Coupled Primordial Nucleosynthesis and Neutrino

Flavor/Decoupling Physics - Implications for CMB S4

Evan GrohsUC Berkeley/LANL

N3AS Annual Meeting11 Jan 2018

In collaboration with:George FullerChad KishimotoMark ParisAlexey Vlasenko

arXiv: 1512.02205, 1706.03391

Outline

❖ The expanding universe➢ Friedmann equation and the Hubble expansion rate

❖ Radiation energy density and neutrino mass➢ The parameter Neff➢ Neutrino energy transport and the plasma equation of state➢ The parameter Σmν➢ (Abundances and baryon content)

❖ Ongoing work➢ Neutrino Quantum Kinetic Equations

❖ CMB Stage IV➢ Overview and timelines➢ Science goals

❖ Summary and future work

Energy Content Hubble Expansion

Credit:www.darkenergysurvey.org

Radiation:

Matter:

Vacuum:

Radiation Energy Density

Definition of Neff

:Three flavors of neutrinosNondegenerate spectraCanonical value of temperature

1. After inflation, relativistic particles comprise energy density budget of universe2. Annihilation events reduce number of relativistic degrees of freedom3. Radiation includes photons, neutrinos, other particles...?

To do CMB physics:1. Photons decouple from matter2. Need free electron fraction3. Need Recombination history4. Need the expansion rate

Summed-Squared Amplitude examples:Channels:

Weak Interactions for neutrino transport

Covariant form:

Geometry simplification:

With collision operator:

Comoving Temperature:

Kinematic Quantity:

Boltzmann equation

Occupation Numbers:

→ Reduce to 2 dimensions→ Parallelize

Equilibrium initial conditionsNonequilibrium evolution

1. Nine-dimensional integral over phase space of particles 2, 3, and 42. Conservation of four-momentum – Five-dimensional integral3. Isotropy – Three-dimensional integral4. Integration Limits Trick – Two-dimensional integral5. Example, neutrinos scattering on neutrinos:

Collision Term Reduction

Parallelize theComputation ofDf/Dt in BURST

Electron mass effects in BBN

Example of sharp decoupling: electron mass and non-ideal equation of state

Nonzero electron mass Finite temperature QED

Canonical Value of temperature:1. Conservation of comoving entropy2. Ideal gas of ultra relativistic particles3. All charged leptons annihilate into photons

With QED effects:

StandardCosmology,Neutrino transport w/o oscillations

and flavor degenerate

Neutrinos and antineutrinos degenerate

Without Transport:

With Transport included:

Relative change:

Nonrelativistic neutrinos at late times

❖ Neutrino momenta redshifts as the universe expands➢ Neutrinos free-stream on large scales; not on small scales➢ Suppression of matter power spectrum

❖ Detect Σmν using weak lensing➢ Large Scale Structure will lens CMB

❖ Degeneracies➢ Optical Depth to Reionization➢ Total matter energy density➢ Number of neutrinos: Neff

❖ Cross-correlation with non-CMB data sets➢ Baryon Acoustic Oscillations and galaxy cluster counts➢ DES, DESI, LSST, ….

Credit:CMB S4 Science Book

Matter Power Spectrum and Lensing Potential

2σ constraint (2015)Planck + Lensing + Ext.:

Multiple assumptions in constructing matter power spectrum

Neutrino Density Matrices

Neutrinos:

Antineutrinos:

Generalized 2n ⨉ 2n density matrices

n : number of flavors2 helicity states

Dirac versus Majorana

Dirac: neutrinos and antineutrinos different particles(opposite helicity inactive states)

Majorana: neutrinos are their own antiparticles

Spin Coherence:Cirigliano, Fuller, Vlasenko (2015)

42 equations of motion, per bin….

Quantum Kinetic Equations (QKEs)

Majorana form (Vlasenko Fuller Cirigliano 2014):

Vlasov operatorPhase-space

evolution

Hamiltonian-like operatorCoherent term

Collision operatorIncoherent term

2n ⨉ 2n matrix; changes neutrino flavor, helicity

2n ⨉ 2n matrix; changes neutrino flavor, helicity, momentum, number

QKEs in the early universe

Change array dimensions (Majorana or Dirac):

2 Generalized 3 ⨉ 3 density matrices ( =0)

Equations of motion for neutrinos:

Nonlinear coupled ODEs

H: Hamiltonian-like potential (coherent)

Ĉ: Collision term from Blaschke & Cirigliano (2016)

Coherent term in the early universe

Vacuum Oscillations

Thermal term(proportional to energy density)

Density Term (proportional to asymmetry)

Incoherent term in the early universeExample:

Notation:

Collision Term:

CMB S4 Overview

I. Stage IV: Fourth generation of ground-based CMB expts.A. More telescopesB. More detectors and new technologyC. More data and analysis tools

II. CollaborationsA. Simons Observatory: ACT and Simons Array (PolarBear)B. South Pole Telescope

III. Other ExperimentsA. Atacama Desert: CLASS and QUIETB. South Pole: Keck Array (BICEP)C. Northern Hemisphere?

IV. Time Scale: Mid 2020’s to begin observation

CMB S4 Research Thrusts

❖ Inflation➢ Tensor to scalar ratio➢ B-mode polarization signal at low mulitpole moment

❖ Neutrino Science➢ Sum of the light neutrino masses Σmν - possible mass hierarchy➢ Structure formation

❖ Light Relics➢ Thermal freeze-out of axions, light vectors, light Fermions, gravitinos….➢ Surplus of radiation energy density ⇒ Neff > 3.046➢ Dark Radiation/BBN abundances

❖ Dark Matter and Dark Energy➢ WIMP annihilation signal and/or nonthermal axions➢ Modified gravity and galaxy cluster physics

Precision Goals and Timeline

CMB S4 Science Book:1610.02743

Summary and Future Work❑ Neutrino quantities in the CMB➛ N

eff● Parameter to measure early universe radiation energy density● Contributions from neutrino decoupling, QED effects, and BSM

➛ Σmν● Parameter to measure later universe mass energy density● Consistent with ΛCDM

➛ Neutrinos do more than contribute to expansion: Abundances!

❑ QKEs in the Early Universe➛ Energy and flavor transport➛ Couple density matrices to nuclear reaction network➛ Charged Current neutron-to-proton rates QKEs

❑ CMB S4