Neutrinos in Cosmology

Neutrinos in Cosmology

Sergio Pastor

(IFIC Valencia) 8th IDPASC school VLC, 21-31 May 2018

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Books

Modern Cosmology, S. Dodelson (Academic Press, 2003)

Kine1c theory in the expanding Universe, Bernstein (Cambridge U., 1988) Neutrino Cosmology, Mangano, Miele, Lesgourgues & SP (Cambridge U., 2013)

Reviews

Massive neutrinos and cosmology, J. Lesgourgues & SP, Phys. Rep. 429 (2006) 307-379 [astro-ph/0603494]

Primordial Nucleosynthesis: from precision cosmology to fundamental physics, F. Iocco, G. Mangano, G. Miele, O. PisanJ & P.D. Serpico

Phys. Rep. 472 (2009) 1-76 [arXiv:0809.0631]

Neutrino mass in cosmology: status and prospects, Y.Y.Y. Wong Ann. Rev. Nucl. Part. Sci. 61 (2011) 69-98 [arXiv:1111.1436]

Neutrino Physics from the CMB and LSS, K.N. Abazajian, M. Kaplinghat Ann. Rev. Nucl. Part. Sci. 66 (2016) 401-420

Cosmological and astrophysical constraints on neutrino proper1es, M. LaSanzi &

M. Gerbino, Fron1ers in Physics 5 (2018) 70 [arXiv:1712.07109]

Suggested References

For more details…

Ed. Cambridge Univ. Press, 2013

Where do neutrinos come from?

Accelerators in

astrophysical sources ?ü

Early Universe

(today 336 ν/cm³)

Indirect evidence Nuclear reactors

ü

Particle accelerators

ü

Earth Atmosphere (Cosmic rays)

ü

Sun

ü

Supernovae

SN 1987A

ü

Earth interior (Natural Radioactivity)

ü

Low Energy Neutrinos VERY LOW

Energy Neutrinos

Role of neutrinos?

IntroducFon: neutrinos and the

history of the Universe

T~MeV t~sec Neutrinos coupled

by weak interacFons

T~MeV t~sec

Decoupled neutrinos (Cosmic Neutrino Background or CNB) Neutrinos coupled

by weak interacFons

T ~ m

Neutrino cosmology is interes5ng because Relic neutrinos are very abundant:

•  The CNB contributes to radia5on at early 5mes and to ma?er at late 5mes (info on the number of neutrinos and their masses)

•  Cosmological observables can be used to test standard or non-standard neutrino proper5es

Outline

Basics of Cosmology

IntroducFon: neutrinos and the history of the Universe

ProducFon and decoupling of relic neutrinos

ν ν

ν ν

ν ν

ν ν ν

ν ν ν

ν ν

ν ν

ν ν

ν ν ν

ν ν ν

Outline

ν ν

ν ν

ν ν

ν ν ν

ν ν ν

ν ν

ν ν

ν ν

ν ν ν

ν ν ν

Neutrino oscillaFons in the Early Universe Neutrinos and Primordial

Nucleosynthesis

The radiaFon content

of the Universe (N

)

Outline

Future sensiFviFes on neutrino physics from cosmology

Present bounds on neutrino properFes from cosmology

Effects of neutrino masses on cosmological observables

ν ν

ν ν

ν ν

ν ν ν

ν ν ν

ν ν

ν ν

ν ν

ν ν ν

ν ν ν

Massive neutrinos as Dark MaVer

Basics of Cosmology

Eqs in the SM of Cosmology

⎟⎟ ⎠

⎞

⎜⎜ ⎝

⎛ + +

− −

=

=

2 2 2

2

sin

1 r dθ r θdφ

kr a(t) dr

dt dx

dx g

ds

µν µν

µν µν

µν

R g R π GT g

G = − = 8 + Λ

2 1

The FLRW Model describes the evoluFon of the isotropic and homogeneous expanding Universe

a(t) is the scale factor and k=-1,0,+1 the curvature

Einstein eqs

Energy-momentum tensor of a perfect

fluid T

= ( p + ρ ) u

u

− pg

-

Eqs in the SM of Cosmology

Eq of state p=αρ ρ = const a

RadiaFon α =1/3 MaVer α =0 Cosmological constant α =-1 ρ

~ 1/a

ρ

~1/a

ρ

~const

00 component (Friedmann eq)

