Neutrinos in Cosmology

ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν

Sergio Pastor (IFIC Valencia) ISAPP 2017 Arenzano, 22-23 June Where do neutrinos come from?

ü Nuclear reactors Sun ü

Supernovae Particle accelerators ü SN 1987A ü

ü Earth Atmosphere Accelerators in (Cosmic rays) astrophysical sources ?ü

Early Universe ü Earth interior (today 336 ν/cm3) (Natural Radioactivity) Indirect evidence History of the Universe

Role of neutrinos? VERY LOW Energy Neutrinos

Low Energy Neutrinos

Introducon: neutrinos and the history of the Universe Neutrinos coupled by weak interacons

T~MeV t~sec Decoupled neutrinos Neutrinos coupled (Cosmic Neutrino by weak interacons Background or CNB)

T~MeV t~sec neutrino properes • on the number of neutrinos and their masses) • Neutrino cosmology is interesng because Relic neutrinos are very abundant: Cosmological observables can be used to test standard or non-standard The CNB contributes to radiaon at early mes and to maer at late mes (info

T~mν Outline Introducon: neutrinos and the history of the Universe

ν ν ν ν ν ν ν ν ν Basics of Cosmology ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν Producon and decoupling of relic neutrinos Outline The radiaon content

of the Universe (Neff)

ν ν ν ν ν ν ν Neutrinos and Primordial ν ν ν ν ν ν ν ν ν ν Nucleosynthesis ν ν ν ν ν ν ν Neutrino oscillaons in the Early Universe Outline Massive neutrinos as Dark Maer

Effects of neutrino masses ν ν ν ν ν ν ν on cosmological observables ν ν ν ν ν ν ν ν ν ν ν ν Present bounds on neutrino ν ν ν ν ν properes from cosmology

Future sensivies on neutrino physics from cosmology Basics of Cosmology Eqs in the SM of Cosmology

The FLRW Model describes the evoluon of the isotropic and homogeneous expanding Universe ⎛ dr 2 ⎞ ds 2 g dx µdx ν dt 2 a(t)2 ⎜ r 2dθ 2 r 2 sin2 θdφ2 ⎟ = µν = − ⎜ 2 + + ⎟ ⎝1− kr ⎠ a(t) is the scale factor and k=-1,0,+1 the curvature

1 Einstein eqs Gµν = Rµν − gµν R = 8πGTµν +- Λgµν 2 Energy-momentum tensor of a perfect T = ( p + ρ)u u − pg fluid µν µ ν µν Eqs in the SM of Cosmology

00 component a˙ 2 8⇡G k H(t)2 = = ⇢ (Friedmann eq) a 3 a2 ✓ ◆ ρ=ρM+ρR+ρΛ H(t) is the Hubble parameter k = ⌦ 1 Ω= ρ/ρ H(t)2a2 crit d⇢ ⇢˙ = = 3H(⇢ + p) 2 dt ρcrit=3H /8πG is the crical density Eq of state p=αρ ρ = const a -3(1+α)

Radiaon α=1/3 Maer α=0 Cosmological constant α=-1 4 3 ρR~1/a ρM~1/a ρΛ~const Evoluon of the Universe a¨ 4⇡G ⇤ = (⇢ +3P )+ a 3 3

accaccéléeleélérationration dslowécélédécélé decelerationrationration lente lente eceleration dfastécélédécélé d rationration rqpide rqpide

accaccéléeleélérationration ?

.. a 4πG inflationinflation RD (radiationradiation= − (ρ +domination)3p) MD mati(matterère domination) édarknergie energy noire domination a 3 a(t)~eHt a(t)~t1/2 a(t)~t2/3 Evoluon of the background densies: 1 MeV → now

Three neutrino species with different masses Background densies: 1 MeV → now

ν b cdm γ ν photons DE neutrinos Λ mν=1 eV crit

/ cdm i mν=50 meV = baryons i

mν=9 meV

mν≈ 0 eV

aeq: ρr=ρm Producon and decoupling of relic neutrinos Neutrinos coupled by weak interacons

