Implications of cosmological observations on neutrino and axion properties

Transcription

1 Implications of cosmological observations on neutrino and axion properties Elena Giusarma Elba XIII Workshop Based on works in collabora6on with: E. Di Valen6no, M. La?anzi, A. Melchiorri, O. Mena arxiv: and arxiv:

2 ü Introduc6on ü Impact of neutrino proper6es on cosmological observables: o Neutrino masses o Rela6vis6c degrees of freedom N eff ü Existence of extra hot relic components as dark radia6on relics, steriles neutrino species or thermal axions and contsraints on the masses of the thermal relics in different scenarios using the aviable cosmological data ü Bounds on the axion cold dark ma?er (ADM) scenario in light of the most recent cosmological data

3 Cosmic Pies DARK MATTER HDM + CDM NEUTRINO AXION

4 ü Introduc6on ü Impact of neutrino proper6es on cosmological observables: o Neutrino masses o Rela6vis6c degrees of freedom N eff ü Existence of extra hot relic components as dark radia6on relics, steriles neutrino species or thermal axions and contsraints on the masses of the thermal relics in different scenarios using the aviable cosmological data ü Bounds on the axions cold dark ma?er (ADM) scenario in light of the most recent cosmological data

5 Cosmic Neutrinos According to standard cosmology, there are three ac6ve Dirac o Majorana neutrinos which decouple from the thermal bath at temperature O(1 MeV): n ν σ ν v H T ~ m e, e + e - annihila6on heats the photons but not the decoupled neutrinos: Temperature: Number density: Energy density: The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. The image cannot be displayed. Your computer may not have enough memory to open the image, or the image may have been corrupted. Restart your computer, and then open the file again. If the red x still appears, you may have to delete the image and then insert it again. 1/3 4 Tν = Tγ Tν,0 = nν = nγ nν, K ~ cm 2 mν 1/3 Ω 2 νh = 7π 4 Massless 93.3eV ρ = T 4 γ ν m Massive m ν >> T νnν ν Neutrino energy density parameter -4 ev

6 Ø Relic neutrinos are very abundant and they influence several cosmological epochs. Ø Cosmological observables can also be used to test non-standard neutrino properties. Big Bang Nucleosynthesis (BBN) Cosmic Microwave Background (CMB) Large Scale Structure (LSS)

7 According to neutrino oscilla6on physics, we know that the number of massive neutrinos must be equal or larger than two, since there are at least two mass squared differences (Δm 2 atm, Δm2 sol ). The lower bound on the total neutrino mass depends on the hierarchy: Inverted hierarchy Normal hierarchy Neutrino oscilla6on experiments only provide the neutrino mass squared differences, i.e. they are not sensi6ve to the absolute scale of neutrino masses.

8 Sub-eV massive neutrinos cosmological signatures... CMB: a) Early Integrated Sachs Wolfe effect. The transition from the relativistic to the non relativistic neutrino regime affect the decays of the gravitational potentials at decoupling period (especially near the first acoustic peak). b) Suppression of lensing potential (with Planck). LSS: Suppression of structure formation on scales smaller than the free streaming scale when neutrinos turn non relativistic. (M. Tegmark)

9 Planck state on neutrino mass 95% CL bounds Planck+WP9 Planck+WP9+ highl Planck+WP9+BAO Planck+WP9+BAO+highL (Ade et al 13 Planck Collaboration ) m υ <0.93 ev m υ <0.66 ev m υ <0.25 ev m υ <0.23 ev

10 Effective Number of Relativistic degrees of freedom N eff Radia6on content of the Universe: Ω r = /3 Standard Scenario: N eff = aier considering non instantaneous neutrino decoupling, neutrino oscilla6ons and QED correc6ons. (Mangano et al, PLB 01 & NPB 05) N eff Ω γ N eff =3.046+ΔN eff Extra rela6vis6c component (Dark Radia6on) Sterile neutrinos, axions, extended dark sectors with light species (as in asymmetric dark ma?er models). (Melchiorri et al PRD 07, Smith et al PRD 06, Calabrese et al PRD 11)

11 N eff Cosmological signatures: CMB enhancement of the early ISW (! b,! m,h,a s,n s,,n e ) 1+z eq =! m! r =! m ( ( 4 11 )4/3 N e )! ) Shii of the acous6c peaks Friedmann equa6on: H H 2 = Ω Ω + Ω + + Ω M γ ν DR Λ 4 0 a a a a increase of the expansion rate H at recombina6on Ω +

