Curvaton model for origin of structure! after Planck

Implications of Planck for Fundamental Physics Manchester, 8 th May 013 Curvaton model for origin of structure! after Planck David Wands Institute of Cosmology and Gravitation, University of Portsmouth

outline l Curvaton non-adiabatic model for origin of structure smoking gun for non-adiabatic models l Non-Gaussianity l Isocurvature perturbations l Planck parameter constraints power spectrum bispectrum anomalies l Conclusions

V(χ) curvaton scenario: Linde & Mukhanov 1997; Enqvist & Sloth, Lyth & Wands, Moroi & Takahashi 001 χ curvaton χ = weakly-coupled, late-decaying scalar field - light field during inflation acquires an almost scale-invariant, Gaussian distribution of field fluctuations on large scales - quadratic energy density for free field, ρ χ =m χ / - spectrum of initially isocurvature density perturbations ζ 1 δρ 1 χδχ + δχ 3 χ χ χ 3 ρχ - transferred to radiation when curvaton decays after inflation with some efficiency, 0 < R χ < 1, where R χ Ω χ,decay ζ = R χ ζ χ R " χ 3 δχ χ + δχ % $ ' # χ & = ζ G + 3 ζ G 4R χ f NL = 5 4Rχ

non- adiaba(c field fluctua(ons see also mul(- field infla(on, modulated rehea(ng, inhomogeneous end of infla(on inflaton δχ! ζ ~ R χ # " δχ χ + δχ χ +... $ & % David Wands 4

Cosmological perturba(ons on large scales adiabatic perturbations e.g., perturb along the background trajectory δx x = δy y = δt n δ n γ B δn n y γ γ δn n B B = 0 adiabatic perturbations stay adiabatic x entropy perturbations perturb off the background trajectory δx δy x y e.g., baryon-photon isocurvature perturbation y x (non-linear) evolution of curvature perturbation on large scales

Dis(nc(ve predic(ons Local non- Gaussianity requires non- adiaba(c field fluctua(ons during infla(on David Wands 6

simplest quadratic curvaton: V=m χ / first-order perturbations # ζ = R χ ζ χ where R χ = 3Ω & χ % ( 1 $ % 4 Ω χ '( decay second-order perturbations f NL = 5 5 4R χ 3 5R χ 5 6 4 third-order perturbations g NL = 5 # 1 R χ 6R χ 18 10R χ 9 R 3 & χ % ( 9 $ 3 ' Predictions of the simplest quadratic curvaton model: for R χ 1 f NL = 5 4, g NL = 9 for R χ << 1 f NL = 5 >>1, τ NL = 36 4R χ 5 f NL >> g NL = 10 3 f NL single source consistency relation

Planck - new standard model of primordial cosmology non- Gaussianity parameter fnl measured by Planck is consistent with zero fnl f NL Bζ ( k1, k, k3 ) = P(k1 )P(k ) + P(k )P(k3 ) + P(k3 )P(k1 )

Constraints on local non-gaussianity WMAP9 constraints using estimators based on optimal templates: Ø Local: -3 < f NL < 77 (95% CL) Bennett et al 01-5.6 < g NL / 10 5 < 8.6 Ferguson et al; Smidt et al 010 LSS constraints on local ng from galaxy power spectrum: Ø Local: -37 < f NL < 0 (95% CL) Giannantonio et al 013-4.5 < g NL / 10 5 < 1.6 [cross-correlating SDSS+NVSS] Planck constraints (Ade et al March 013) Ø Local: f NL =.7 ± 5.8 (68% CL)

Constraints on local non-gaussianity WMAP9 constraints using estimators based on optimal templates: Ø Local: -3 < f NL < 77 (95% CL) Bennett et al 01-5.6 < g NL / 10 5 < 8.6 Ferguson et al; Smidt et al 010 LSS constraints on local ng from galaxy power spectrum: Ø Local: -37 < f NL < 0 (95% CL) Giannantonio et al 013-4.5 < g NL / 10 5 < 1.6 [cross-correlating SDSS+NVSS] Planck constraints (Ade et al March 013) Ø Local: -9.8 < f NL < 14.3 (95% CL)

Quadra(c curvaton non- linearity parameter Sasaki, Valiviita & Wands (006) see also Malik & Lyth (006) Planck σ bound R χ > 0.08 inflaton f NL =0.01 R χ

Dis(nc(ve predic(ons Local non- Gaussianity requires non- adiaba(c field fluctua(ons during infla(on absence of evidence is not evidence of absence! Curvaton model can produce almost Gaussian primordial perturba(ons, fnl ~1 constraints on fnl do give important constraints on curvaton models David Wands 1

f NL bounds on quadra(c curvaton V ( χ) = 1 m χ Fonseca & Wands (011) see also Nakayama et al (010) R χ 1 R χ m Γ χ * M Pl <<1 Planck bounds f NL David Wands 13