T~MeV t~sec

Distribution function of particle momenta in equilibrium Equilibrium thermodynamics Thermodynamical variables RELATIVISTIC VARIABLE NON REL. BOSE FERMI

Particles in equilibrium when T are high and interactions effective

T~1/a(t) Neutrinos in Equilibrium

⌫↵⌫ ⌫↵⌫ 1MeV. T . mµ $ ⌫ ⌫¯ ⌫ ⌫¯ ↵ $ ↵ T = T = T ⌫ e± ⌫ e± ⌫ e± ↵ $ ↵ + ⌫ ⌫¯ e e ↵ ↵ $ Neutrino decoupling

As the Universe expands, parcle densies are diluted and temperatures fall. Weak interacons become ineffecve to keep neutrinos in good thermal contact with the e.m. plasma

Rough, but quite accurate esmate of the decoupling temperature

Rate of weak processes ~ Hubble expansion rate

2 8⇡⇢rad 2 5 8⇡⇢rad W W v n, H = G T Tdec(⌫) 1MeV ⇡ | | 3M 2 ! F ⇡ 3M 2 ! ⇡ P s P

Since ν have both CC and NC interacons with e± e T (⌫ ) 2MeV T (⌫ ) 3MeV dec e ' dec µ,⌧ ' Neutrino decoupling

Weak Processes Collisions less Effecve: and less

ν in eq important: (thermal ν decouple spectrum) (spectrum keeps th. form) 1 f = exp(p/T )+1

Expansion of the Universe Neutrinos coupled by weak interacons

1 f (p, T )= ⌫ exp(p/T )+1

T~MeV t~sec Free-streaming neutrinos Neutrinos coupled (decoupled): Cosmic by weak interacons Neutrino Background

1 f (p, T )= ⌫ exp(p/T )+1

Neutrinos keep the energy spectrum of a relavisc fermion with eq form

T~MeV t~sec Neutrino and photon (CMB) temperatures

At T~me, electron- positron pairs annihilate + - e e → γγ heating photons but not the decoupled neutrinos 1/3 T 11 1 = f (p, T )= T 4 ⌫ ⌫ ✓ ◆ exp(p/T⌫ )+1 Neutrino decoupling and e± annihilaons

T 11 1/3 Weak = Processes T 4 Collisions less ⇥ ⇥ Effecve: and less 1 ν in eq important: f = (thermal ν decouple exp(p/T )+1 spectrum) (spectrum keeps th. form) 1 f = exp(p/T )+1

e+e- → γγ

Expansion of the Universe Neutrino and Photon (CMB) temperatures

Photon temp falls At T~me, slower than 1/a(t) electron- positron pairs annihilate + - e e → γγ heating photons but not the decoupled neutrinos 1/3 T 11 1 = f (p, T )= T 4 ⌫ ⌫ ✓ ◆ exp(p/T⌫ )+1 The Cosmic Neutrino Background

Neutrinos decoupled at T~MeV, keeping a 1 f⌫ (p, T )= spectrum as that of a relavisc species exp(p/T⌫ )+1

• Number density

dd33pp 3 36ζ (3) 6⇣(3) n n== f (p,Tf (p,) T= )=n = n =T 3 T 3 ⌫ ν ∫ ((22π⇡)3)3ν ⌫ ν ⌫11 γ 1111π 2 CMB11⇡2 CMB Z • Energy density

2 4/3 7⇡ 4 4 TCMB d3p 120 11 ⇢ = p2 + m2 f (p, T ) ✓ ◆Massless ⌫i ⌫i (2⇡)3 ⌫ ⌫ ! Z q m n ⌫i ⌫ Massive mν>>T

The Cosmic Neutrino Background

Neutrinos decoupled at T~MeV, keeping a 1 f⌫ (p, T )= spectrum as that of a relavisc species exp(p/T⌫ )+1

• Number density

3 d p 3 6ζ (3) 3 At presentn = 112 ( f +¯(p,T ) )cm= -3 pern =flavour T ν ∫ ( 2π)3 ν ν 11 γ 11π 2 CMB

• Energy density

Massless Contribution to the energy density of the Universe Massive

mν>>T

Evoluon of the background densies: 1 MeV → now

photons i = i/crit neutrinos Λ mν=1 eV m ⌦ h2 = ⌫i cdm ⌫ 93.2eV P m =0.05 eV baryons ν

mν=0.009 eV

mν≈ 0 eV

aeq: ρr=ρm VERY LOW Energy Neutrinos Non-relativistic?