12 N eff Cosmological signatures: CMB Fixed: Fixed: z eq, z ω b, θ s, A eq s (l=200) (Hou et al, PRD 13) Increase of the Silk damping: Higher N eff, higher H(z), modifying the photon diffusion scale at recombination r 2 d / R a? 0 da a 3 T n e H Increasing the damping at high multipoles. 1+z eq =! m =! r! m ( ( 4 11 )4/3 N e )! )

13 N eff Cosmological signatures: BBN N eff affects the expansion rate during BBN: MeV: Particles in thermal equilibrium lost of equilibrium n/p freezes out at T<0.7MeV ( Γ np ~ H ) residual free neutrons β-decay MeV Formation of the light elements starting from D Larger N eff, higher expansion rate, higher freeze out temperature, higher 4 He fraction: (Ade et al 13 Planck Collaboration )

14 Planck state on N eff N eff = ( 95%; Planck + WP + highl) N ( 95%, Planck + WP + highl + BAO) N eff = eff = ( 95%, Planck + WP + highl + H ) 0 P/Pmax Planck+WP+highL +BAO +H 0 +BAO+H 0 (Ade et al 13 Planck Collaboration ) N eff = ( 95%, Planck + WP + highl + BAO + H ) N e

15 BICEP2 measurements BICEP2: detection at about 5.9σ for B-mode polarization on large scales Effect of foregrounds Likelihood r = at 68% CL Apparent tension with Planck+WP limit: r<0.11 at 95% cl Ade et al 14 BICEP2 Collaboration Tensor to scalar ratio r How to solve the tension? Larger N eff?

16 ü Introduc6on ü Impact of neutrino proper6es on cosmological observables: o Neutrino masses o Rela6vis6c degrees of freedom N eff ü Existence of extra hot relic components as dark radia6on relics, steriles neutrino species or thermal axions and contsraints on the masses of the thermal relics in different scenarios using the aviable cosmological data ü Bounds on the axions cold dark ma?er (ADM) scenario in light of the most recent cosmological data

17 Candidates for extra hot relic components v Massless sterile neutrino species: e.g. extra degrees of freedom produced by the annihilation of asymmetric Dark Matter v Extra steriles massive neutrino species: motivated by the so-called neutrino oscillation anomalies v Thermal axion: motivated by the strong CP problem m a = f p m R f a 1+R =0.6 ev 107 GeV R = ± f π = 93 MeV f a P These extra species Have an associated free streaming scales, reducing the growth of matter fluctuations at small scales Contribute to the effective number of relativistic degrees of freedom N " eff rad = /3 4 N e # 8 11 N eff = ΔN eff

18 Data1 ü CMB: o o o o Planck temperature anisotropies, including lensing potential WMAP 9-year polarization ACT and SPT measurements at small scales B-mode polarization measurements from BICEP2 ü Large scale structure: o SDSS Data Release 7 o 6-degree Field Galaxy Survey o BOSS Data Release 11 o Baryon Acoustic Oscillation (BAO) data WiggleZ survey (the full shape of the matter power spectrum and the geometrical BAO information )

19 ü σ 8 measurements: Data2 ü Hubble constant measurements: o Hubble Space Telescope o CFHTLens survey o Planck Sunyaev-Zeldovich cluster catalog ü Big Bang Nucleosynthesis light elements abundance: (D / H ) P = (2.87 ± 0.22) 10 5 [Iocco et al. PRD '09] (D / H ) P = (2.53 ± 0.04) 10 5 [Cooke et al. arxiv: ] Y P = ± [Izotov et al. arxiv: ]

20 Cosmological parameters 1. ΛCDM model with 3 massive neutrino species: {! b,! c, s,,n s, log[10 10 A s ], X m } 2. ΛCDM model with 3 massive neutrino species and thermal axion: {ω b, ω c, Θ s, τ,n s, log[10 10 A s ], m ν,m a } N e = 4 4/3 3 n a 7 2 n n ν = 112 cm 3 {ω b, ω c, Θ s, τ,n s, log[10 10 A s ], m ν,n eff } Extra Radiation Component at the BBN period 3. ΛCDM model with 3 massive neutrino and ΔN eff massless dark radiation species:

21 Cosmological parameters 4. ΛCDM model with 3 active massive neutrinos plus ΔN eff massive steriles neutrino species: T m e s =(T s /T ) 3 m s =( N e ) 3/4 s, T ν current temperature of the m s sterile and active neutrino species. m s real mass of sterile neutrino ΔN eff =N eff =(T s /T ν ) 4 species. UNIFORM PRIORS for the cosmological parameters: Parameter Prior b h ! 0.1 c h ! 0.99 s 0.5! ! 0.8 n s 0.9! 1.1 ln P (10 10 A s ) 2.7! 4 m [ev] 0.06! 3 m a [ev] 0.1! 3 N e 0(3.046)! 10 m e s [ev] 0! 3 N eff priors refer to the massless (massive) case

22 Main Results(1) 1. ΛCDM model with 3 massive neutrino species: 68% and 95% CL allowed regions in the ( m ν, H 0 ) and in the ( m ν, σ 8 ) plane The allowed neutrino mass regions are displaced after considering Planck cluster data and a non zero value on m ν is favoured. CMB+DR11+BAO+HST: CMB+DR11+BAO+HST+SZ Cluster: CMB+DR11+BAO+HST+CFHTLens: m ν < 0.22 ev at 95% CL m ν = ev at 95% CL m ν < 0.27 ev at 95% CL The addition of the constraints on σ 8 and Ω m from the CFHTLens survey displaces the bounds on the neutrino mass to higher values. Giusarma et al arxiv:

23 Main Results(2) 2. ΛCDM model with 3 massive neutrino species and thermal axion: 68% and 95% CL allowed regions in the ( m ν, m a ) plane for different combinations of data CMB+DR11+BAO+HST+SZ Cluster: CMB+DR11+WZ+HST+SZ Cluster: Only with Planck SZ cluster data a non zero value of axion mass is favoured at the 2.2σ No evidence for non-zero neutrino masses nor for non-zero axion mass. m a = Giusarma et al arxiv: ev at 95% CL m ν = ev at 95% CL Evidence for neutrino mass of 0.2 ev at 3σ on only for one case

24 Main Results(3) 3. ΛCDM model with 3 massive neutrino and ΔN eff =N eff massless dark radiation species: 68% and 95% CL allowed regions in the ( m ν, N eff ) and in the (N eff, H 0 ) plane The prior on the value of the Hubble constant from HST increases the mean value on N eff m ν < 0.31 ev at 95% CL N eff = at 95% CL m ν < 0.31 ev at 95% CL N eff = at 95% CL Giusarma et al arxiv: CMB+DR11+WZ+HST+BBN (Cooke et al.): NO EVIDENCE FOR N eff >3 m ν < 0.24 ev at 95% CL N eff = at 95% CL CMB+DR11+WZ+HST+BBN (Iocco et al.): EVIDENCE FOR N eff >3 m ν < 0.31 ev at 95% CL N eff = at 95% CL

25 Main Results(4) 4. ΛCDM model with 3 active massive neutrinos plus ΔN eff massive steriles neutrino species: 68% and 95% CL allowed regions in the ( m ν, N eff ) and in the ( m ν, m s eff ) plane The bound on N eff ( m ν ) is slightly larger (more stringent) than in massless sterile neutrino scenario due to the degeneracy with m s eff m ν < 0.28 ev at 95% CL m s eff < 0.60 ev at 95% CL N eff < 3.89 at 95% CL m ν < 0.31 ev at 95% CL m s eff < 0.25 ev at 95% CL N eff = at 95% CL Giusarma et al arxiv: CMB+DR11+WZ+HST+BBN(Cooke et al.): NO SIGNIFICANT PREFERENCE FOR N eff >3 m ν < 0.27 ev at 95% CL m eff s < 0.14 ev at 95% CL N eff = at 95% CL CMB+DR11+WZ+HST+BBN(Iocco et al.): SIGNIFICANT PREFERENCE FOR N eff >3 m ν < 0.28 ev at 95% CL m eff s < 0.23 ev at 95% CL N eff = at 95% CL

26 What is the impact of BICEP2 measurements on neutrino properties? ΛCDM +r model with 1 massive neutrino (0.06 ev) and ΔN eff =N eff massless dark radiation species: ΛCDM +r model with 3 massive neutrino: N eff = 4.00 ± 0.41 at 68% CL m ν < 0.56 ev at 68% CL Evidence for N eff >3 but no indication for neutrino masses r = 0.103±0.043at 68% CL Giusarma et al arxiv: Extra relativistic component seems to solve the tension between the Planck and BICEP2 experiments on r

