Large Primordial Non- Gaussianity from early Universe. Kazuya Koyama University of Portsmouth

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1 Large Primordial Non- Gaussianity from early Universe Kazuya Koyama University of Portsmouth

2 Primordial curvature perturbations Proved by CMB anisotropies nearly scale invariant n s = ± nearly adiabatic nearly Gaussian α < 0.16, S / ζ α 3 ζ( x) = ζ g( x) + f ζ ( x) 5 local g 9 < local < 111 Generation mechanisms inflation curvaton collapsing universe (Ekpyrotic, cyclic) f Komatsu et.al al. 008

3 Generation of curvature perturbations Delta N formalism curvature perturbations on superhorizon scales = fluctuations in local e-folding number t = ζ = Ntx (, i ) N() t i i Ntx (, ) dtht ' (', x) t i Starobinsky ;85, Stewart&Sasaki Sasaki 95 B ζ =Ψ δρ 3( ρ + P) ζ in = 0

4 How to generate delta N entropy perturbations Sasaki. 008 adiabatic perturbations single field inflation multi-field inflation, new Ekpyrotic isocurvature curvaton, modulated reheating, multibrid inflation

5 Suppose delta N is caused by some field fluctuations at horizon crossing Lyth&Rodriguez 05 i N 1 N ζ(, tx) = δϕi + δϕiδϕj +... IJ, ϕi ϕi ϕj Bispectrum B ( k, k, k ) ζ 1 3 N N N r r r r r r ζ( k ) ζ( k ) ζ( k ) = π δ ( k + k + k ) B ( k, k, k ) ( ) ( ) D 1 3 ζ 1 3 P ( k ) P ( k ) perm. N N N B ( k, k, k ), I, J, IJ = ζ 1 ζ + +, I, J, K IJK 1 3 N, IN, I Local type ( classical ) (local in real space =non-local in k-space) Equilateral type ( quantum ) (local in k-space)

6 Observational constraints local type maximum signal for k 3 ζ( x) = ζ g( x) + f ζ g( x) 5 WMAP5 9 < f 111 local local < k, k 3 1 k r 1 k r k r 3 Equilateral type maximum signal for k1 k k3 k r 3 WMAP5 < < equil 151 f 53 k r 1 k r

7 Theoretical predictions Standard inflation Non-standard scenario Single field Multi field f local, equil f local depending on the trajectory K-inflation, DBI inflation = O( εη, ) 1 equil f = 1/ c 1 = O(1) Rigopoulos, Shellard, van Tent 06 Wands and Vernizzi 06 Yokoyama, Suyama and Tanaka 07 Features in potential Ghost inflation DBI inflation equil s RS curvaton s f = (1 / c ) / (1 + T ) > 1 ( ) local f ρ ρ (5 / 4) / curvaton decay new Ekpyrotic (simplest model) f local > ( n 1) s 1 isocurvature perturbations (axion CDM) f local 10 α 5 3

8 Three examples for non-standard scenarios (multi-field) K-inflation, DBI inflation Arroja, Mizuno, Koyama JCAP (simplest) new ekpyrotic model Koyama, Mizuno, Vernizzi, Wands JCAP (axion) CDM isocurvature model Hikage, Koyama, Matsubara, Takahashi, Yamaguchi (hopefully) to appear soon

9 K-inflation Non-canonical kinetic term Amendariz-Picon et.al 99 μ S = d x gp( X, φ), X = μφ φ 4 1 Field perturbations (leading order in slow-roll) c = P, X s P, X + XP, XX 1 H PT Pζ, r = = 16c csε M pl Pζ sound speed s ε Garriga&Mukhanov 99

10 k r 3 LoVerde et.al al. 07 Bispectrum k r 1 k r P Bk (, k, k) Fk (, k, k), 1 3 ζ = kkk 1 3 DBI inflation 1 PX ( ) = ( 1 f( φ) X 1 ) V( φ) f ( φ) cf local-type Fk (, k, k) Aishahiha et.al al cs local 3 local F ( k1, k, k3) = f ( k1 + k + k3) 10 1 k r 1 k r k r 3

11 Observational constraints (too) large non-gaussianity eff 35 1 f 108 cs Lyth bound r 1 M p = for equilateral configurations Δφ = ΔN = 16c ε < 10 s 6r 7 1 n 4ε 0.04 ± s f > eff 300 D3 anti-d3 inflaton Huston et.al 07, Kobayashi et.al 08 φ < φ UV

12 Multi-field model S = d x gp X X = 4 IJ IJ 1 I μ J (, φ), μφ φ b P( X ) = P% ( X% ), X% = X + X X X Adiabatic and entropy decomposition adiabatic sound speed c entropy sound speed ( ) I J IJ J I P%, X% ad = P% + X, X 0P % %, XX % % c en = 1+ bx δσ 0 Arroja, Mizuno, Koyama 08 Renaux-Petel Petel, Steer, Langlois Tanaka 08 δ s X% entropy = X 0 0 adiabatic

