Neutrinos in Cosmology

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1 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 Olga Mena & Sergio Pastor (IFIC Valencia) Cosmology School in the Canary Islands, Fuerteventura, Sep 2017

2 History of the Universe Role of neutrinos?

3 Prologue: the physics of (massive) neutrinos

(~10-6 m) Átomo (~10-10 m) Quark (<10-18

m) Leptones Leptons Carga Charge +2/3 +2/3

Family Arriba up u Abajo down d Electrón

Family charm c strange s muon µ µ-neutrino

4 Elementary parhcles Electrón (<10-18 m) Terrón de azúcar (~1 cm=10-2 m) Cristal (~10-6 m) Átomo (~10-10 m) Quark (<10-18 m) Núcleo (~10-15 m) Quarks Protón (~10-16 m) Leptones Leptons Carga Charge +2/3 +2/3 Carga -1/3 Charge -1/3 Carga Charge 1st Family Arriba up u Abajo down d Electrón electron e Neutrino-e νe e-neutrino 2nd Family charm c strange s muon µ µ-neutrino νµ 3er Family top t bottom Neutrón b tau τ τ-neutrino ντ Gravity Weak interaction ElectromagnetismProtón Strong interaction -1-1 Carga Charge 00

... and neutrino masses Neutrinos in the Standard Model of parhcle physics Each type (flavour) of neutrino is associated to a charged lepton They belong to SU(2) lepton

5 ... and neutrino masses Neutrinos in the Standard Model of parhcle physics Each type (flavour) of neutrino is associated to a charged lepton They belong to SU(2) lepton doublets e µ e µ L Neutrinos are only sensi;ve to the weak force In the SM, there exist (e R, µ R, τ R ) but no SU(2) neutrino singlets Neutrinos are massless in the SM L L

6 Weak interachons conserve flavour Neutrinos are always produced together with an associated charged lepton (e, µ, τ) e FLAVOUR IS PRESERVED µ τ or or Source ν e ν µ ν τ NEVER µ ν e

7 ProducHon and detechon of neutrinos Neutrino detec;on at experiments is related to the corresponding charged lepton e e Source µ ν e FLAVOURS DO NOT MIX Detector µ Source ν µ Detector

during their propaga;on e µ Source ν e long enough distance ν µ Detector Born

8 Flavour neutrino conversions? Some experimental data can only be explained if neutrinos change type (flavour) during their propaga;on e µ Source ν e long enough distance ν µ Detector Born as ν e Maybe ν e Maybe ν µ Detected as ν µ Flavour neutrinos are produced and detected, but mass eigenstates propagate (ν 1, ν 2 )

(flavour) during their propaga;on e µ Source ν e long enough distance ν

9 Flavour neutrino conversions? Some experimental data can only be explained if neutrinos change type (flavour) during their propaga;on e µ Source ν e long enough distance ν µ Detector Conversion probability ν e ν µ Amplitude Oscillation lenght time or espace Bruno Pontecorvo ( )

We know that flavour neutrino oscillahons exist From present evidences of oscillations from experiments measuring From present evidences of oscillations from experiments measuring

10 We know that flavour neutrino oscillahons exist From present evidences of oscillations from experiments measuring From present evidences of oscillations from experiments measuring atmospheric, solar, reactor and accelerator neutrinos atmospheric, solar, reactor and accelerator neutrinos (e, µ, τ) ( ν1, ν2, ν3) Evidence for Particle Physics beyond the Mixing Standard matrix U Model!

Mixing Parameters... de Salas et al, arxiv:1708.

11 Mixing Parameters... de Salas et al, arxiv: see also Capozzi et al, PRD 95 (2017) ; Esteban et al, JHEP 01 (2017) 087

12 Neutrino masses Present evidences for flavour neutrino oscillations: data on solar, atmospheric, reactor and accelerator neutrinos Possible neutrino mass hierarchy patterns Possible neutrino mass hierarchy payerns

13 Neutrino masses Neutrino masses (Dirac or Majorana): m( i ) eV

14 Neutrino masses Data on flavour oscilla;ons do not fix the absolute scale of neutrino masses ev ev atm solar NORMAL solar atm INVERTED m 0 What is the value of m 0?

