ 4 exponentially small!= inflaton Silverstein, Tong, hep-th/ Alishahiha, Silverstein, Tong, hep-th/ R! r = "3 h A = warping at bottom of throat

11 Probability with N e-folds: P (N e ) N 3 e D3 N. Agarwal, R. Bean, L. McAllister, G. Xu,

12 Other Possibilities Some simple scenarios Features: D7 Mobile D3s warped throats D3 D3 D3 anti-d3s in throats Wrapped D7s DBI D3

13 Testing Brane Inflation Compare power spectrum and its running Tensor mode (B mode polarization) Non-Gaussianity Steps (from Gauge-gravity duality)

14 A blip in CMB power spectrum ACBAR Kuo etc., astro-ph/

15 A small step in the potential can generate such a blip Adam, Cresswell, Easther, astro-ph/

16 As the D3 brane moves down the throat: Cascade Klebanov-Strassler throat SU((K + 1)M) SU(KM) l = 1 r = r 0 r = r SU((K 1)M) SU(KM) 1 l = 2 SU((K 1)M) SU((K 2)M) r = r 2 D SU(2M) SU(M)

17 RG Flow and Seiberg Duality T = 8π2 g 2 T2(2) ˆb = 2 SU(N) T2(1) Cascade SU(N M) T 1 (2) SU(N) SU(N + M) T 1 (1) ˆb = 0 ln(r 2 /r 0 ) ln(r 1 /r 0 ) 0 ln(r/r 0 ) The anomalous mass dimension has a correction that depends on which step the RG flow is at. This means that the coupling flows depend on which step the flow is at. Using gauge/gravity duality, we see that the dilaton runs and it has a kink at the position where Seiberg duality transition takes place. this leads to steps in the warp factor, which then leads to steps in the inflaton potential.

18 Predictions After fitting the feature at l ~ 20 in WMAP data, it predicts additional steps : their positions, their heights and their widths. p l T/T l p it also predicts non- Gaussianity features due to the steps. X. Chen, R. Easther, E. Lim, astro-ph/ Girma Hailu and HT, Hep-th/ R. Bean, X. Chen, G. Hailu, HT and J. Xu,

19 At the end of brane inflation: D3-Brane and anti-d3-brane annihilate: All energy released goes to strings: fundamental strings and D1-branes Callan and

20 Well-known important cosmological properties: Monopoles : density ~ Disastrous Domain walls : density ~ 1/a Dangerous cosmic strings : density ~ interaction cuts it down to a 3 a 2 a 4 during radiation <Gµ<10 6 Safe N. Jones, H. Stoica, H.T., hep-th/ S. Sarangi, H.T., hep-th/

21 Cosmic strings Cosmic string interactions produce a scaling cosmic string network.

22 History of cosmic strings Early 1980s : proposed to generate density perturbation as seed for structure formation; as an alternative to inflation; Kibble, Zeldovich, Vilenkin, Turok, Shellard, In 1985, Witten attempted to identify the cosmic strings as fundamental strings in superstring (heterotic) theory. He pointed out a number of problems with this picture: tension too big, no production and the stability issue. In early 1990s, COBE data disfavors cosmic strings. By late 1990s, CMB data supports inflation and ruled out cosmic string as an explanation to the density perturbation. In 1995, Polchinski and others pointed out the presence of D- branes in string theory. This led to the brane world/brane inflation scenarios, which led to a revival of cosmic strings, which can have much lower tensions and can be quite stable. These cosmic strings were produced cosmologically. Gµ > 10 6

23 (p,q) Superstrings In contrast to vortices in Abelian Higgs model, cosmic strings from brane inflation should have a spectrum in tension. This is the (p,q) strings, where p and q are coprime. (1,0) strings are fundamental strings while (0,1) strings are D1-strings. The spectrum depends on the particular brane inflationary scenario or 1!2 Gµ p,q = p 2 g 2 s + q 2 Gµ They have non-trivial interactions. E. Copeland, R. Myers and J. Polchinski, hep-th/ G. Dvali and A. Vilenkin, hep-th/

24 D1-string inside D3-brane S = M G dc ξc 2 G 2 + 2πnaδ 2 (x ) C 2 D3-brane a = 2τ 1 κ 4 the D1-string D1-vortex loop D1-string D1-vortex L. Leblond and HT hep-th/

25 Strings and axions A point particle can be charged under a gauge field, a one-form field. A string is charged under a two-form field. In 4-dim., a two-form field (NS-NS or RR) is dual to an axion. In a typical realistic stringy vacuum, there are a number of axions. So we expect a variety of cosmic string types.

