Probing dark radiation with inflationary gravitational waves - PowerPoint PPT Presentation

Probing dark radiation with inflationary gravitational waves Kazunori Nakayama (The University of Tokyo) R.Jinno, T.Moroi, KN, arXiv:1208.0184 JGRG22 @ University of Tokyo (2012/11/12) 12 年 11 月 11 日日曜日

Contents • Observational evidence of dark radiation • Effects of dark radiation on inflationary gravitational waves 12 年 11 月 11 日日曜日

Dark radiation � 4 � � 4 / 3 � 7 Radiation energy density 1 + N e ff ρ rad = ρ γ 8 11 N e ff = 3 . 04 in the standard model Helium abundance N e ff = 3 . 68 +0 . 80 − 0 . 70 (2 σ ) Izotov, Thuan , 1001.4440 WMAP+ACT+BAO N e ff = 4 . 56 ± 0 . 75 (68%) Dunkley et al., 1009.0866 WMAP+SPT+BAO N e ff = 3 . 86 ± 0 . 42 (68%) Keiser et al., 1105.3182 WMAP+ACT+SPT+BAO N e ff = 4 . 08 +0 . 71 − 0 . 68 (95%) Archidiacono, Calabrese, Melchiorri, 1109.2767 12 年 11 月 11 日日曜日

Dark radiation Dark radiation ? ∆ N e ff � 1 Dark radiation (X) should satisfy : X interaction is negligibly small X is relativistic at the CMB epoch Many models are proposed so far... Ichikawa, Kawasaki, KN, Senami, Takahashi (2007), KN, Takahashi, Yanagida (2010), Fischler, Meyers (2011), Kawasaki, Kitajima, KN (2011), Hasenkamp (2011) Menestrina, Scherrer (2011), Jeong, Takahashi (2012), K.Choi et al (2012) and many others What is unique signature of dark radiation ? 12 年 11 月 11 日日曜日

Inflationary GWs Inflation generates primordial GWs as quantum tensor fluctuations in de-Sitter spacetime ds 2 = a 2 ( t )[ − d τ 2 + ( δ ij + h ij ) dx i dx j ] d 3 k 1 � � k ( t ) e i kx e λ (2 π ) 3 / 2 h λ h ij = ij M P λ =+ , − k � � = H 2 k h λ � 2 k 3 δ 3 ( k � k � ) δ λλ � � h λ inf Quantization � H inf � 2 Dimensionless power ∆ 2 h ( k ) = 2 π M P spectrum almost scale invariant 12 年 11 月 11 日日曜日

Evolution of GW Eq.of.m of GW (without dark radiation) h λ � const for k � aH ¨ h λ + 3 H ˙ h λ + ( k/a ) 2 h λ = 0 h λ � a ( t ) − 1 for k � aH GW energy density at horizon entry ρ GW ( k ) ∼ M 2 P ∆ 2 h ( k )( k/a ) 2 ∼ M 2 P H in ( k ) 2 ∆ 2 h ( k ) ρ tot ∼ M 2 P H in ( k ) 2 Ω GW ( k ) = ρ GW ( k ) ∼ ∆ 2 h ( k ) ∼ const at horizon entry ρ tot Ω 0 GW ( k ) � Ω 0 rad ∆ 2 h ( k ) at present for k � k eq 12 年 11 月 11 日日曜日

KN, J.Yokoyama (2010) horizon entry horizon entry at M.D. era at R.D. era horizon entry at M.D. era (inflaton oscillation) GW spectrum traces thermal history of the Universe ! N.Seto, J.Yokoyama (2003), Boyle, Steinhardt (2005), KN, Saito, Suwa, Yokoyama (2008) 12 年 11 月 11 日日曜日

Dark radiation and GW Dark radiation affects GW spectrum in two ways ¨ h ij + 3 H ˙ h ij + ( k/a ) 2 h ij = 16 π G Π ij Anisotropic stress of X Modified expansion rate cf ) For standard neutinos, see S.Weinberg (2003), Y.Watanabe, E.Komatsu (2005) Modified expansion rate by parent field of X Modification on GW spectrum at high frequency Anisotropic stress is turned on after X production Modification on GW spectrum at low frequency 12 年 11 月 11 日日曜日