Primordial power spectrum constraints Inflaton P ζ 1 " $ 8π ε # H * M Pl % ' & Curvaton P ζ R " χ H * 9π $ # χ * % ' & tilt: n 1 = 6ε + η ϕ P T " H $ * π # M Pl % ' & tensor-scalar ratio: r T =16ε slow roll parameters ε = H H, η i = m i Planck 013: n = 0.964 ± 0.0075 r T < 0.01 tilt: n 1 = ε + η χ P T " H $ * π # M Pl % ' & tensor-scalar: r T =18 χ * 3H / R χ M Pl <<16ε David Wands 14

Different perspec(ves Inflaton viewpoint Tensor- scalar ra(o bounds ε < 0.01 Scalar (lt n=0.96 then favours η ϕ < 0 E.g., axion e.g., axion V(ϕ)=Λ 4 (1- cos(ϕ/f)) Curvaton viewpoint Tensor- scalar ra(o bounds H inf (model- independent), not ε Scalar- (lt either Large- field infla(on: ε 0.0 and η χ 0 e.g., λϕ 4 (with N 60) or m ϕ (with N 30 and late entropy from curvaton decay) Small- field with η χ < 0 and ε << 0.0 e.g., axion V(χ)=Λ 4 (1- cos(χ/f)) David Wands 15

Mixed inflaton+curvaton P ζ 1 # % 8π (1 w χ )ε $ H * M Pl & ( ' where w χ = 8εR M Pl 8εR M Pl + 9χ * tilt: n 1 = (6 4w χ )ε + (1 w χ )η ϕ + w χ η χ P T # H % * π $ M Pl & ( ' tensor-scalar ratio: r T =16(1 w χ )ε 16ε slow roll parameters ε = H H, η i = m i 3H David Wands 16

f NL + r T quadra(c curvaton + inflaton: ε=0.0 Fonseca & Wands (01) V ( χ) = 1 m χ inflaton curvaton f NL 5 w χ 4R χ Planck bounds f NL and r T David Wands 17

local trispectrum has terms at leading order τ NL = (f NL ) g NL N N N N N N N N can dis(nguish by different momentum dependence mul(- source consistency rela(on: τ NL (f NL ) David Wands 18

g NL + τ NL quadra(c curvaton + inflaton: ε=0.0 Fonseca & Wands (01) V ( χ) = 1 m χ inflaton curvaton τ NL f NL w χ g NL f NL w χ Planck bounds f NL and r T David Wands 19

self-interacting curvaton V ( χ) = 1 m χ ± m χ 4 f +... assume curvaton is Gaussian at Hubble exit during inflation, but allow for non-linear evolution on large scales before oscillating about quadratic minimum χ osc 1 = g osc δχ ( χ ) χ = g + g' δχ + g'' ( )... * + Enqvist & Nurmi (005) Huang (008) Enqvist et al (009) e.g. axion curvaton: n=0.96 => m =-0.06H * => hill-top curvaton: g >0 Kawasaki, Kobayashi & Takahashi (01) f NL = 5 4R χ! # " g''g g' $ &, τ NL = 36 % 5 f NL ~ g NL = 7 4R χ! # " g''g g' + g'''g 3g' 3 $ & %

asymmetries in the data: Hemispherical power asymmetry Dipole modulation? 3 f NL ζ G ζ G +... 5 short+long wavelength split: ζ G = ζ S + ζ L ζ = ζg + ( ) 3 f NL ζ S + ζ Sζ L + ζ L ζ S + ζ L +... 5 # 6 & 3 ζ = %1+ f NLζ L (ζ S + f NL ζ S ζ S +... $ 5 ' 5 ζ = (ζ S + ζ L ) + ) ( ( i.e., long-wavelength modulation ) ζ = (1+ AL )ζ S Grishchuk-Zeldovich effect (Lyth 013): where AL = AL < 0.01 fnl 6 f NLζ L 5

Conclusions: Curvaton provides a simple non-adiabatic model for origin of structure Local non-gaussianity ( f NL >1) requires non-adiabatic model but, non-adiabatic model does not require significant non-gaussianity Tensor-scalar ratio bounds inflation energy scale, not ε Quadratic curvaton well-described by simplest local f NL n 0.96 requires large-field inflation, ε 0.0 Many variants self-interactions (τ NL and g NL still small) curvaton+inflaton (τ NL could be large, scale-dependent f NL ) Many potential observables: trispectrum, isocurvature (bi)spectra, large-scale power modulation