15 Neutrino masses Data on flavour oscilla;ons do not fix the absolute scale of neutrino masses ev 3 1 NH IH solar! (ev) 0.3 atm NORMAL atm INVERTED 0.1 solar m 0 (ev)

16 IntroducHon: the Cosmic Neutrino Background

17 The Cosmic Neutrino Background Role of neutrinos?

18 The Cosmic Neutrino Background Neutrinos coupled by weak interachons T ' 1MeV

19 Neutrino decoupling f = Weak Processes Effec;ve: ν in eq (thermal spectrum) 1 exp(p/t )+1 Collisions less and less important: ν decouple (spectrum keeps th. form) Expansion of the Universe

20 Neutrino and photon (CMB) temperatures At T~m e, electronpositron pairs annihilate e + e - γγ heating photons but not the decoupled neutrinos T = T /3 f (p, T )= 1 exp(p/t )+1

21 Neutrino decoupling and e ± annihilahons f = Weak Processes Effec;ve: ν in eq (thermal spectrum) 1 exp(p/t )+1 Collisions less and less important: ν decouple (spectrum keeps th. form) f = T = 11 1/3 T 4 1 exp(p/t ) e e γγ Expansion of the Universe

22 The Cosmic Neutrino Background Neutrinos coupled by weak interachons T ' 1MeV Decoupled neutrinos (Cosmic Neutrino Background or CNB) f = 1 exp(p/t )+1 Neutrinos keep the energy spectrum of a rela;vis;c fermion with eq form

23 The Cosmic Neutrino Background RelaHvisHc neutrinos (radiahon) At least 2 NR neutrino states today (mayer) T ' m i /3

24 The Cosmic Neutrino Background RelaHvisHc neutrinos (radiahon) At least 2 NR neutrino states today (mayer) T ' m i /3 Neutrino cosmology is interes;ng because Relic neutrinos are very abundant: The CNB contributes to radia;on at early ;mes and to macer at late ;mes (info on the number of neutrinos and their masses) Cosmological observables can be used to test standard or non-standard neutrino proper;es

25 Background densi;es: 1 MeV now b ν γ ν photons neutrinos cdm DE i = i/ crit cdm baryons Λ m ν =1 ev P m i h 2 = 93.2eV m ν =50 mev m ν =9 mev m ν 0 ev

26 The radiahon content of the Universe (N eff )

27 RelaHvisHc parhcles in the Universe At T<m e, the radia;on content of the Universe is EffecHve number of relahvishc neutrino species Tradi;onal parametriza;on of ρ stored in rela;vis;c par;cles N eff is a way to measure the ra;o + x Ø standard neutrinos only: N eff 3 (3.045) Bounds on N eff from Primordial Nucleosynthesis and other cosmological observables (CMB+LSS) Ø N eff > 3 (delays equality ;me) from addi;onal rela;vis;c par;cles (scalars, pseudoscalars, decay products of heavy par;cles, ) or non-standard neutrino physics (primordial neutrino asymmetries, totally or par;ally thermalized light sterile neutrinos, non-standard interac;ons with electrons, )

(small spectral distorsions) T T 0 < f = f eq 11 4 1/3 + f N e =3.

28 N eff > 3 : small neutrino heahng f = Weak Processes Effec;ve: ν in eq (thermal spectrum) 1 exp(p/t )+1 ν decoupling depends on ν momentum (small spectral distorsions) T T 0 < f = f eq /3 + f N e =3.045 P.F. de Salas & SP, JCAP 07 (2016) e e γγ Expansion of the universe

29 Cosmological bounds on neutrino properhes Primordial abundances of light elements: Big Bang Nucleosynthesis (BBN) BBN: last epoch sensi;ve to neutrino flavour Bound on N eff (typically N eff <4)

30 Neutrinos as Dark MaYer

31 Neutrino masses Data on flavour oscilla;ons do not fix the absolute scale of neutrino masses ev 3 1 NH IH solar! (ev) 0.3 atm NORMAL atm INVERTED 0.1 solar m 0 (ev)

