Non-Gaussianity from Curvatons Revisited

Transcription

1 RESCEU/DENET Summer Kumamoto July 28, 2011 Non-Gaussianity from Curvatons Revisited Takeshi Kobayashi (RESCEU, Tokyo U.) based on: arxiv: with Masahiro Kawasaki, Fuminobu Takahashi

2 The Curvaton Mechanism Linde, Mukhanov 97 Enqvist, Sloth 01 Lyth, Wands 01 Moroi, Takahashi 01 seeds cosmological density perturbations from scalar field fluctuations sourced during inflation (or Horava-Lifshitz gravity, Galilean mechanism, etc.) has only been studied for rather trivial curvaton potentials, e.g. quadratic however, a quadratic curvaton potential (or more generally, a positively curved potential) cannot produce the red-tilted perturbation spectrum concrete microscopic curvaton models also realize intricate energy potentials

3 The Curvaton Mechanism Linde, Mukhanov 97 Enqvist, Sloth 01 Lyth, Wands 01 Moroi, Takahashi 01 seeds cosmological density perturbations from scalar field fluctuations sourced during inflation (or Horava-Lifshitz gravity, Galilean mechanism, etc.) We need to go beyond simple quadratic curvatons! has only been studied for rather trivial curvaton potentials, e.g. quadratic however, a quadratic curvaton potential (or more generally, a positively curved potential) cannot produce the red-tilted perturbation spectrum concrete microscopic curvaton models also realize intricate energy potentials

4 This Work we investigate density perturbations sourced by a curvaton with a generic energy potential new features for non-quadratic curvatons case study: curvaton = pseudo-ng boson

5 The Curvaton Scenario log ρ V ρ φ : inflaton ρ σ : curvaton a 4 σ 2 σ a 3 log a

6 The Curvaton Scenario log ρ ρ φ : inflaton V H δρ σ ρ σ : curvaton a 4 σ 2 σ a 3 log a

7 The Curvaton Scenario log ρ ρ φ : inflaton V H δρ σ ρ σ : curvaton a 4 σ 2 σ a 3 log a ζ c 1 δρ σ ρ σ

8 Curvatons with Arbitrary Potentials log ρ ρ φ : inflaton V H a 4 δρ σ ρ σ : curvaton σ a 3 log a ζ c 1 δρ σ ρ σ

9 Curvatons with Arbitrary Potentials log ρ ρ φ : inflaton V H a 4 δρ σ ρ σ : curvaton σ a 3 log a ζ c 1 δρ σ ρ σ

10 Curvatons with Arbitrary Potentials log ρ non-uniform onset of oscillation for non-quadratic potentials! ρ φ : inflaton V H δρ σ ρ σ : curvaton a 4 σ a 3 δh osc log a ζ c 1 δρ σ ρ σ

11 Curvatons with Arbitrary Potentials log ρ non-uniform onset of oscillation for non-quadratic potentials! ρ φ : inflaton V H a 4 ρ σ : curvaton δρ σ σ a 3 δh osc log a ζ c 1 δρ σ ρ σ c 2 δh osc H osc Additional contributions to the density perturbations!

12 Density Perturbations P ζ = N H σ 2π 2 N σ = r 4+3r (1 X(σ osc )) 1 V (σ osc ) V (σ osc ) 3X(σ osc) σ osc V (σ osc ) V (σ ) r ρ σ ρ curvaton decay horizon exit osc onset of curvaton oscillation X(σ osc ) 1 2(c 3) σosc V (σ osc ) V (σ osc ) 1 : effects due to non-uniform onset of oscillation

13 Density Perturbations P ζ = N H σ 2π 2 N σ = r 4+3r (1 X(σ osc )) 1 V (σ osc ) V (σ osc ) 3X(σ osc) σ osc V (σ osc ) V (σ ) r ρ σ ρ curvaton decay horizon exit osc onset of curvaton oscillation spectral index n s 1 d ln P ζ d ln k = 2 3 V (σ ) H 2 +2Ḣ H 2 observational data n s =0.963 ± (WMAP7, 68%CL) requires the curvaton to be tachyonic during inflation (or Ḣ/H , implying large-field inflation)