A model A scalar field φ decays into X at H ∼ Γ φ with branching ratio B X ρ Background evolution : B X = 1 ρ rad ρ φ + 3 H ρ φ = − Γ φ ρ φ , ˙ ρ rad + 4 H ρ rad = Γ φ (1 − B X ) ρ φ , ˙ ρ X + 4 H ρ X = Γ φ B X ρ φ , ˙ ρ φ φ nearly dominate at decay for ∆ N e ff � 1 ρ X Example) φ : saxion t t dec X : axion 12 年 11 月 11 日日曜日

A model A scalar field φ decays into X at H ∼ Γ φ with branching ratio B X ρ Background evolution : ρ rad ρ φ + 3 H ρ φ = − Γ φ ρ φ , ˙ ρ rad + 4 H ρ rad = Γ φ (1 − B X ) ρ φ , ˙ ρ X + 4 H ρ X = Γ φ B X ρ φ , ˙ φ nearly dominate at decay for ∆ N e ff � 1 Example) φ : saxion t t dec X : axion 12 年 11 月 11 日日曜日

A model A scalar field φ decays into X at H ∼ Γ φ with branching ratio B X ρ Background evolution : B X � 1 ρ rad ρ φ + 3 H ρ φ = − Γ φ ρ φ , ˙ ρ φ ρ rad + 4 H ρ rad = Γ φ (1 − B X ) ρ φ , ˙ ρ X + 4 H ρ X = Γ φ B X ρ φ , ˙ ρ rad φ nearly dominate at decay for ∆ N e ff � 1 ρ X Example) φ : saxion t t dec X : axion 12 年 11 月 11 日日曜日

A model 0.66 0.64 0.62 B X =0.26 0.6 B X =0.5 tH 0.58 B X =0.7 0.56 B X =1.0 0.54 0.52 0.5 10 -3 10 -2 10 -1 10 0 10 1 10 2 t/t dec Deviation from R.D., tH=0.5, around Φ decay 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (SM) Ω GW / Ω GW 1.2 1 0.8 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 k/k dec 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (nearly)matter (SM) Ω GW / Ω GW dominate 1.2 1 0.8 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 k/k dec 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (nearly)matter (SM) Ω GW / Ω GW dominate 1.2 1 anisotropic 0.8 stress 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 k/k dec 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (nearly)matter (SM) Ω GW / Ω GW dominate 1.2 1 anisotropic Dip appears 0.8 stress here 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 k/k dec 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (SM) Ω GW / Ω GW 1.2 1 0.8 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 k/k dec 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (SM) Ω GW / Ω GW 1.2 1 0.8 Normalization depends on 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 inflation scale k/k dec 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (SM) Ω GW / Ω GW 1.2 1 0.8 Normalization Position depends depends on on Φ lifetime 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 inflation scale k/k dec 12 年 11 月 11 日日曜日

Numerical result 1.6 B X = 1 w/o anisotropic stress w/ anisotropic stress 1.4 (SM) Ω GW / Ω GW 1.2 1 0.8 Normalization Position depends depends on on Φ lifetime 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 inflation scale k/k dec T φ ∼ 10 7 GeV Detectable at DECIGO for r � 10 − 3 and 12 年 11 月 11 日日曜日

1.6 1.6 w/o anisotropic stress w/o anisotropic stress 1.4 w/ anisotropic stress w/ anisotropic stress 1.4 1.2 B X = 0 . 26 B X = 0 . 5 (SM) (SM) 1 Ω GW / Ω GW Ω GW / Ω GW 1.2 0.8 1 0.6 0.4 0.8 0.2 0.6 0 10 -2 10 -1 10 0 10 1 10 2 10 3 10 -2 10 -1 10 0 10 1 10 2 10 3 k/k dec k/k dec 1.6 1.6 w/o anisotropic stress w/o anisotropic stress w/ anisotropic stress w/ anisotropic stress 1.4 1.4 B X = 0 . 7 B X = 1 (SM) (SM) Ω GW / Ω GW Ω GW / Ω GW 1.2 1.2 1 1 0.8 0.8 0.6 0.6 10 -2 10 -1 10 0 10 1 10 2 10 3 10 -2 10 -1 10 0 10 1 10 2 10 3 k/k dec k/k dec 12 年 11 月 11 日日曜日

