Testing the string theory landscape in cosmology

Transcription

1 別府 Testing the string theory landscape in cosmology 佐々木節

2 1. Cosmology Today Big Bang theory has been firmly established wavelength[mm] COBE/FIRAS CMB spectrum at T=.75K 00 sigma error-bars frequency[ghz]

3 Strong evidence for Inflation 3 WMAP 7yr T ( n1) T ( n) 1 C 4 0 P (cos ). highly Gaussian fluctuations almost scale-invariant spectrum only to be confirmed (by tensor modes?)

4 standard cosmological model = LCDM with scale inv spectrum 4 cosmological parameters (~ 5% accuracy) baryon density CDM density vacuum density curvature pert amplitude spectral index reionzation optical depth tensor/scalar ratio Larson et al 10 1% accuracy expected by PLANCK

5 What s next? 5

6 . String theory landscape Lerche, Lust & Schellekens ( 87), Bousso & Pochinski ( 00), Susskind, Douglas, KKLT ( 03),... There are ~ vacua in string theory vacuum energy r v may be positive or negative typical energy scale ~ M P 4 some of them have r v <<M P 4 6 which?

7 7 Is there any way to know what kind of landscape we live in? Or at least to know what kind of neighborhood we live in?

8 distribution function in flux space 8 Vacua with enhanced gauge symmetry may explain the origin of gauge symmetry in our Universe by courtesy of T. Eguchi

9 A universe jumps around in the landscape by quantum tunneling 9 it can go up to a vacuum with larger r v ( ds space ~ thermal state with T =H/ ) if it tunnels to a vacuum with negative r v, it collapses within t ~ M P / r v 1/. so we may focus on vacua with positive r v : ds vacua r v 0 Sato et al. ( 81)

10 Anthropic landscape 10 Not all of ds vacua are habitable. anthropic landscape Susskind ( 03) A universe jumps around in the landscape and settles down to a final vacuum with r v,f ~ M P H 0 ~(10-3 ev) 4. r v,f must not be larger than this value in order to account for the formation of stars and galaxies. Just before it has arrived the final vacuum (=present universe), it must have gone through an era of (slow-roll) inflation and reheating, to create matter and radiation. r vac r matter ~ T 4 : birth of Hot Bigbang Universe

11 Most plausible state of the universe before inflation is a ds vacuum with r v ~ M P4. ds = O(4,1) O(5) ~ S 4 11 false vacuum decay via O(4) symmetric (CDL) instanton O(4) O(3,1) inside bubble is an open universe Coleman & De Luccia ( 80) bubble wall false vacuum x R t x R

12 Natural outcome would be a universe with W 0 <<1. 1 V(f) empty universe: no matter, no life f previous vacuum V ~ M P 4 present vacuum V ~ M P H 0

13 Anthropic principle suggests that # of e-folds of inflation inside the bubble (N=Ht) should be ~ : just enough to make the universe habitable. Garriga, Tanaka & Vilenkin ( 98), Freivogel et al. ( 04) 13 Observational data excluded open universe with W 0 <1. Nevertheless, the universe may be slightly open: 1 W 10 ~ may be tested by PLANCK+BAO Colombo et al. ( 09)

14 14 What if 1-W 0 is actually confirmed to be non-zero:~ ? revisit open inflation! see if we can say anything about Landscape

15 3. Open inflation in the landscape constraints from scalar-type perturbations Simplest polynomial potential m 3 4 f 4 potential: V f f f 3 4 tunneling to a potential maximum ~ stochastic inflation Hawking & Moss ( 8) Starobinsky ( 84) 15 HM transition slow-roll inflation V H f too large fluctuations of f unless # of e-folds >> 60 Linde ( 95)

16 Two- (multi-)field model: quasi-open inflation heavy field s = false vacuum decay light field f = inflaton V mf f s s s f, V ~ perhaps naturally/easily realized in the landscape 16 Linde, Linde & Mezhlumian ( 95) If N ~< 60, too large supercurvature perturbation of f f sc H H? ~ F R s (3) p psc K ; K p K Ypl m( r, W) H F : Hubble at false vacuum H R : Hubble after fv decay MS & Tanaka ( 96) f 0

17 creation of open universe & supercurvature mode 17 wavelength > curvature radius supercurvature mode open universe ds vacuum bubble wall