Low Energy 2 m2 Δm21 Δ 31 Neutrinos

€ € The radiaon content

of the Universe (Neff)

Relavisc parcles in the Universe

At T>>me, the radiaon content of the Universe is

π 2 7 π 2 ' 7 * ρ = ρ + ρ = T 4 + 3× × T 4 = 1+ × 3 ρ r γ ν 15 8 15 () 8 +, γ

At T

2 2 4/3 € π 4 7 π 4 ⎡ 7 ⎛ 4 ⎞ ⎤ ρr = ργ + ρν = Tγ + 3× × Tν = ⎢1+ ⎜ ⎟ 3⎥ργ 15 8 15 ⎣⎢ 8 ⎝11⎠ ⎦⎥

4 Tν 4 Tγ

# of flavour neutrinos: N = 2.984 ± 0.008 (LEP data) ν €

Relavisc parcles in the Universe

At T

Effecve number of relavisc neutrino species

Tradional parametrizaon of ρ stored in relavisc parcles

+ ⇥ x Bounds on N from Neff is a way to measure the rao eff Primordial Nucleosynthesis and other cosmological Ø standard neutrinos only: N 3 (3.045) eff observables (CMB+LSS) Ø Neff > 3 (delays equality me) from addional relavisc parcles (scalars, pseudoscalars, decay products of heavy parcles,…) or non-standard neutrino physics (primordial neutrino asymmetries, totally or parally thermalized light sterile neutrinos, non-standard interacons with electrons,…)

Neutrinos and Primordial Nucleosynthesis BBN: last epoch sensive Primordial abundances of to neutrino flavour light elements: Big Bang Bound on Neff Nucleosynthesis (BBN) (typically Neff<4) Decoupled neutrinos Neutrinos coupled (Cosmic Neutrino by weak interactions Background or CNB)

T~MeV t~sec BBN: Creaon of light elements

Produced elements: D, 3He, 4He, 7Li and small abundances of others

Theorecal inputs: BBN: Creaon of light elements

Range of temperatures: from 0.8 to 0.01 MeV

Phase I: 0.8-0.1 MeV n-p reacons

n/p freezing and neutron decay BBN: Creaon of light elements

Phase II: 0.1-0.01 MeV Formaon of light nuclei starng from D

Photodesintegraon prevents earlier formaon for temperatures closer to nuclear binding energies

0.07 0.03 MeV MeV BBN: Creaon of light elements

Phase II: 0.1-0.01 MeV Formaon of light nuclei starng from D

Photodesintegraon prevents earlier formaon for temperatures closer to nuclear binding energies

0.03 MeV BBN: Creaon of light elements

Phase II: 0.1-0.01 MeV Formaon of light nuclei starng from D

Photodesintegraon prevents earlier formaon for temperatures closer to nuclear binding energies BBN: Measurement of Primordial abundances Difficult task: search in astrophysical systems with chemical evoluon as small as possible

Deuterium: destroyed in stars. Any observed abundance of D is a lower limit to the primordial abundance. Data from high-z, low metallicity QSO absorpon line systems

Helium-3: produced and destroyed in stars (complicated evoluon) Data from solar system and galaxies but not used in BBN analysis

Helium-4: primordial abundance increased by H burning in stars. Data from low metallicity, extragalac HII regions

Lithium-7: destroyed in stars, produced in cosmic ray reacons. Data from oldest, most metal-poor stars in the Galaxy BBN: Predicons vs Observaons

nB/n 2 ⌘10 = 10 274 ⌦Bh 10 '

