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

SLIDE 1

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

SLIDE 2

Outline

Background Information

I. brief history of the universe
II. temperature power spectrum:

acoustic oscillation, diffusion damping

Signatures of Neutrinos (number)

I. on background: diffusion damping
II. on perturbation: phase shift

Signatures of Neutrinos (mass)

I. on background: expansion history
II. on perturbation: large scale structure

1000 2000 3000 4000 5000 6000

D TT

ℓ

Planck 2015

500 1000 1500 2000 2500

ℓ

200 150 100 50 50 100 150 200

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 2 / 10

SLIDE 3

Background Information:

a brief introduction

Recombination z ≃ 1100

Before Recombination: γ + e− → γ + e− z ≃ 1100 Recombination: e− + p → H After Recombination: γ → γ last scattering surface

Yℓm(θ,φ) ∼cos(ℓθ) λ/2 =π/k θ ∼π/ℓ η0 −η

Observer Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 3 / 10

SLIDE 4

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 ≡ δT/T Θ(ˆ γ)|

x=0,η=η0 ≃ Θ0|ˆ γ(η0−η⋆)

last scattering surface

Yℓm(θ,φ) ∼cos(ℓθ) λ/2 =π/k θ ∼π/ℓ η0 −η

Observer Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 3 / 10

SLIDE 5

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 ≡ δT/T Θ(ˆ γ)|

x=0,η=η0 ≃ Θ0|ˆ γ(η0−η⋆)

Θ(ˆ γ)|

x=0,η=η0 = ∞

ℓ=1

m=ℓ

m=−ℓ

aℓmYℓm(ˆ γ) aℓma⋆

ℓ′m′ = δℓℓ′δmm′C TT ℓ

last scattering surface

Yℓm(θ,φ) ∼cos(ℓθ) λ/2 =π/k θ ∼π/ℓ η0 −η

Observer

Figure : Θ2

0(k, η⋆) ≃ C TT ℓ≃k(η0−η⋆)

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 3 / 10

SLIDE 6

acoustic oscillation + diffusion damping

Tight Coupling Approximation (TCA): rmfp ≪ λ

¨ Θ0 + k2c2

s Θ0 = − k2Φ+

Inflation inspired initial conditions: Θ0(η = 0) = ..., ˙

Θ0(η = 0) = 0.

Θ0 ∼ cos(k

csdη) = cos(krs(η))

Taking diffusion into account: rd ∝ √η ∼

1/H

Hou et.al. (2011)

Θ0 ∼ cos(krs)e−(krd)2

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 4 / 10

SLIDE 7

acoustic oscillation + diffusion damping

Tight Coupling Approximation (TCA): rmfp ≪ λ

¨ Θ0 + k2c2

s Θ0 = − k2Φ+

Inflation inspired initial conditions: Θ0(η = 0) = ..., ˙

Θ0(η = 0) = 0.

Θ0 ∼ cos(k

csdη) = cos(krs(η))

Taking diffusion into account: rd ∝ √η ∼

1/H

Hou et.al. (2011)

Θ0 ∼ cos(krs)e−(krd)2 Nν → H → rd → e−(krd)2

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 4 / 10

SLIDE 8

phase shift

Forced Oscillator: ¨

Θ0 + k2c2

s Θ0 = −k2Φ+

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

SLIDE 9

phase shift

Forced Oscillator: ¨

Θ0 + k2c2

s Θ0 = −k2Φ+

Θ0(krs) = Θ0(0) cos(krs) − krs d(kr′

s)Φ+(kr′ s) sin(krs − kr′ s),

Θ0 ∼ cos(krs + θ)

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

SLIDE 10

phase shift

Forced Oscillator: ¨

Θ0 + k2c2

s Θ0 = −k2Φ+

Θ0(krs) = Θ0(0) cos(krs) − krs d(kr′

s)Φ+(kr′ s) sin(krs − kr′ s),

Θ0 ∼ cos(krs + θ)

Neglecting Neutrinos: k2Φ+ ∝ ργδγ, vp(γ) = cs

θ(η → ∞) = 0

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

SLIDE 11

phase shift

Forced Oscillator: ¨

Θ0 + k2c2

s Θ0 = −k2Φ+

Θ0(krs) = Θ0(0) cos(krs) − krs d(kr′

s)Φ+(kr′ s) sin(krs − kr′ s),

Θ0 ∼ cos(krs + θ)