18 4. Tensor perturbation in open inflation Yamauchi, Linde, MS, Naruko & Tanaka ( 11) if r fv ~ M p4, the universe will most likely tunnel to a point where the energy scale is still very high. Linde, MS & Tanaka ( 99) 18 rapid-roll stage will follow right after tunneling. perhaps no strong effect on scalar-type pert s: H F FV decay R H ~ f& rapid roll slow roll inflation C suppressed by 1/f & at rapid-roll phase need detailed analysis future issue f F

19 19 but tensor perturbations may not be suppressed at all. h TT ~ H M P? Memory of H F (Hubble rate in the false vacuum) may remain in the perturbation on the curvature scale could lead to strong constraints/implications

20 Log 10 [r/h * ] potential inside bubble: exponential model V exp f/ M P V / V * * f f* const. const. V H H exp / M H R P R * this realizes slow-roll inflation H? H * R * 0.5 * 10 4 * 10 * 1 curvature term potential kinetic term Log 10 [a(t) H * ]

21 two effects from tunneling: bubble wall + rapid roll 1 bubble-nucleation at r c =0 r C =0 C R C-region: ~ outside the bubble ds a ( ) d dr cosh r dw C C C C C time Bubble wall R-region: inside the bubble,, r r i i a ia ds a ( ) d dr sinh r dw R C R C R C R R R R R time open space Euclidean vacuum C-region R-region

22 Effect of tunneling/bubble wall on high freq continuum + low freq resonance p 1 p ~ 0 P ( ) T p wall fluctuation mode s ~0.0 s ~0.1 s ~1 s ~0.7 s ~ s 1 M P d f S 1 s ~ ; S1 dt & Cf MP V wall tension scale-invariant

23 rapid-roll phase ( * -)dependence of P T (p) 3 <<1: usual slow roll ~1: small p modes remember H at false vacuum >>1: No memory of H at false vacuum

24 CMB anisotropy due to wall fluctuation (W-)mode MS, Tanaka & Yakushige ( 97) ( C ) ( W ) 1 C C PW C% l l l ; PW dp P ( ) 0 T p s scale-invariant part 0 ( W ) C% 1 W l l 4 C H / s l * l= s = 10-5 s = 10-4 s = 10-3 s = 10 - W-mode dominates l= *

25 CMB anisotropy from rapid roll phase 5 <<1: the same as usual slow roll inflation ~1: small l modes remember initial Hubble >>1: No memory of initial Hubble l scales as (1 W ) 0 l at small l, scale-invariant at large l small l modes enhanced for * ~1

26 5. Summary 6 Open inflation has attracted renewed interest in the context of string theory landscape anthropic principle + landscape 1-W 0 ~ Landscape is already constrained by observations If inflation after tunneling is short (N ~ 60): simple polynomial potentials af bf 3 + cf 4 lead to HM-transition, and are ruled out simple -field models, naturally realized in string theory, are ruled out due to large scalar-type perturbations on curvature scale

27 Tensor perturbations may also constrain the landscape single-field model not easy to implement models with short slow-roll inflation right after tunneling in the string landscape. if <<1, energy scale must have been already very low. there will be a rapid-roll phase after tunneling. M P V ~ 1 V right after tunneling unless >>1, the memory of pre-tunneling stage persists in the IR part of the tensor spectrum large CMB anisotropy at small l (1 W0) l due to either wall fluctuation mode or evolution during rapid-roll phase We are already testing the landscape! 7

28 6. Other signatures? 8 CMB cold/hot spots = bubble collision? Aguirre & Johnson 09, Kleban, Levi & Sigurdson 11,... NG?? Non-Gaussianity from bubbles / NG hot spots? Blanco-Pillado & Salem 10, Sugimura et al. in progress

29 Populating landscape / resonant tunneling? Tye & Wohns 09, Brown & Dahlen 11 Measure problem / etc. etc Garriga & Vilenkin 08, Freivogel 11, Vilenkin 11,... finally, extrapolating history... bigbang theory ~ 1940 strong evidence 1965 (+5), confirmation 1990 (+50) inflation theory ~ 1980 strong evidence 000 (+0), confirmation 00? (+40?) string landscape ~ 000 strong evidence 015? (+15?), confirmation 030? (+30?)