Cosmology of moving branes and spinflation

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1 Cosmology of moving branes and spinflation 8 Dark Energy in the Universe Damien Easson University of Tokyo

2 Outline Brane Inflation, Moduli Stabilization and Flux Compactifications Cyclic, Mirage cosmologies (using angular momentum) Spinflation DE, Gregory, Tasinato, Zavala hep-th/ DE, Gregory, Mota,Tasinato, Zavala DE, Gregory in progress

3 Inflationary Paradigm At early times the Universe experienced a short burst of extremely rapid (accelerated) expansion. Inflation solves conceptual and theoretical problems of the SBB model. Basic predictions are all supported by the data.

4 Brane Inflation Dvali, Tye 99 Coulomb attraction D3 D3 (geometric inflation) lightest string = 4D particle, Tachyon You live here! d M 2 T = d 2 M 4 s M 2 s d l s M 2 T 0 Brane/anti-brane separation (in X 6 ) acts like an inflaton...like Higgs in SM, T condenses, ending inflation

5 Observational Predictions In the annihilation the anti-brane destroys a brane and (observable) cosmic strings can be produced. There are also possible signatures in cosmological perturbations (in the CMB)...

6 In ordinary slow roll inflation, perturbations are Gaussian. In brane inflation non-gaussianities are possible and Planck can see them. Garriga, Mukhanov 99, Alishahiha, Silverstein, Tong 04 Significant non-gaussianity detection would be strong evidence of new physics in the inflaton sector.

7 Moduli Fields The metric in the extra dimensions (sizes and shapes of cycles of Calabi-Yau space) depends on continuous parameters called moduli. The parameters of a solution correspond to scalar fields (unconstrained by EOM, i.e. massless) in four dimensions. In a realistic compactification there can be many of these moduli fields.

8 Moduli Problems These scalar fields have nonuniversal couplings to matter: f i (ϕ i )L m (ψ i ) Different types of matter get different accelerations from these forces, violating the equivalence principle. Fifth force experiments constrain such forces to be very weak, but if fields remain massless we do not expect them to interact with matter more weakly than gravity. Need to stabilize moduli using fluxes and branes.

9 S IIB = 1 2κ 2 Concrete Stringy Model d 10 x g s { e 2φ [ R + 4( φ) 2] F (1) F 2 } 2 3! G (3) Ḡ(3) (5) 4 5! + 1 8iκ 2 e φ C (4) G (3) Ḡ(3) + S loc G (3) = F (3) τh (3) τ = C (0) + ie φ

10 S loc = R 4 Σ d p+1 ξt p g + µp R 4 Σ C p+1 In IIB RR potentials are: C (0),C (2),C (4),C (6),C (8) Compactify this on a CY manifold and turn on fluxes and wrap branes to stabilze moduli fields. Giddings, Kachru, Polchinski 2001 Kachru, Kallosh, Linde, Trivedi 2003 Study dynamics of brane probes in this background Kachru, Kallosh, Linde, Maldacena, McAllister, Trivedi 2003

11 ... Turn Compactify on the FLUX!! on CY ds 2 = e A(y) g µν dx µ dx ν + e A(y) g mn dy m dy n ds 2 = g µν dx µ dx ν + g mn dy m dy n Warping!

12 Brane Cosmologies 6 G(3) = ig(3) Σ4 6d Calabi Yau with fluxes D3 inflaton warped throat region (looks like point) Brane World process process N D3 (large hierarchy) IR UV N D7 Moving brane acts as inflaton aρ W = W + Ae 0 Moving branes experience expansion/ contraction as they move in the throat mirage cosmology Need nonperturbative effects to stabilize Kähler moduli

13 Klebanov Strassler 3 A Based on deformed conifold:! (wa )2 = z! A 1 F3 = 2πM! 2πα A! 1 H3 = 2πK! 2πα B!! z= Ω W = G3 Ω A A 2πK/gs M z=e e 70 h 50 h B A Η can bounce! 20 A large hierarchy warp factor h S S2 B Η 6 8 V ol(t (1,1) 16π 3 )= 27

14 Brane Dynamics & Mirage Cosmology DAE, Gregory, Tasinato, Zavala 07 The probe brane evolves according to the DBI action: [ S DBI = m d 4 x h 1 ( ] 1 hv 2 1 Induced mirage cosmology Kehagias, Kiritsis 99 ds 2 = h 1/2 ( (1 hv 2 ) dt 2 + dx i dx i) = dτ 2 + a 2 (τ)dx i dx i

15 Bounces are possible. The 4D effective theory on the brane is a scalar-tensor gravity that can violate the NEC. Represents a string theory resolution of a spacelike singularity.