14 Non-Gaussianity f NL = + 40(1 + r) 5(4 + 3r) V (σ osc ) + 3r(4 + 3r) 6r V (σ osc ) 3X(σ 1 osc) (1 X(σ osc )) 1 X (σ osc ) σ osc V (σ osc ) V (σ osc ) 3X(σ 1 osc) V (σ osc ) σ osc V (σ osc ) V (σ osc ) 2 V (σ osc ) 2 3X (σ osc ) + 3X(σ osc) σ osc σ 2 osc + V (σ osc ) V (σ osc ) (1 X(σ osc)) V (σ ) V (σ osc ) r ρ σ ρ curvaton decay horizon exit osc onset of curvaton oscillation

15 Non-Gaussianity f NL = + 40(1 + r) 5(4 + 3r) V (σ osc ) + 3r(4 + 3r) 6r V (σ osc ) 3X(σ 1 osc) (1 X(σ osc )) 1 X (σ osc ) σ osc V (σ osc ) V (σ osc ) 3X(σ 1 osc) V (σ osc ) σ osc V (σ osc ) V (σ osc ) 2 V (σ osc ) 2 3X (σ osc ) + 3X(σ osc) σ osc σ 2 osc + V (σ osc ) V (σ osc ) (1 X(σ osc)) V (σ ) V (σ osc ) r ρ σ ρ curvaton decay cf. quadratic curvatons f NL = 5 12 horizon exit osc onset of curvaton oscillation 3+ 4 r r f NL 1 only for curvatons decaying when subdominant ( ) r 1

16 Non-Gaussianity 40(1 + r) 5(4 + 3r) V (σ osc ) f NL = + 3r(4 + 3r) 6r V (σ osc ) 3X(σ 1 osc) (1 X(σ osc )) 1 X (σ osc ) σ osc V (σ osc ) + V (σ osc ) 3X(σ 1 osc) V (σ osc ) σ osc V (σ osc ) V (σ osc ) 2 V (σ osc ) 2 3X (σ osc ) + 3X(σ osc) σ osc σosc 2 Large fnl (with either sign) + V possible for both (σ osc ) V (σ osc ) (1 X(σ osc)) V (σ ) V (σ osc ) dominant/subdominant curvatons! r ρ σ ρ curvaton decay cf. quadratic curvatons f NL = 5 12 horizon exit osc onset of curvaton oscillation 3+ 4 r r f NL 1 only for curvatons decaying when subdominant ( ) r 1

17 case study : Curvaton = pseudo-ng boson of a broken U(1) symmetry V (σ) =Λ 4 1 cos σ f V 0 πf σ curvaton decay rate : Γ σ 1 16π m 3 f 2 = 1 16π Λ 6 f 5

18 case study : Curvaton = pseudo-ng boson of a broken U(1) symmetry V (σ) =Λ 4 1 cos σ f V 0 πf gives a red-tilted pert. spectrum σ curvaton decay rate : Γ σ 1 16π m 3 f 2 = 1 16π Λ 6 f 5

19 Density Pert. from a NG-Curvaton V curvaton dominant case, i.e. r ρ σ ρ r 1 dec 0 πf σ When varying only σ : P ζ f NL σ πf σ πf

20 Density Pert. from the Hilltop V 0 πf When varying only σ : σ curvaton dominant case, i.e. r ρ σ ρ r 1 dec log Pζ 20 f NL σ πf σ πf

21 Density Pert. from the Hilltop V 0 πf σ curvaton dominant case, i.e. r ρ σ ρ r 1 dec Strong enhancement of linear-order density pert. with mild increase of fnl When varying only : towards the hilltop. σ log Pζ 20 f NL σ πf σ πf