H(t) is the Hubble parameter

ρ=ρ

+ρ

+ρ

ρ

=3H

/8πG is the criFcal density

Ω= ρ/ρ

H (t)

=

✓ a ˙ a

◆

= 8⇡G

3 ⇢ k a

k

H (t) 2 a 2 = ⌦ 1

˙

⇢ = d⇢

dt = 3H (⇢ + p)

EvoluFon of the Universe

) 3 3 (

.. 4

G p a

a=− π ρ+ accélération

accélération décélération lente

décélération rqpide accélération

accélération décélération lente

décélération rqpide

inflation radiation matière énergie noire

acceleration

acceleration slow deceleration

fast deceleration

?

inflation RD (radiation domination) MD (matter domination) dark energy domination

a (t)~t

a (t)~t

a (t)~e

¨ a

a = 4⇡ G

3 (⇢ + 3P ) + ⇤

3

EvoluFon of the background densiFes: 1 MeV → now

Three neutrino species with different masses

photons neutrinos

cdm

baryons

Λ

m_ν=50 meV m_ν=9 meV m_ν≈ 0 eV m_ν=1 eV

Background densi5es: 1 MeV → now

i

=

/

ν

DE cdm

b

a

: ρ

=ρ

ProducFon and decoupling

of relic neutrinos

T~MeV t~sec Neutrinos coupled

by weak interacFons

Equilibrium thermodynamics

Particles in equilibrium when T are high and interactions effective

T~1/ a(t)

Distribution function of particle momenta in equilibrium

Thermodynamical variables

VARIABLE RELATIVISTIC

NON REL.

BOSE FERMI

Neutrinos in Equilibrium

⌫ ↵ ⌫ $ ⌫ ↵ ⌫

⌫ ↵ ⌫ ¯ $ ⌫ ↵ ⌫ ¯

⌫ ↵ e ± $ ⌫ ↵ e ±

⌫ ↵ ⌫ ¯ ↵ $ e + e 1 MeV . T . m µ

T ⌫ = T e

= T

Neutrino decoupling

As the Universe expands, par5cle densi5es are diluted and temperatures fall. Weak interac5ons become ineffec5ve to keep neutrinos in good thermal contact with the e.m. plasma

Rate of weak processes ~ Hubble expansion rate

Rough, but quite accurate es5mate of the decoupling temperature

Since

have both CC and NC interac5ons with e

W ⇡ ^W|v|n, H² = 8⇡⇢_rad

3M_P² ! G²_FT⁵ ⇡

s8⇡⇢_rad

3M_P² ! T_dec(⌫) ⇡ 1 MeV

T

(⌫

) ' 2 MeV T

(⌫

) ' 3 MeV

Neutrino decoupling

Expansion of the Universe Weak

Processes Effec5ve:

ν  in eq (thermal spectrum)

Collisions less and less

important:

ν  decouple (spectrum

keeps th. form)

f = 1

exp(p/T) + 1

T~MeV t~sec Neutrinos coupled

by weak interacFons

f

(p, T ) = 1

exp(p/T ) + 1

T~MeV t~sec Neutrinos coupled

by weak interacFons

f

(p, T ) = 1

exp(p/T ) + 1

Free-streaming neutrinos (decoupled): Cosmic

Neutrino Background

Neutrinos keep the energy spectrum of a rela5vis5c

fermion with eq form

At T~m

, electron-

positron pairs annihilate

heating photons but not the

decoupled neutrinos

→ γγ

+

e

e

Neutrino and photon (CMB) temperatures

f

(p, T ) = 1

exp(p/T

) + 1 T

T

=

✓ 11 4

◆

Neutrino decoupling and e

annihilaFons

Expansion of the Universe Weak

Processes Effec5ve:

ν  in eq (thermal spectrum)

Collisions less and less

important:

ν  decouple (spectrum

keeps th. form)

