Signatures of Cosmic Neutrinos on Cosmic Microwave Background Zhen - PowerPoint PPT Presentation

Signatures of Cosmic Neutrinos on Cosmic Microwave Background Zhen Pan University of California, Davis Dec 16, 2015 @ ACFI, Umass Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 1 / 10

Outline Background Information I. brief history of the universe II. temperature power spectrum: 6000 acoustic oscillation, diffusion damping D TT 5000 ℓ 4000 Planck 2015 Signatures of Neutrinos (number) 3000 2000 I. on background: diffusion damping 1000 II. on perturbation: phase shift 200 0 150 100 50 0 50 Signatures of Neutrinos (mass) 100 150 200 0 500 1000 1500 2000 2500 I. on background: expansion history ℓ II. on perturbation: large scale structure Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 2 / 10

Y ℓm ( θ,φ ) ∼ cos( ℓθ ) λ/ 2 = π/k last scattering surface η 0 − η θ ∼ π/ℓ Observer Background Information: a brief introduction Recombination z ≃ 1100 Before Recombination: γ + e − → γ + e − z ≃ 1100 Recombination: e − + p → H After Recombination: γ → γ Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 3 / 10

Y ℓm ( θ,φ ) ∼ cos( ℓθ ) λ/ 2 = π/k last scattering surface η 0 − η θ ∼ π/ℓ Observer Background Information: a brief introduction Recombination z ≃ 1100 Before Recombination: γ + e − → γ + e − z ≃ 1100 Recombination: e − + p → H After Recombination: γ → γ Projection Θ ≡ δ T / T Θ(ˆ γ ) | � x =0 ,η = η 0 ≃ Θ 0 | ˆ γ ( η 0 − η ⋆ ) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 3 / 10

Background Information: a brief introduction Recombination z ≃ 1100 Before Recombination: γ + e − → γ + e − z ≃ 1100 Recombination: e − + p → H Y ℓm ( θ,φ ) ∼ cos( ℓθ ) After Recombination: γ → γ λ/ 2 = π/k Projection last scattering surface Θ ≡ δ T / T η 0 − η Θ(ˆ γ ) | � x =0 ,η = η 0 ≃ Θ 0 | ˆ θ ∼ π/ℓ γ ( η 0 − η ⋆ ) m = ℓ Observer ∞ � � Θ(ˆ γ ) | � x =0 ,η = η 0 = a ℓ m Y ℓ m (ˆ γ ) Figure : Θ 2 0 ( k , η ⋆ ) ≃ C TT ℓ =1 m = − ℓ ℓ ≃ k ( η 0 − η ⋆ ) � a ℓ m a ⋆ ℓ ′ m ′ � = δ ℓℓ ′ δ mm ′ C TT ℓ Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 3 / 10

acoustic oscillation + diffusion damping Tight Coupling Approximation (TCA): r mfp ≪ λ Θ 0 + k 2 c 2 ¨ s Θ 0 = − k 2 Φ + Inflation inspired initial conditions: Θ 0 ( η = 0) = ..., ˙ Θ 0 ( η = 0) = 0 . � Θ 0 ∼ cos ( k c s d η ) = cos ( kr s ( η )) Taking diffusion into account: r d ∝ √ η ∼ � 1 / H Hou et.al. (2011) Θ 0 ∼ cos ( kr s ) e − ( kr d ) 2 Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 4 / 10

acoustic oscillation + diffusion damping Tight Coupling Approximation (TCA): r mfp ≪ λ Θ 0 + k 2 c 2 ¨ s Θ 0 = − k 2 Φ + Inflation inspired initial conditions: Θ 0 ( η = 0) = ..., ˙ Θ 0 ( η = 0) = 0 . � Θ 0 ∼ cos ( k c s d η ) = cos ( kr s ( η )) Taking diffusion into account: r d ∝ √ η ∼ � 1 / H Hou et.al. (2011) Θ 0 ∼ cos ( kr s ) e − ( kr d ) 2 N ν → H → r d → e − ( kr d ) 2 Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 4 / 10

phase shift Forced Oscillator: ¨ Θ 0 + k 2 c 2 s Θ 0 = − k 2 Φ + Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

phase shift Forced Oscillator: ¨ Θ 0 + k 2 c 2 s Θ 0 = − k 2 Φ + � kr s d ( kr ′ s )Φ + ( kr ′ s ) sin( kr s − kr ′ Θ 0 ( kr s ) = Θ 0 (0) cos( kr s ) − s ) , 0 Θ 0 ∼ cos( kr s + θ ) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

phase shift Forced Oscillator: ¨ Θ 0 + k 2 c 2 s Θ 0 = − k 2 Φ + � kr s d ( kr ′ s )Φ + ( kr ′ s ) sin( kr s − kr ′ Θ 0 ( kr s ) = Θ 0 (0) cos( kr s ) − s ) , 0 Θ 0 ∼ cos( kr s + θ ) Neglecting Neutrinos: k 2 Φ + ∝ ρ γ δ γ , v p ( γ ) = c s θ ( η → ∞ ) = 0 Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