26 Scaling of the Cosmic Superstring Network independent of initial conditions Insensitive to the details of the interactions Ω cs = 10ΓGµ g 2 s M. Jackson, N. Jones and J. Polchinski, hep-th/ H.T., I. Wasserman, M. Wyman, astro-ph/

27 Relative density of (p,q) strings n p,q µ 8 p,q

28 Cosmic string tension spectrum in a warped deformed conifold One may view the strings as D3-branes wrapping a 2- cycle inside the S 3 at the bottom of the throat. T p,q h2 A 2 b = (Klebanov-Strassler) q 2 gs 2 M is the RR flux wrapping S 3. + ( bm )2 sin 2 ( p M ), S. Gubser, C. Herzog, I. Klebanov, hep-th/ , H. Firouzjahi, L. Leblond, H.T., hep-th/

29 Example : M=5 A baryon with mass M 3/2 h A / α (M-p,0) (p,0) X. Siemens, X. Martin and K. Olum, astro-ph/ , T. Matsuda, hep-th/ ,....

30 Search for Cosmic Strings Lensing Cosmic Microwave Background Radiation Gravitational Wave Burst T/T (Doppler effect) Pulsar Timing Stochastic Gravitation Radiation Background

31 Possible CMB B-mode detection ^ ^

32 cosmic string lensing cosmic string introduces a deficit angle identify cosmic string earth

33 CSL-1 Sazhin etc. astro-ph/ z=0.46 ± identical spectra with confidence level above 99.9% 1.9 arc sec Gµ~ 4 x 10-7

34 Radio telescope? Recall Cowen and Hu. National Radio Astronomy Observatory

35 Shami Chatterjee, Jim Cordes, H.T., Ira Wasserman

36 Unfortunately not (higher resolution Hubble pictures): January 2006 If it is cosmic string lensing

37 Bound on cosmic string tension log(gµ) U. Seljak and A. Slosar, astro-ph/ n s =0.95 WMAP 0 β 0.05 n s β log r β log Gµ β n s 1.03 Gµ < 10 8 S. Shandera and H.T.,

38 A cusp Blanco-Padillo and Olum

39 Gravitational wave radiation from cusps Damour and Vilenkin prediction Log

40 Search for Cosmic Strings with low tension Lensing X Cosmic Microwave Background X Radiation Gravitational Wave Burst T/T (Doppler Xeffect) Pulsar Timing? Stochastic Gravitation Radiation Background Micro-lensing Cusp Doppler effect?

41 Low tension strings 10 8 >Gµ>10 14 Warped geometry can provide very low tension cosmic strings. They radiate gravitational waves much slower, so they live much longer, in particular the small loops. The small loops can cluster like dark matter; thus their local density is 5 orders of magnitude larger than that from the scaling cosmic string network. David Chernoff and HT, Chernoff

42 E = 8 Gµ Micro-lensing = Gµ = E Gµ 100kpc R l g = R Gµt today = 40pc t RGµ 10 8 t osc l g c 135yrs c = sec R 100kpc t today 13.5Gyr RGµ 10 8 Gµ GAIA : N L 0.03 Hogan and Narayan, 1984 David Chernoff

43 Typical scenario t 300s(R/10 kpc )(Gµ/10 10 )andt osc 70 yr (Gµ/10 10 ). Repetition : 10 3 Flux Time

44 Rate for LSST (Large Synoptic Survey Telescope)... similar to European GAIA LSST : stars observed 10 3 times each with a 15 s exposure over a 10 year period. Red for 10 kpc and blue for 100 kpc. Figure with G = 1; expect G Log N L 10, 100 kpc Log Μ 1 2

45 Superstring theory may be tested Instead of searching for tiny particles or signatures in accelerators, we can search for distinctive features suggested by string theory. Steps in the CMB power spectrum suggested by gaugegravity duality in a warped throat. Production of cosmic superstrings that stretch across the universe. The string tensions have the right values so these cosmic superstrings are compatible with all present day observational bounds and yet can be detected in the near future. Micro-lensing detection offers the best hope to reach to very low tensions and provide very distinctive signatures.

46 Thank you!