Fields, Molaro & Sarkar, PDG 2016 BBN: Predicons vs Observaons

Planck 2015, arXiv:1502.01589 Effect of neutrinos on BBN

1. Neff fixes the expansion rate during BBN

8⇡⇢ H = 3.4 3.2 2 3.0 s3Mp

4 ρ(Neff)>ρ0 → ↑ He

Burles, Nolle & Turner 1999

2. Direct effect of electron neutrinos and anneutrinos on the n-p reacons + ⌫ + n p + e e + n p +¯⌫ e $ $ e BBN: allowed ranges for Neff

Deuterium-only bounds Planck 2015, arXiv:1502.01589 Marcucci et al, PRL 116 (2016) 102501 [arXiv:1510.07877] Neutrino oscillaons in the Early Universe Neutrino oscillaons in the Early Universe Neutrino oscillaons are effecve when medium effects get small enough Coupled neutrinos Compare oscillaon term with effecve potenals

Oscillaon terms prop. to Δm2/2E Second order maer effects prop. to 2 - + GF(E/MZ )[ρ(e )+ρ(e )] First order maer effects prop. to - + GF[n(e )-n(e )]

Expansion of the Universe Strumia & Vissani, hep-ph/0606054 Flavour neutrino oscillaons in the Early Universe

Standard case: all neutrino flavours equally populated oscillations are effective below a few MeV, but have

no effect (except for mixing the small distortions δfν) Cosmology is insensitive to neutrino flavour after decoupling!

Non-zero neutrino asymmetries: flavour oscillations lead to (approximate) global flavour equilibrium the restrictive BBN bound on the asymmetry applies to all flavors, but fine-tuned initial asymmetries always allow for a large surviving neutrino excess radiation that may show up in precision cosmological data (value depends on θ13)

SP, Pinto & Raffelt, PRL 102 (2009) 241302 Acve-sterile neutrino oscillaons

What if additional, light sterile neutrino species are mixed with the flavour neutrinos? ♣ If oscillations are effective before decoupling: the additional species can be brought into equilibrium: Neff=4

♣ If oscillations are effective after decoupling: Neff=3 but the spectrum of active neutrinos is distorted (direct effect of νe and anti-νe on BBN)

Results depend on the sign of Δm2 (resonant vs non-resonant case) Neff & Acve-sterile neutrino oscillaons

Oscillaons effecve

BEFORE decoupling: the

addional species can be Weak brought into eq: Neff=4 Processes Effecve:

ν in eq (thermal Oscillaons effecve Collisions less spectrum) and less AFTER decoupling: important: spectrum of acve ν decouple neutrinos distorted (spectrum but Neff=3 keeps th. form)

e+e- → γγ

Expansion of the universe Neff & Acve-sterile neutrino oscillaons

1 1 Addional 0.5 neutrino in

0.8 ) 2 0 full eq, Neff=4 / eV |) 2 s −0.5 0.6 m δ

(| −1 10 −1.5 0.4 Contribuon log of addional

−2 to ρrad in Neff 0.2 units −2.5

−3 0 −4 −3.5 −3 −2.5 −2 −1.5 −1 log (sin22θ ) 10 s Hannestad, Tamborra & Tram, JCAP 07 (2012) 025 Neff & Acve-sterile neutrino oscillaons

Addional neutrino fully in eq

Flavour neutrino spectrum depleted

Dolgov & Villante, NPB 679 (2004) 261 Active-sterile neutrino oscillations

Addional neutrino fully in eq Kirilova, astro-ph/0312569

Flavour neutrino spectrum depleted

Dolgov & Villante, NPB 679 (2004) 261 Exercises: try to calculate…

0 • The present number density of massive/massless neutrinos nν in cm-3 0 • The present energy density of massive/massless neutrinos Ων and 0 0 0 find the limits on the total neutrino mass from Ων <1 and Ων < Ωm • The final rao Tγ/Tν using the conservaon of entropy density before/aer e± annihilaons

• The decoupling temperature of relic neutrinos using ΓW≈H

• The photon temperature / redshi of the maer radiaon equality

for mν = 1 eV

End of 1st lecture