phase shift Forced Oscillator: ¨ Θ 0 + k 2 c 2 s Θ 0 = − k 2 Φ + � kr s d ( kr ′ s )Φ + ( kr ′ s ) sin( kr s − kr ′ Θ 0 ( kr s ) = Θ 0 (0) cos( kr s ) − s ) , 0 Θ 0 ∼ cos( kr s + θ ) Neglecting Neutrinos: k 2 Φ + ∝ ρ γ δ γ , v p ( γ ) = c s θ ( η → ∞ ) = 0 Including Neutrinos: k 2 Φ + ∝ ( ρ γ δ γ + ρ ν δ ν ) , v p ( ν ) = c > c s θ ( η → ∞ ) = 0 . 19 π R ν + O ( R 2 ν ) Bashinsky (2004,2007), Baumann et.al. (2015) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

Signatures of neutrinos (number) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 6 / 10

Signatures of neutrinos (number) Planck13 TT N δφ = 3 . 50 ± 0 . 65 Follin ,.., Pan (2015) ν Planck XVI (2013) N δφ + δθ D = 3 . 36 ± 0 . 33 ν Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 6 / 10

Signatures of neutrinos (number) Planck13 TT Planck15 TT, EE,TE N δφ N δφ = 3 . 50 ± 0 . 65 = 2 . 99 ± 0 . 30 Follin ,.., Pan (2015) ν Baumann et.al. (2015) ν Planck XVI (2013) N δφ + δθ D Planck III (2015) N δφ + δθ D = 3 . 36 ± 0 . 33 = 2 . 99 ± 0 . 20 ν ν Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 6 / 10

Signatures of neutrinos (mass) 1.04 DESI 1.02 ( H ( z ) r s ) fid Expansion History: H ( z ) r s 1.00 0.98 rs ,⋆ DA ,⋆ = (1 . 04096 ± 0 . 00032) × 10 − 2 (Planck 2015) θ s ,⋆ ≡ 0.96 0.94 � z ⋆ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 dz 1.04 D A ,⋆ = ( D A ( z ) /r s ) fid 1.02 H ( z ) D A ( z ) /r s 0 1.00 0.98 ( M ν ↑ +Ω Λ ↓ ) ⇒ Fixing θ s ,⋆ 0.96 M ν =50 meV M ν =100 meV M ν =200 meV 0.94 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 z Pan and Knox (2015) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 7 / 10

Signatures of neutrinos (mass) 1.04 DESI 1.02 ( H ( z ) r s ) fid Expansion History: H ( z ) r s 1.00 0.98 rs ,⋆ DA ,⋆ = (1 . 04096 ± 0 . 00032) × 10 − 2 (Planck 2015) θ s ,⋆ ≡ 0.96 0.94 � z ⋆ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 dz 1.04 D A ,⋆ = ( D A ( z ) /r s ) fid 1.02 H ( z ) D A ( z ) /r s 0 1.00 0.98 ( M ν ↑ +Ω Λ ↓ ) ⇒ Fixing θ s ,⋆ 0.96 M ν =50 meV M ν =100 meV M ν =200 meV 0.94 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 z Pan and Knox (2015) ω m and M ν are negatively correlated from BAO. Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 7 / 10

Signatures of neutrinos (mass) Structure Growth: r fs ∼ vt ∼ T ν ( z ) 1 M ν H ( z ) > r fs neutrinos cluster < r fs neutrinos freely stream Wu et.al (2014) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 8 / 10

Signatures of neutrinos (mass) Structure Growth: r fs ∼ vt ∼ T ν ( z ) 1 M ν H ( z ) > r fs neutrinos cluster < r fs neutrinos freely stream Wu et.al (2014) ω m and M ν are positively correlated from lensing. Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 8 / 10

Contraints on M ν 0.1445 0.1440 0.1435 σ ( M ν ) = 38 meV ω m 0.1430 CMB-S4 σ ( M ν ) = 15 meV 0.1425 + DESI BAO 0.1420 σ ( M ν ) = 9 meV + DESI RSD CMB − S4 0.1415 CMB − S4 +DESI BAO CMB − S4 +DESI BAO +DESI RSD 0.1410 0.00 0.05 0.10 0.15 0.20 M ν [eV] Pan and Knox (2015) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 9 / 10

Summary � m i �� � σ m i CMB − S 4+ DESI BAO = 15 meV ∆ m 2 � � + neutrino oscillation experiments → m i ij Model dependent (flat ΛCDM model). Degeneracy with Ω k , w broken by external datasets ? N ν ( δθ D , δφ ) N δφ = 2 . 99 ± 0 . 30 | Planck 2015 TT , TE , EE ν Implications : consistent with 3 . 046 neutrinos , no sign of ν ¯ ν interaction σ ( N δφ ν ) cosmic variance limit ≈ 0 . 05 Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 10 / 10