Neglecting Neutrinos: k2Φ+ ∝ ργδγ, vp(γ) = cs

θ(η → ∞) = 0

Including Neutrinos: k2Φ+ ∝ (ργδγ + ρνδν), vp(ν) = c > cs

θ(η → ∞) = 0.19πRν + O(R2

ν)

Bashinsky (2004,2007), Baumann et.al. (2015) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 5 / 10

SLIDE 12

Signatures of neutrinos (number)

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

SLIDE 13

Signatures of neutrinos (number)

Planck13 TT

Follin ,.., Pan (2015)

Nδφ

ν

= 3.50 ± 0.65

Planck XVI (2013) Nδφ+δθD

ν

= 3.36 ± 0.33

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

SLIDE 14

Signatures of neutrinos (number)

Planck13 TT

Follin ,.., Pan (2015)

Nδφ

ν

= 3.50 ± 0.65

Planck XVI (2013) Nδφ+δθD

ν

= 3.36 ± 0.33 Planck15 TT, EE,TE

Baumann et.al. (2015)

Nδφ

ν

= 2.99 ± 0.30

Planck III (2015) Nδφ+δθD

ν

= 2.99 ± 0.20

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

SLIDE 15

Signatures of neutrinos (mass)

Expansion History:

θs,⋆ ≡

rs,⋆ DA,⋆ = (1.04096 ± 0.00032) × 10−2 (Planck 2015)

DA,⋆ = z⋆ dz H(z) (Mν ↑ +ΩΛ ↓) ⇒ Fixing θs,⋆

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.94 0.96 0.98 1.00 1.02 1.04

H(z)rs (H(z)rs)fid

DESI

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

z

0.94 0.96 0.98 1.00 1.02 1.04

DA (z)/rs (DA (z)/rs)fid

Mν =50 meV Mν =100 meV Mν =200 meV

Pan and Knox (2015) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 7 / 10

SLIDE 16

Signatures of neutrinos (mass)

Expansion History:

θs,⋆ ≡

rs,⋆ DA,⋆ = (1.04096 ± 0.00032) × 10−2 (Planck 2015)

DA,⋆ = z⋆ dz H(z) (Mν ↑ +ΩΛ ↓) ⇒ Fixing θs,⋆

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 0.94 0.96 0.98 1.00 1.02 1.04

H(z)rs (H(z)rs)fid

DESI

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

z

0.94 0.96 0.98 1.00 1.02 1.04

DA (z)/rs (DA (z)/rs)fid

Mν =50 meV Mν =100 meV Mν =200 meV

Pan and Knox (2015)

ωm and Mν are negatively correlated from BAO.

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 7 / 10

SLIDE 17

Signatures of neutrinos (mass)

Structure Growth: rfs ∼ vt ∼ Tν(z) Mν 1 H(z) > rfs neutrinos cluster < rfs neutrinos freely stream

Wu et.al (2014) Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 8 / 10

SLIDE 18

Signatures of neutrinos (mass)

Structure Growth: rfs ∼ vt ∼ Tν(z) Mν 1 H(z) > rfs neutrinos cluster < rfs neutrinos freely stream

Wu et.al (2014)

ωm and Mν are positively correlated from lensing.

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 8 / 10

SLIDE 19

Contraints on Mν

0.00 0.05 0.10 0.15 0.20

Mν[eV]

0.1410 0.1415 0.1420 0.1425 0.1430 0.1435 0.1440 0.1445

ωm

CMB−S4 CMB−S4 +DESI BAO CMB−S4 +DESI BAO +DESI RSD

Pan and Knox (2015)

σ(Mν) = 38 meV

CMB-S4

σ(Mν) = 15 meV

+ DESI BAO

σ(Mν) = 9 meV

+ DESI RSD Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 9 / 10

SLIDE 20

Summary

mi

σ

mi
CMB−S4+DESI BAO = 15meV

+

∆m2

ij

neutrino oscillation experiments → mi

Model dependent (flat ΛCDM model). Degeneracy with Ωk, w

broken by external datasets ?

Nν(δθD, δφ)

Nδφ

ν

= 2.99 ± 0.30|Planck 2015 TT,TE,EE Implications: consistent with 3.046 neutrinos,

no sign of ν¯ ν interaction

σ(Nδφ

ν )cosmic variance limit ≈ 0.05

Zhen Pan University of California, Davis CMB & Cosmic Neutrinos Dec 16, 2015 @ ACFI, Umass 10 / 10