32 Evolu;on of the background densi;es: 1 MeV now photons neutrinos i = i / crit Λ m ν =1 ev cdm baryons m ν =0.05 ev m ν =0.009 ev m ν 0 ev a eq : ρ r =ρ m

33 Neutrinos as Dark Macer Neutrinos are natural DM candidates h 2 = i m i 93.2 ev < 1 i m i 46 ev < m 0.3 m i 15 ev i They stream freely un;l non-rela;vis;c (collisionless phase mixing) Neutrinos are HOT Dark MaYer (large thermal mo;on) First structures to be formed when Universe became macer dominated are very large Ruled out by structure forma;on CDM Massive Neutrinos can s;ll be subdominant DM: limits on m ν from Structure Forma;on (combined with other cosmological data)

34 baryons and CDM (mayer) experience gravitahonal clustering Structure forma;on aqer equality

35 baryons and CDM (mayer) experience gravitahonal clustering Structure forma;on aqer equality

36 baryons and CDM (mayer) experience gravitahonal clustering Structure forma;on aqer equality

37 ! Structure forma;on aqer equality baryons and CDM (mayer) experience gravitahonal clustering growth of δρ/ρ (k,t) fixed by gravity vs expansion balance! δρ/ρ α a

38 Structure forma;on aqer equality baryons and CDM (mayer) experience gravitahonal clustering neutrinos experience free-streaming with v = c or <p>/m

39 Structure forma;on aqer equality baryons and CDM (mayer) experience gravitahonal clustering neutrinos experience free-streaming with v = c or <p>/m

40 Structure forma;on aqer equality baryons and CDM (mayer) experience gravitahonal clustering neutrinos experience free-streaming with v = c or <p>/m neutrinos cannot cluster below a diffusion length λ = v dt < c dt

41 Structure forma;on aqer equality baryons and CDM (mayer) experience gravitahonal clustering neutrinos experience free-streaming with v = c or <p>/m

42 Neutrinos as Hot Dark Macer Massive Neutrinos can s;ll be subdominant DM: limits on m ν from Structure Forma;on (combined with other cosmological data) i m i = 0 ev i m i =6.9 ev S. Hannestad, Cosmology Group, Univ. Aarhus

non-linear calcula;ons: addi;onal suppression at large k

43 Effect of massive neutrinos on P(k) Observable signature on P(k) : P(k) massive P(k) massless various f ν + non-linear calcula;ons: addi;onal suppression at large k Brandbyge et al 2008, Viel et al 2010, Villaescusa-Navarro et al 2013

44 Effects of neutrino masses on cosmological observables

45 Cosmological Observables Recombination Hubble constant H 0 & cosmic distances measurements: SN Ia and Baryon Acoustic Oscillations (BAO) matter density fluctuations Large-Scale Structures [ galaxy / cosmic shear / Lyα ] LSS spectrum Photon momentum after decoupling CMB secondary anisotropy spectrum Photon density fluctuations before decoupling CMB primary anisotropy spectrum (temp+pol) from J. Lesgourgues

46 Effects of m ν on the CMB Neutrinos contribute to radia;on at early ;mes and non-rela;vis;c macer at late ;mes If m ν < 0.6 ev, neutrinos are rela;vis;c at photon decoupling. In principle the primary CMB TT spectrum sensi;ve only to Σm ν > 1.5 ev effect of m ν depends on what combina;on of parameters is kept fixed Leave both early cosmology and angular diameter dist. to decoupling invariant: Possible by fixing photon, cdm and baryon densi;es, while tuning H 0, Ω Λ then increase in m ν goes with decrease in H 0 : nega;ve correla;on between the two base model in Planck has (0.06, 0, 0) ev masses: shiqs best-fivng H 0 by -0.6 h/km/mpc with respect to massless case

47 Effects of m ν on the CMB

Effects of m ν on the CMB Leaving both early

to decoupling invariant: fixing photon, cdm and

C l TT for degenerate masses vs massless: m ν

decoupling: less free-streaming and shiqing Σm

m ν Perturba0on Feature coming from early ISW:

48 Effects of m ν on the CMB Leaving both early cosmology and angular diameter dist. to decoupling invariant: fixing photon, cdm and baryon densi;es, while tuning H 0, Ω Λ unlensed C l TT for degenerate masses vs massless: m ν Perturba0on Not fully rela;vis;c before decoupling: less free-streaming and shiqing Σm ν Background Later M/Λ equality, less late ISW m ν Perturba0on Feature coming from early ISW: φ evolu;on at non-rela;vis;c transi;on + different lensing effect Σm ν

49 Effects of N eff on cosmological observables

50 Effects of N eff on the CMB N eff is a parameter for the rela;vis;c density in general background effects (change in expansion history) versus perturba;on effects (gravita;onal interac;ons between photons and rela;vis;c species) effect of N eff depends on what is kept fixed. Fixing quan;;es best probed by CMB (angular peak scale, redshiq of equality, ): possible with simultaneous enhancement of radia;on, macer, Λ densi;es, with fixed photon and baryon densi;es then increase in N eff goes with increase in H 0 : posi;ve correla;on between the two

51 Evolu;on of the background densi;es: 1 MeV now photons neutrinos i = i / crit Λ m ν =1 ev cdm baryons m ν =0.05 ev m ν =0.009 ev m ν 0 ev a eq : ρ r =ρ m

52 Effects of N eff on the CMB Hinshaw et al, arxiv:

Effects of N eff on the CMB Fixing quan;;es best probed by CMB (angular peak

densi;es, with fixed photon and baryon densi;es unlensed C l TT for N eff =3

of acous;c oscilla;ons Perturba0on Neutrino drag: c < c s, influence on phase

53 Effects of N eff on the CMB Fixing quan;;es best probed by CMB (angular peak scale, redshiq of equality, ): simultaneous enhancement of radia;on, macer, L densi;es, with fixed photon and baryon densi;es unlensed C l TT for N eff =3 vs N eff =0 : Perturba0on Neutrino freestreaming: less gravita;onal driving of acous;c oscilla;ons Perturba0on Neutrino drag: c < c s, influence on phase of oscilla;ons Background Change in diffusion damping scale: extra Silk damping

54 Present bounds on neutrino properhes from cosmology

55 Probing neutrino masses with cosmo data Indirect probe of HDM frac;on Massive neutrinos macer today but radia;on at eq. Direct probe of free-streaming (via scale-dependent growth factor) Primary CMB spectrum Galaxy P(k) / BAO CMB / galaxy lensing Clusters Not probing directly neutrino masses but removing parameter degeneracies Lyman-α H 0, SNe-Ia

1-parameter extensions of the ΛCDM model 68+95% Conf regions 0.06 ev 3.

56 1-parameter extensions of the ΛCDM model 68+95% Conf regions 0.06 ev Planck TT + lowp Planck TT,TE,EE + lowp Planck TT,TE,EE + lowp + BAO

57 Measuring N eff Indirect detec;on of CNB at 10-17σ All 68%CL

58 Neutrino masses Data on flavour oscilla;ons do not fix the absolute scale of neutrino masses ev 3 1 NH IH solar! (ev) 0.3 atm NORMAL atm INVERTED 0.1 solar m 0 (ev)

59 Measuring m ν with Planck (+other cosmo data) Cosmological upper limits on the sum of neutrino masses 3 NH IH 1 Planck TT+lowP! (ev) Planck TT+lowP+ TE,EE+ lensing Planck TT+lowP+lensing+ext Latest analyses Planck BAO / Ly-α see e.g. Vagnozzi et al Capozzi et al m 0 (ev)

60 Measuring m ν with Planck (+other cosmo data) Cosmological upper limits on the sum of neutrino masses 3 NH IH 1! (ev) 0.3 data dependence for minimal model model dependence for conservahve data m 0 (ev)