→ γγ

+

e

e

T

T

= 11 4

⇥

f = 1

exp(p/T ) + 1

f = 1

exp(p/T) + 1

At T~m

, electron-

positron pairs annihilate

heating photons but not the

decoupled neutrinos

→ γγ

+

e

e

Photon temp falls slower than 1/a(t)

Neutrino and Photon (CMB) temperatures

f

(p, T ) = 1

exp(p/T

) + 1 T

T

=

✓ 11 4

◆

The Cosmic Neutrino Background

•  Number density

•  Energy density

3 2

3 3

11 3 ( 6 11

3

2

ν

T

π ) n ζ

) (p,T π) f

(

p

n = ∫ d = =

Neutrinos decoupled at T~MeV, keeping a

spectrum as that of a rela5vis5c species

f

(p, T ) = 1

exp(p/T

) + 1

n

=

Z d

p

(2⇡)

f

(p, T

) = 3

11 n = 6⇣ (3)

11⇡

T

Massless Massive m_ν>>T

⇢

= Z q

p

+ m

d

p

(2⇡)

f

(p, T

) !

m

n

7⇡

120

✓ 4 11

◆

T

The Cosmic Neutrino Background

•  Number density

•  Energy density

3 2

3 3

11 3 ( 6 11

3

2

ν

T

π ) n ζ

) (p,T π) f

(

p

n = ∫ d = =

At present 112 cm^-3 per flavour

Contribution to the energy density of the Universe

Neutrinos decoupled at T~MeV, keeping a spectrum as that of a rela5vis5c species

( + ¯)

Massless

Massive m_ν>>T

f

(p, T ) = 1

exp(p/T

) + 1

photons neutrinos

cdm

baryons

Λ

m_ν=0.05 eV m_ν=0.009 eV m_ν≈ 0 eV m_ν=1 eV

Evolu5on of the background densi5es: 1 MeV → now

i

=

/

a

: ρ

=ρ

⌦_⌫h² =

P m_⌫i 93.2 eV

Low Energy Neutrinos VERY LOW

Energy Neutrinos Non-relativistic?

€

Δm₃₁²

€

Δm₂₁²

The radiaFon content

of the Universe (N eff )

At T>>m

, the radia5on content of the Universe is

At T<m

, the radia5on content of the Universe is

RelaFvisFc parFcles in the Universe

γ ν

γ ν

γ

π π ρ

ρ ρ

ρ

⎥ ⎥

⎦

⎤

⎢ ⎢

⎣

⎡ ⎟

⎠

⎜ ⎞

⎝ + ⎛

=

×

× +

= +

= 3

11 4 8 1 7 15

8 3 7 15

3 / 4 4

2 4

2

r

T T

€

ρ

ρ

ρ

π

15 T⁴ + 3× 7

8 ×

π

15 T⁴ = 1+ 7 8 × 3 '

( ) * + ,

ρ

€

T

T

data) (LEP

008 .

0 984

.

2 ±

ν

=

# of flavour neutrinos: N

RelaFvisFc parFcles in the Universe

At T<m_e, the radia5on content of the Universe is

EffecFve number of relaFvisFc neutrino species

Tradi5onal parametriza5on of ρ stored in rela5vis5c par5cles

N

is a way to measure the ra5o

Ø  standard neutrinos only: N_eff 3 (3.045)

Ø  N_eff > 3 (delays equality 5me) from addi5onal rela5vis5c par5cles (scalars, pseudoscalars, decay products of heavy par5cles,…) or non-standard neutrino physics (primordial neutrino asymmetries, totally or par5ally thermalized light sterile neutrinos, non-standard interac5ons with electrons,…)

⇥

+

and other cosmological observables (CMB+LSS)

Exercises: try to calculate…

•  The present number density of massive/massless neutrinos n

in cm

•  The present energy density of massive/massless neutrinos Ω

and find the limits on the total neutrino mass from Ω

<1 and Ω

< Ω

•  The final ra5o T

/T

using the conserva5on of entropy density before/aper e

annihila5ons

•  The decoupling temperature of relic neutrinos using Γ

≈H

•  The photon temperature / redship of the ma?er radia5on equality

for m

= 1 eV

End of 1st lecture