Summary • Recent observation suggest extra light species : dark radiation • Dark radiation leaves characteristic signature in primordial GW spectrum • It also contains information on the production mechanism of dark radiation. 12 年 11 月 11 日日曜日

Backup Slides 12 年 11 月 11 日日曜日

GW normalization Standard model GW spectrum at horizon entry � 2 � k � n t Ω GW ( k = aH ) = ∆ 2 8 � H inf h ( k ) ∆ 2 h ( k ) ≡ , M 2 2 π k 0 24 P GW spectrum at present ( k � k eq ) Ω (SM) GW ( k ) = γ (SM) Ω (SM) × Ω GW ( k = aH ) , rad � 4 / 3 � � � g (SM) Expansion history : g ∗ ( T in ( k )) γ (SM) = ∗ s 0 , g (SM) g ∗ s ( T in ( k )) ∗ 0 12 年 11 月 11 日日曜日

GW normalization Standard model plus dark radiation GW spectrum at present ( k � k eq ) Ω GW ( k ) = γ Ω rad × Ω GW ( k = aH ) , � 1 / 3 Expansion history � g ∗ s ( T φ ) 1 + 7 ∆ N e ff 43 10 . 75 γ = , modified by X : � 1 / 3 � 1 / γ (SM) + 7 g ∗ s ( T φ ) ∆ N e ff 43 10 . 75 Radiation � 4 � � 4 / 3 � 7 density : e Ω rad = Ω (SM) × ( g ∗ 0 /g (SM) g ∗ 0 = 2 1 + N e ff ) 8 11 ∗ 0 rad Overall normalization is affected 12 年 11 月 11 日日曜日

GW normalization Parameterize normalization 2.2 Ω GW ( k ) C 1 xC 2 = C 1 × C 2 , 2 Ω (SM) C 1 GW ( k ) 1.8 C 2 1.6 Modified BG by X : 1.4 C 1.2 g ∗ 0 γ 1 C 1 ≡ γ (SM) g (SM) 0.8 ∗ 0 0.6 Anisotropic stress X : 0.4 0 0.5 1 1.5 2 2.5 3 analytically Δ N eff C 2 derived in C1xC2 accidentally close to unity Dicus, Repko (2004) 12 年 11 月 11 日日曜日

Anisotropic stress dF B X p 0 − m φ Boltzmann eq. for X � � dt = , 4 π ( p 0 ) 3 Γ φ ρ φ δ 2 F : distribution function of X ∂ t + p i p i p j dF = ∂ F ∂ x i + 1 ∂ F ∂ F p j p k dp i = 1 cf) Geodesic eq . 2 g ij,k , 2 g jk,i p 0 . p 0 p 0 ∂ p k dt dt GW effect here p j ¯ = a ∂ 2 ¯ Perturbed : ∂ ¯ p k p i +1 ¯ F F ∂ ( δ F 1 + δ F 2 ) + ¯ ∂ ( δ F 1 + δ F 2 ) ∂ p ∂ t δ p 0 . 2( δ g jk ) ,i p 0 ∂ x i p 0 ∂ t ¯ ¯ ∂ p i F ( t, ( g ij p i p j ) 1 / 2 /a ) − ¯ ¯ δ F 2 ( t, x i , p i ) ≡ F − ¯ δ F 1 ( t, x i , p i ) ≡ F − δ F 1 . F ( t, p ) , Contributes to ∂ ¯ ∂δ F 2 + ˆ p i ∂δ F 2 ∂ x i = 1 ∂ h ij F anisotropic stress ∂ p p ˆ p i ˆ p j . ∂ t a 2 ∂ t 12 年 11 月 11 日日曜日