[PPT] - Neutrino Dynamics in Big Bang Nucleosynthesis Evan Grohs PowerPoint Presentation

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Neutrino Dynamics in Big Bang Nucleosynthesis

Evan Grohs University of California Berkeley 13 Sep 2019 Extraordinary Seminar: University College London

George Fuller Luke Johns Chad Kishimoto Alexey Vlasenko Daniel Blaschke Vincenzo Cirigliano Mark Paris Shashank Shalgar Contributors:

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a e

Network for Neutrinos, Nuclear Astrophysics and Symmetries

❖ Funded by National Science Foundation ❖ 11 Institutions headquartered in Berkeley, CA.

➢

10 Universities

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1 National Laboratory

❖ 8 postdoctoral

research fellows

❖ Research thrusts including

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Nucleosynthesis and the origin of the elements

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Neutrinos and fundamental symmetries

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Dense matter

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Dark matter

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Outline and preliminaries

❖ Observational Cosmology

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The coming era of precision cosmology

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Neutrino observables

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Current status and future goals

❖ Big Bang Nucleosynthesis

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Overview

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Weak decoupling

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Neutron-to-proton rates

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Neutron life time

❖ Neutrino Quantum Kinetics

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Generalized Neutrino Density Matrices

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Preliminary Calculations

❖ Summary and future work

Useful constructs:

f (FD)(✏) = 1 e✏ + 1

Fermi-Dirac Equilibrium (non-degenerate):

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The coming era of precision cosmology

I. Cosmic Microwave Background Experiments

A.

CMB Stage IV: Simons Observatory & South Pole Observatory

B.

Other Ground-Based CMB experiments: CLASS and QUIET

C.

Future satellites: PICO & LiteBIRD

II. Thirty-meter class telescopes

A.

EELT and GMT - Atacama

B.

TMT – Site to be determined

III. Surveys

A.

DES - Cerro Tololo, Chile

B.

DESI - Kitt Peak, AZ

C.

LSST – Cerro Pachón, Chile

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Primordial Helium Mass Fraction CMB Polarization data Simons Observatory/Future Satellites Sum of the light neutrino masses Large Scale Structure/Lensing CMB Stage-IV & DESI Deuterium Abundance QSO Absorption Lines Thirty-Meter Class Telescopes Neutrino Energy Density High-ℓ Temperature Data SPT & SO Baryon Density Temperature Power Spectrum CMB Stage IV

5 Observables in Neutrino Cosmology

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Cosmological Neutrino Observables: Current Status

Number of relativistic degrees of freedom, Planck VI, 2018 Sum of the Neutrino Masses, Planck VI, 2018 Primordial Mass Fraction of Helium, Aver et al, 2015 Primordial Abundance of Deuterium, Cooke et al, 2018

YP = 0.2449 ± 0.0040 (1σ)

105(D/H) = 2.527 ± 0.030 (1σ)

Neff = 2.99+0.34

−0.33 (2σ)

Σmν < 120 meV (2σ)

Baryon Density, Planck VI, 2018

ωb = 0.02242 ± 0.00014 (1σ)

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BBN Epochs of Interest

Equilibrium initial conditions Nonequilibrium evolution

time Temp.

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Weak Decoupling: Overview

1. Initially: neutrinos at the same temperature as electrons and positrons
2. Electrons and positrons annihilate to produce photon pairs, slightly

raising temperature of plasma

3. Two processes create heat flow between neutrinos and plasma
4. Three processes redistribute energy within neutrino seas
5. End result: neutrinos cooler than photons

νi + e± ↔ νi + e± νi + νi ↔ e− + e+

νi + νj ↔ νi + νj νi + νj ↔ νi + νj νi + νi ↔ νj + νj

}

Charged Current (𝜉#) Neutral Current (𝜉#, 𝜑', 𝜑()

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Boltzmann Neutrino Transport Deviation from FD spectra

1-D array for each neutrino flavor; 100 Bins in epsilon 0 ≤ 𝜗 ≤ 25

Neff = 3.044

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−1.5 −1.0 −0.5 0.0 0.5

log10(Tcm/MeV)

2 4 6 8 10

✏

3He

D

4He 7Li

Differential Visibility of Neutrino-Electron Scattering

c/o Matthew J. Wilson

Γ0

νi

H eτνi

Red contours of constant differential visibility for electron flavor

Low Tcm Γ0

νi << H

High Tcm τνi >> 1

Out-of-Equilibrium Neutrino Transport

νi + νi ↔ e− + e+ νi + e± ↔ νi + e±

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Entropy flow out of the plasma into the neutrino seas Total entropy in the universe increases Charged leptons are hotter than neutrinos