13 Multi-field k-inflation Langlois&Renaux Renaux-Petel 08 IJ PX ( ) = PX ( ) c = en 1 Multi-field DBI inflation 1 ( ) ( det( ( ) ) 1 ) IJ I J PX = gμν fφ GIJ μφ νφ V( φ) f ( φ) c = c en ad Renaux-Petel Petel, Steer, Langlois Tanaka 08 Final curvature perturbation ζ = + ζ T S * RS * H H ζ = δσ, S = δ s & σ s&

14 Transfer from entropy mode Tensor to scalar ratio T RS Renaux-Petel Petel, Steer, Langlois Tanaka 08 r = 16ε c Bispectrum k-dependence is the same as single field case! 3 eff ζ eff ζ f = f, 108 cs 1+ T ζ RS ζ large transfer from entropy mode eases constraints Trispectrum s 1 1+ T RS Mizuno, Koyama, Arroja 09 different k-dependence from single field case? 1+ T RS 1+ T 3 RS

15 New ekpyrotic models Collapsing universe H a k 1 t bounce t Ekpyrotic collapse Khoury et.al al. 01 n at () = ( t), n 1

16 Old ekpyrotic model V = c V0e ϕ Khoury et.al al. 01 at / () = ( t) c spectrum index for ζ is n = 3 the bounce may be able to creat a scale invariant spectrum but it depends on physics at singularity New ekpyrotic model s at Lyth 03 / () = ( t) c B V = Ve V e cϕ 1 / c () ( ), at c ϕ = t = + c c c 1 Lehners et.al, Buchbinder et.al al. 07 at / () = ( t) c at / () = ( t) c B 1

17 Multi-field scaling solution is unstable entropy perturbation which has a scale invariant spectrum is converted to adiabatic perturbations Koyama, Mizuno & Wands 07 δ s B B δ s B B δ s ζ c H π 0 = δ s δϕ1 B: B: ζ δϕ = c c + c 1 HT π

18 Delta-N formalism log H B δ s δ s δ N B B B dn 1 d N δ N = δs+ δs ds ds N = log a

19 Predictions 1 1 ns 1= > c1 c r = f = c > ( n 1) 1 3 local 1 1 s Generalizations changing potentials Buchbinder et.al 07 conversion to adiabatic perturbations in kinetic domination Koyama, Mizuno, Vernizzi & Wands 07 Lehners &Steinhardt 08

20 Non-Gaussianity from isocurvature perturbations (CDM) Isocurvature perturbations are subdominant PS α = < ( ns = 1) P + P S ζ < ( ns = 1.5) <0.001 ( n = ) Non-Gaussianity can be large S Boubekeur& Lyth 06, Kawasaki et.al 08, Langlois et.al 08

21 Axion CDM Massive scalar fields without mean δρ CDM m σ Linde&Mukhanov 97, Peebles 98, Kawasaki et.al al 08 Entropy perturbations S = δρcdm 3δρr η ρ 4ρ CDM r η g g S S 3 3/ O(1) Dominant ng may come from isocurvature perturbations S f α α ζ ζ eff /

22 Bispectrum of CMB from the isocurvature perturbation S N = I l1 l l 3 l 1 l l 3 b l1 l l 3 C l1 C l C l3 Δ l1 l l 3 Noise: WMAP 5-year Equilateral triangle Adiabatic (f =10) S S = N N eff f adi iso α = / The isocurvature perturbations can generate large non-gaussianity (f ~40)

23 WMAP5 constraints -Minkowski functional Hikage, Koyama, Matsubara, Takahashi, Yamaguchi 08 Minkowski functional measures the topology of CMB map (=weighted some of bispectrum) no detection of non-g from isocurvature perturbations and get constraints α < ( n = 1) α < 0.04 ( n = 1.5) α < ( n = ) η η η comparable to constraints from power spectrum

24 Theoretical predictions Standard inflation Non-standard scenario Single field Multi field f local, equil f local depending on the trajectory K-inflation, DBI inflation = O( εη, ) 1 equil f = 1/ c 1 = O(1) Features in potential Ghost inflation DBI inflation curvaton s f = (1 / c ) / (1 + T ) > 1 ( ) local f ρ ρ (5 / 4) / curvaton decay new Ekpyrotic (simplest model) f equil s RS local > ( n 1) s 1 isocurvature perturbations (axion CDM) f local 10 α 5 3

25 Conclusions Power spectrum from pre-wmap to post-wmap bispectrum WMAP 8year Planck Do everything you can now!

26 Axion CDM Classical mean of axion a = faθa quantum fluctuations δ a = H /π inf if f θ < H π a a inf / δρa ρ a δ a =, a* = a* Hinf π δρa Ω S = r, r = ρ Ω r a a cdm 0.8 Fa a* GeV 10 GeV Ωcdmh =