16 Turning on angular momentum What if the brane spins as it moves in the throat? Conserved angular momentum: l r = g rs θ s 1 hv 2 v 2 = g ηη η 2 + l 2 (η) 1+hl 2 (η) l 2 (η) =g rs l r l s

17 Mirage cyclic cosmology ds 2 10 = h 1/2 (η) dx µ dx µ + h 1/2 (η)ds 2 6 h(η) ɛ 8/3 η dx x coth x 1 sinh 2 x (sinh (2 x) 2 x) 1/3 Introducing angular momentum generates a centrifugal barrier for the brane. Bound states near tip cyclic Universes. H 2

18 The mirage pictures has serious drawbacks, but it does provide an example of a time-dependent bounce and cyclic toy cosmologies in string theory. Try using spinning moving branes as inflatons instead. (We live somewhere off the inflaton brane) DE, Gregory, Mota, Tasinato, Zavala 07

19 Backreaction Easiest first step is to couple DBI to Einstein Hilbert action. Silverstein, Tong 2003 There are no NEC violating sources, making cyclic cosmologies impossible. Can have bounces in the radial field due to angular momentum or passing through a nonsingular tip (KS). Brane position: φ = T 3 r

20 DBI(nflation) in the Throat S = M 2 Pl 2 P (X, φ m )= g 1 s A moving brane sources inflation. d 4 x gr + d 4 x gp(x, φ m ) [ h 1 ] 1+hg mn g µν µ φ m ν φ n qh 1 + V (φ m ) For D3 moduli space is the internal space: γ 1 1 hv 2 {η, ψ, θ 1, θ 2, φ 1, φ 2 } v 2 = g mn ϕ m ϕ n Brane speed limit! E = 1 h P = 1 h [γ q]+v [ q γ 1 ] V

21 Ḣ = 3β 2h Position in throat given by field: φ ( h 2 g φφ φ2 = h 1 ) 2 ( H 2 β V +2qH H 2 ( 1 q + h q + h ) β V + q 2 1 H 2 β V ) 1+h l(φ)2 ( a 6 ) H 2 β V bounces due to angular momentum still possible but not with sufficient efoldings of inflation. ε = spinflatons prolong inflation 3β 2H 2 { [ q + f ( 3H 2 β V )] φ 2 + l2 (φ) a 6 [ q + f ( 3H 2 β )] 1 } V

22 Inflationary V (φ) =m 2 φ 2 trajectories (using full KS) 1 ah Inflating inflaton couples to SM fields t Number of e-foldings can increase slightly reheating L = 1 2 g2 φ 2 χ 2 h ψψφ Brodie, DE 03 Mukohyama 07

23 Non-Gaussianities For a brane moving through a warped background: S = DBI dt d x h 1 (φ) 1 h(φ) µ φ µ φ In standard slow roll inflation In DBI f NL γ 2 n s 1 << 1 (gaussian ground state of QHO) γ 1 1 hv 2

24 Brane inflation is a multi field model with non-standard kinetic terms. {η, ψ, θ 1, θ 2, φ 1, φ 2 } s "! # In general, adiabatic and isocurvature modes travel at different speeds (due to gammas) DE, Gregory, Mota, Tasinato, Zavala 07 Arroja, Mizuno, Koyama 08...but DBI is special Langois, Renauz-Petel, Steer, Tanaka 08

25 Conclusions Considering brane dynamics with angular momentum and cycling behavior gives rich, new phenomenology. Models can make general observational predictions (e.g. cosmic strings, non-gaussianity, gravitational waves). Much more work needs to be done to build explicit stringy models.