Entropy flows

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Without Transport: With Transport included: Relative change:

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Neutron to proton rates I

6 Neutron-to-proton rates set n/p

𝜑# capture on neutron, normalized to neutron lifetime

λνen→pe− = G2

F (1 + 3g2 A)

2π3

∞

Z dEνC(Eν + δmnp)Z(Eν + δmnp, Eν) ×E2

ν(Eν + δmnp)

q (Eν + δmnp)2 − m2

e

×[fνe(Eν)][1 − ge−(Eν + δmnp)]

1 τn = G2

F (1 + 3g2 A)

2π3

δmnp−me

Z dEνC(δmnp − Eν)Z(δmnp − Eν, Eν) ×E2

ν(δmnp − Eν)

q (δmnp − Eν)2 − m2

e

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Neutron to proton rates II

10−3 10−2 10−1 100 101 Tcm (MeV) 10−10 10−8 10−6 10−4 10−2 100 102 104 rate (s−1)

λνen λe+n λn decay H λe−p λ¯

νep

λ¯

νee−p

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Neutron to proton ratio – Primordial Helium

Common Approximation at late times after Weak Freeze-Out (WFO):

n/p(t) = e−δmnp/TWFOe−(t−tWFO)/τn

How Accurate is the WFO approximation?

YP ' 2n/p 1 + n/p

f.o.

Equilibrium:

µνe + µn = µp + µe− n/p = exp  −δmnp T + φe − ξνe

𝑈WFO ≃ 0.7 MeV

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0.0 0.2 0.4 0.6 0.8 1.0 TWFO (MeV) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 δYP

Helium-4 Deviation from Baseline Lepton capture rates set to zero at 𝑈WFO No Pauli blocking in free neutron decay

arXiv: 1607.02797

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875 880 885 890 895 τn (s) 0.244 0.245 0.246 0.247 0.248 0.249 0.250 0.251 Y (base)

P

Helium vs. Neutron lifetime

Bottle expt. Steyerl et al (2016) Beam expt. (1309.2623)

τn = 882.5 ± 2.1 s τn = 887.7 ± 3.1 s

UCN𝜐 (1707.01817)

τn = 877.7 ± 1.1 s

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Beyond the Boltzmann Approach

Mass eigenbasis is not coincident with Weak eigenbasis

1. Unitary Transformation in vacuum: PMNS matrix
2. Neutrinos oscillate between weak eigenstates
3. Generalized density matrix for neutrino ensemble

U = U23U13U12

U12 =   cos θ12 sin θ12 − sin θ12 cos θ12 1  

δm2

= 7.5 × 105 eV2

δm2

atm = 2.6 × 103 eV2

Mixing angles: Mass squared differences:

θ23, θ13, θ12

c/o George Fuller

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Neutrinos: Antineutrinos: Generalized 2n𝒈 ⨉ 2n𝒈 density matrices n𝒈: number of flavors 2 helicity states

Neutrino Density Matrices

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Change array dimensions (Majorana or Dirac): 2 Generalized 3 ⨉ 3 density matrices (no spin coherence) Equations of motion for neutrinos: → Nonlinear coupled ODEs H: Hamiltonian-like potential (coherent) Ĉ: Collision term from Blaschke & Cirigliano (2016)

QKEs in the Early Universe

See Sigl & Raffelt (1993); Vlasenko, Fuller, & Cirigliano (2013); Blaschke & Cirigliano (2016)

d f dt = −i[H, f]− + C[f]

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2 4 6 8 10 ✏ = E⌫/Tcm −1 1 2 3 4 5 102× fii

i = e, Q i = µ, Q i = ⌧, Q i = e, B i = ⌧, B

Freeze-Out Spectra

Full collision term, vacuum Potential in QKE calc. Full collision term in Boltzmann transport calc. Preliminary Calc.

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Concurrent epochs of BBN

Weak interactions between leptons EM interactions between leptons and photons Weak interactions between leptons and baryons Strong and EM interactions between baryons and photons Equilibrium initial conditions Nonequilibrium evolution

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Summary and future work

1. Neutrino cosmology

a) 𝑂eff and Σ𝑛=: energy densities b) D/H and 𝑍

?: convolution in rates

2. Weak Decoupling & Weak Freeze-Out

a) Neutrino spectra influence 𝑜/𝑞 b) Neutron lifetime may be important

3. Quantum Kinetic Equations

a) Coherent terms up to 𝐻D

E

b) Collisions with 𝑓±, 𝜉, ̅ 𝜉 up to 𝐻D

E

4. Future calculations