22 Windows for Inflation/Reheating Scales 2Λ 4 0 πf σ (f, Λ, H inf,t reh,σ )

23 Windows for Inflation/Reheating Scales 2Λ 4 0 πf σ (f, Λ, H inf,t reh,σ ) COBE norm. spectral index

24 Windows for Inflation/Reheating Scales 2Λ 4 σ πf = πf σ (f, Λ, H inf,t reh,σ ) log 10 Ρreh 14 GeV 10 5 COBE norm. 0 spectral index log 10 H inf GeV curvaton dominant case

25 Windows for Inflation/Reheating Scales 2Λ 4 σ πf = πf σ (f, Λ, H inf,t reh,σ ) log 10 Ρreh 14 GeV 10 5 f NL 10 COBE norm. 0 spectral index log 10 H inf GeV curvaton dominant case

26 Windows for Inflation/Reheating Scales 2Λ 4 σ πf = πf σ (f, Λ, H inf,t reh,σ ) log 10 Ρreh 14 GeV 10 5 f NL 20 COBE norm. 0 spectral index log 10 H inf GeV curvaton dominant case

27 Windows for Inflation/Reheating Scales 2Λ 4 σ πf = πf σ (f, Λ, H inf,t reh,σ ) log 10 Ρreh 14 GeV 10 5 f NL 30 COBE norm. 0 spectral index log 10 H inf GeV curvaton dominant case

28 Windows for Inflation/Reheating Scales 2Λ 4 σ πf = πf σ (f, Λ, H inf,t reh,σ ) COBE norm. log 10 Ρreh 14 GeV 10 spectral index f NL 30 Allowed window broadens significantly towards the hilltop,with non-gaussianity 10 f NL 30. log 10 H inf GeV curvaton dominant case

29 Summary We investigated density perturbations sourced by a curvaton with a generic potential. A non-quadratic curvaton experiences a non-uniform onset of its oscillations, which can strongly enhance/ suppress the density perturbations. fnl can be large with either sign, no matter the curvaton dominates/subdominates the universe upon decay. NG-curvatons at the hilltop work with a wide range of inflation/reheating scales, while predicting 10 f NL 30. Opens up new possibilities for the curvaton paradigm.

30 Backup Slides

31 δn case : t reh <t osc N σ = 2 N σ 2 = r 4+3r 16(1 + r) (4 + 3r)r t reh >t osc case : N σ = r 4+3r σ N ln ρ σosc 3 4 ln H2 osc σ 2 + r 4+3r ln ρσosc ln H 2 osc σ 2 σ 2 ln ρ σosc 3 4 ln H2 osc 2 N σ 2 = 16(1 + r) (4 + 3r)r N σ 2 + r 4+3r 2 σ 2 ln ρσosc ln H 2 osc

32 Curvaton Dynamics EOM : σ +3H(t) σ + V (σ) σ =0 ch(t) σ V (σ) σ where c =3+ 3(w + 1) 2 necessary condition : V ch 2 1, under which the above approximation is a stable attractor

33 Onset of Curvaton Oscillation σ Hσ =1 Hosc 2 = V (σ osc ) osc cσ osc 1 H osc H osc σ osc = 1 2 V (σ osc ) V (σ osc ) 1 σ osc σ osc σ = = c(c 3) 1 2(c 3) V 1 (σ osc ) H osc V (σ osc ) Hosc 3 σ osc V (σ ) σosc V 1 (σ osc ) V (σ osc ) V 1 (σ osc ) V (σ )

34 Hilltop Curvatons V (σ) =V m2 (σ σ 0 ) 2 under σ osc σ 0 σ osc 1, V 0 m 2 (σ osc σ 0 ) 2 1, P 1/2 ζ 3r 4+3r σ 0 σ osc σ 0 σ H inf 2πσ osc Σ osc Σ 0 f NL 5(4 + 3r) 18r σ osc σ 0 σ osc n s 1= 2 3 m 2 H 2 inf Log 10 Σ 0 Σ Σ 0