61 Probing Direct the laboratory absolute neutrino bounds mass on scale m ν Searching for non-zero neutrino mass in laboratory experiments Tritium beta decay: measurements of endpoint energy 3 H! 3 He + e + e m β < 2.2 ev (95% CL) Mainz Current experiment (KATRIN) m(ν e ) ~ mev Neutrinoless double beta decay: if Majorana neutrinos (A, Z)! (A, Z + 2) + 2e experiments with 76 Ge, 130 Te, 136 Xe and other isotopes: m ββ < mev, depending on NME

62 Probing the absolute neutrino mass scale Absolute mass scale searches Tri;um β decay m = U ei 2 m 2 i i 1/2 2.2 ev Neutrinoless double beta decay m = i U 2 eim i < mev Cosmology i m i < mev

63 TriHum β decay, 0ν2β and Cosmology KATRIN CURRENT 0ν2β Planck TT+lowP +lensing+ext Planck TT+lowP +lensing+ext Σm ν Σm ν

64 Future sensihvihes on neutrino physics from cosmology

65 Future cosmological data Hannestad & Wong, JCAP 07 (2007) cm H Takada et al, PRD 73 line (2006) surveys Wang et al, PRL 95 (2005) Hannestad et al, JCAP 06 (2006) 025 Song & Knox, PRD 70 (2004) Galaxy Cluster Perotto et al, JCAP 10 Surveys (2006) 013 Lesgourgues et al, PRD 73 (2006) CMB PolarizaHon (beyond Planck) Forecasts indicate mev sensihvihes to Σm ν are possible!! CMB lensing Cosmic Shear Surveys Loeb & Wyithe, PRL 100 (2008) Lyman-α Pritchard & Pierpaoli, PRD 78 (2008)

66 Future sensi;vi;es on N eff and neutrino masses Summary of future sensitivities CMB-S4 Science Book,

Future sensi;vi;es to N eff and Σm ν Example of forecast: PLANCK + Euclid-like photometric galaxy cluster survey Hannestad & Wong, JCAP 07 (2007) 004 Takada et al, PRD 73 (2006) 083520 Wang et al,

67 Future sensi;vi;es to N eff and Σm ν Example of forecast: PLANCK + Euclid-like photometric galaxy cluster survey Hannestad & Wong, JCAP 07 (2007) 004 Takada et al, PRD 73 (2006) Wang et al, PRL 95 (2005) Hannestad et al, JCAP 06 (2006) 025 Song & Knox, PRD 70 (2004) Perotto et al, JCAP 10 (2006) 013 Lesgourgues et al, PRD 73 (2006) M.C.A. Cerbolini et al, JCAP 06 (2013) 020 [arxiv: ]

68 m ν N eff Conclusions ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ν ü With Planck, including CMB lensing, and LSS data, we can measure combina;ons of cosmological parameters with high precision. S;ll ΛCDM fits very well the data ü No evidence yet for nonzero neutrino masses or an enhanced radia;on density (N eff ). Bounds Σm ν < ev (95% CL) and N eff = 3.15±0.23 (68% CL), depending on data ü Improved sensi;vi;es from a variety of future cosmological data to reach the minimal values Σm ν = 60 or 100 mev

69 For more details

70 Exercises: try to calculate The present number density of massive/massless neutrinos n ν 0 in cm -3 The present energy density of massive/massless neutrinos Ω ν 0 and find the limits on the total neutrino mass from Ω ν0 <1 and Ω ν 0 < Ω m 0 The final ra;o T γ /T ν using the conserva;on of entropy density before/aqer e ± annihila;ons The decoupling temperature of relic neutrinos using Γ W H The evolu;on of Ω(ν,γ,b,cdm) with the expansion for neutrino masses (3,0,0), (1,1,1) and (0.05,0.009,0) [masses in ev] The photon temperature / redshiq of the macer-radia;on equality for m ν = 1 ev

71 The end, thanks!

Neutrinos in Cosmology (IV)

Neutrinos in Cosmology (IV) Sergio Pastor (IFIC Valencia) Cinvestav 8-12 June 2015 Outline Prologue: the physics of (massive) neutrinos IntroducBon: neutrinos and the history of the Universe Basics of