CMB Features of Brane Inflation

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1 CMB Features of Brane Inflation Jiajun Xu Cornell University With R. Bean, X. Chen, G. Hailu, S. Shandera and S.H. Tye hep-th/ , arxiv: , arxiv: Cosmo 08

2 Brane Inflation (Dvali & Tye, KKLMMT, DBI) throat r = r 0 D3 φ D3 r ~ R Calabi! Yau

3 Brane Inflation in Warped Throat Consider D3 Branes moving in the AdS 5 X 5 background ds 2 = h 2 (r)( dt 2 + a(t) 2 dx 2 ) + h 2 (r)(dr 2 + r 2 ds 2 X 5 ), S = in the UV region, d 4 x g ds 2 X5 = ds 2 T 1,1 e Φ T (φ) 1 φ 2 T (φ) + T (φ) V (φ) T 3 m4 s g s = m4 s g s e Φ(r) T (φ) = T 3 h 4 (φ) V (φ) = V D D(φ) + corrections ( V D D(φ) = V 0 1 V ) 0 1 4π 2 v φ 4 V 0 = 2T 3 h 4 A

4 Our Current Understanding of the Early Universe - Homogeneous and isotropic - Primordial perturbations are: nearly Gaussian 9 <f local NL < <f eq NL < R = nearly adiabatic nearly scale invariant - Tensor perturbation S/R < O(0.2) n s 1 < O(0.05), dn s /d ln k < O(0.05) r<0.2

5 Three Scenarios non-relativistic slow roll (KKLMMT) e Φ T (φ) 1 φ 2 T (φ) + T (φ) V (φ) = 1 2 e Φ φ2 [ T (φ)(e Φ 1) + V (φ) ] If e Φ 1, geometric features in warp factor shows up in power spectrum and non-gaussianity. (Bean, Chen, Hailu, Tye, JX, arxiv: ) DBI (UV) : steep potential attracting the brane to the bottom. (Silverstein & Tong) f eq NL M 4 pl φ 4 V (φ) =m 2 φ 2 φ M pl 1 KM (Baumann & McAllister, hep-th/ ) (Bean, Shandera, Tye, JX, hep-th/ ) DBI (IR) : steep potential driving the brane out of the throat. (Chen) V (φ) = m 2 φ dn s d ln k f eq NL 70 Due to a stringy suppression of power spectrum on large scales (Bean, Chen, Peries, JX, arxiv: )

6 Sharp features in Brane Inflation Background geometry is not smooth and dilaton runs. (Hailu & Tye) hh(r) ln(r p+1 ) ln(r p ) 2π 3g s M h 4 (r) r4 R 4 B K p l (1 + ), = K p i 3g s M 16π 1 p 3 [ ( )] r rp 1 + tanh d p r r For slow roll, steps in the potential V eff (φ) =T (φ)(e Φ 1) + V (φ) V V c For DBI, steps in the speed limit T (φ) T T b

7 The Power Spectrum ( ) The power spectrum v k + ( k 2 c 2 s z z ) v k = 0 P R k3 2π 2 u k 2 z /z encodes all the information from the inflationary background Define three parameters v k zu k, ( H 2 2π φ ) 2 z a 2ɛ/c s ɛ Ḣ ɛ, η H2 Hɛ, s ċs. Hc s z z = 2a2 H 2 ( 1 ɛ η 4 3s 2 ɛ η 4 + ɛs 2 + η2 8 ηs 2 + s2 2 + η 4H ṡ 2H ) dominant in slow-roll dominant in DBI inflation

8 The Slow-Roll Power Spectrum 7 z z 2a2 H 2 ( 1 c ɛ 1 N 2 e ) V V c 9 10 R P In KKLMMT, ɛ c ɛ 1, N e 1 observable c observable!! 2 Best Fit: k(/mpc) c/ɛ = 0.2 c/d = O(1) (Adams, Ross, Sarkar 1997, Leach, Liddle, 2001 Hunt, Sakar, 2004, 2007 Adams, Creswell, Easther, 2001 Peiris et al, 2003 Covi et al, 2006, 2007)

9 The DBI Power Spectrum z z 2a2 H 2 ( 1 b N 2 e ) 2000 T T b b N e 1 c 3 s need b=-0.3, too large for steps due to duality cascade

10 Slow-roll: Estimations of Non-Gaussianity ui a 2 ɛ η u 1 u 2 u 3 non G O( η) ɛ V/H 2 5c t accel φ/ φ d/ cv, c/d = O(1) c/ɛ = 0.2 η η = ɛ Hɛ 7c3/2 dɛ non G O(1), DBI: b N e 1 c 3 s a 3 ɛ 2c 2 s (a 3 ɛ/c 4 s )ζ ζ 2 non G O(c 2 d dt ( η Given ) ζ 2 ζ non G η c 2 s c 2 s aɛ c 2 sζ( ζ) 2 non G s s c 2 s s ) s c s 1 c s b N e H t c s c 3 s b = 0.01, N e = 0.001, c s = 0.1, 1 c s b N e 100, b c 2 s b c 2 s 1

11 Multiple Steps Duality cascade gives a series of steps, ln(r p+1 ) ln(r p ) 2π 3g s M Feature on scale k in the power spectrum shows up on angular scale on CMB l π l k 1 H 1 0 dn e d ln k d ln l Hdt Ḣ φ dφ, Take l=2, l=20 as two steps for example, d ln l dφ ln(2) ln(20) = ln(20) ln(l 3 ) l 3 = 200, l 4 = 2000

12 Summary Brane inflation with D3 branes in KS throat is very rich in CMB phenomenology. ( f NL, dn s /d ln k, local features) Generically the dilaton runs, and features in the warp geometry translate into features in the slow-roll potential. The sensitivity to the steps is controlled by c/ɛ. Brane inflation is highly sensitive to small features in the inflaton potential because its small field nature. DBI scenario: sharp features in warp factor gives features in non-guassianity on top of the smooth f NL c 2. Sharp features if shows up in CMB power spectrum, they appears on several correlated scales, and accompanied by non-g. If no signal in CMB power spectrum, non-g has a better chance to see it. s

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