27 ü Introduc6on ü Impact of neutrino proper6es on cosmological observables: o Neutrino masses o Rela6vis6c degrees of freedom N eff ü Existence of extra hot relic components as dark radia6on relics, steriles neutrino species or thermal axions and contsraints on the masses of the thermal relics in different scenarios using the aviable cosmological data ü Bounds on the axions cold dark ma?er (ADM) scenario in light of the most recent cosmological data

28 Axions as Dark Matter q HOT Produced thermally in the early universe (axion with sub-ev masses) q COLD Produced by misalignment mechanism Produced by axion string decay

29 Axions Cold Dark Matter (for axions to be 100% of Cold Dark Matter) Axions are the quanta of the axion fiels a(x). The history of axions starts at the PQ scale f a (the scale at which the U(1) PQ symmetry is broken). At T~10 2 MeV the QCD instanton effects generate an axion potential: Misalignement angle In a flat Friedmann-Robertson-Walker metric, the evolution of the field is: At T>>Λ QCD the axion is massless.

30 Axions Cold Dark Matter The phenomenology of axion CDM depends on the value of the Hubble parameter H I at the end of inflation. As the universe expands, two different scenarios occur for cosmic axion production. Scenario I: PQ symmetry breaks after the end of inflation The cosmic axion energy density contains contributions from string decays and from coherent oscillations (misalignement mechanism) Scenario II: PQ symmetry breaks before the end of inflation Rule out after the BICEP2 results for H I ~10 14 GeV (requires a value for f a several order of magnitude above the Planck scale)

31 Axions Cold Dark Matter (Scenario I) In the misalignement mechanism the axion number density at temperature T 1 is : where The present mass-energy density of axions reads: Considering the recent BICEP2 results Considering the contribution from axion string decay:

32 Data ü CMB: o o o Planck temperature anisotropies, including lensing potential WMAP 9-year polarization B-mode polarization measurements from BICEP2 ü Baryon Acoustic Oscillation: o SDSS Data Release 7 o 6-degree Field Galaxy Survey o BOSS Data Release 11 o WiggleZ survey

33 Cosmological models 1. ACDM model : 2. ACDM model with 3 massive neutrino species: 3. ACDM model with a free effective number of relativistic degrees of freedom: 4. ACDM model with 3 massive active neutrinos and ΔN eff massless dark radiation species:

34 Cosmological models 5. ACDM model with ΔN eff steriles masive neutrino species: m e s =(T s /T ) 3 m s =( N e ) 3/4 m s 6. ACDM model with a free, constant, dark energy equation-ofstate parameter: 7. ACDM model with a free tensor spectral index: 8. ACDM model with a running of the scalr spectral index:

35 1. ACDM model : Main Results(1) Plank+WP Planck+WP+ BICEP2 Planck+WP+ BICEP2+BAO m a (µev) 81.5 ± ± ± ACDM model with 3 massive neutrino species: Plank+WP Planck+WP+ BICEP2 m a (µev) 81.56± ± 1.1 Σm ν (ev) <0.97 <0.78

36 Main Results(2) 3. ACDM model with a free effective number of relativistic degrees of freedom: Plank+WP Planck+WP+ BICEP2 Planck+WP+ BICEP2+BAO m a (µev) 76.8 ± ± ± 2.6 N eff 3.79 ± ± ± 0.30 From CMB data 2-3σ evidence for extra dark radiation speciesc Giusarma et al arxiv:

37 Main Results(3) 4. ACDM model with 3 massive active neutrinos and ΔN eff massless dark radiation species: Plank+WP Planck+WP+ BICEP2 m a (µev) 77.0 ± ± 2.8 N eff 3.71 ± ± 0.44 Σm ν (ev) <0.58 < ACDM model with ΔN eff steriles masive neutrino species: Plank+WP+ BICEP2 Planck+WP+ BAO m a (µev) 75.3 ± ± 2.6 N eff 4.08 ± ± 0.32 m s eff (ev) <0.63 <0.51 Giusarma et al arxiv: Fix Σm ν =0.06 ev

38 Main Results(4) 6. ACDM model with a free, constant, dark energy equation-ofstate parameter: Plank+WP Planck+WP+ BICEP2 Planck+WP+ BICEP2+BAO w ± ± ± 0.12 H 0 (Km/s/Mpc) 84 ± ± ± ACDM model with a free tensor spectral index: r=0.172±0.047 Axion mass constraints are unaffected by the presence of a free n T r <0.055 Giusarma et al arxiv:

39 Main Results(5) 8. ACDM model with a running of the scalr spectral index: Planck+WP Planck+WP+ BICEP2 Planck+WP+ BICEP2+BAO dn s /dlnk ± ± ± Axion mass constraints are unaffected Giusarma et al arxiv:

40 Summery and Conclusions ü The bounds on neutrino proper6es ( m ν and N eff ) depend on the combina6on of data sets and on the cosmological model. ü Constraints on the masses of the different thermal relics in different scenarios using the most recent comological data ü In the minimal three ac6ve massive neutrino scenario we found that CFHTLens survey displaces the bound on neutrino masses to higher value. Planck cluster data favours a non zero value on m ν of about 0.3 ev at 4σ. ü Considering B- mode polariza6on measurements by BICEP2 experiment +Planck+WP data, we found that an extra realivis6c component could solve the tension between the two experiments on the amplitude of tensor mode. ü Axion dark ma?er scenario (ADM), in which axions account for all of the dark ma?er in the Universe, in light of the most recent cosmological data. ü A non zero value for Neff is prefered at more than 95% CL using BICEP2 measurement. In none extended models (with running, nt and w) the results for ma change significantly ü Bicep2 preferes a non- zero tensor spectral index and a non- zero scalar running

41 Ø If we relax the assumption that axions make up for all the dark matter the our values of the mass become lower limits. The same happens if we admit complete ignorance on the string fraction. Ø uncertainties in the QCD scale and in the anharmonicity factor can bias the result. Also the assumptions concerning the QCD phase transition temperature can change in a non negligible way our constraints : 1 ) Lambda=320 MeV: omega_ah^2= 1.94 (f_a/10^12 GeV)^1.182 omega_ah^2= 2,26 (f_a/10^12 GeV)^1.182 (aier string contribu6ons) from Planck+WP m_a= 75.6 \pm1.4 (units of micro ev in the following!) 2) Lambda=380 MeV: omega_ah^2= 1.71 (f_a/10^12 GeV)^1.184 omega_ah^2= 1.99 (f_a/10^12 GeV)^1.184 (aier string contribu6ons) from Planck+WP m_a= 69,0\pm1.3 3)Lambda=440 MeV: omega_ah^2= 1.53 (f_a/10^12 GeV)^1.185 omega_ah^2= 1.79 (f_a/10^12 GeV)^1.185 (aier string contribu6ons) from Planck+WP m_a= 63.7\pm1.2 our constraints are 81.5 \pm 1.6 for Lambda=200 MeV

42 Planck constraints on H 0 Ø No evidence for extra dark radia6on from CMB measurements Ø When others data sets are including there is a be?er agreement with N eff =3.046 Ø In par6cular only with HST data we have an evidence for extra dark radia6on at about 2.7 σ. N eff = Planck+WP+HST Ø This is due to the tension between Planck and HST on the value of the Hubble constant H H = [km/s/mpc] = [km/s/mpc] Planck+WP HST (Riess et al) Under the assump6on of N eff = H = [km/s/mpc] Planck+WP If N eff free parameter Only when N eff >3.046, Planck and HST are compa6ble

43 r s 1 H = (1 f ν ) 0.25 r d 1 n e H = (1 Y P ) 0.5 n e (1 Y P ) H 2 ρ r (1 f ν ) N eff increase, f ν increase, we have to reduce Y P θ d = (1 f ν )0.25 θ s (1 Y P ) 0.5

44 Neutrino Mass Measurements Neutrino Oscilla6ons Sensi6ve to the mass differences Uses quantum mechanical effects Sources: Solar, atmospheric reactor Single Beta Decay Sensi6ve to the absolute neutrino mass scale Uses conserva6on of energy Model independent Cosmology Sensi6ve to the total neutrino mass Uses General Rela6vity Measured by satellites and ground- based observatories 0ν Double Beta Decay Sensi6ve to the Majorana masses Uses decay Probes the nature of neutrinos

45 Lensing PotenGal The trajectories of CMB photons are slightly deflected by ma?er fluctua6ons localized at z 3. The deflec6on field is the difference between the direc6on ˆn in which photons have been eme?ed from LSS and the direc6on in which they are actually observed ( ˆn + ˆd( ˆn) ). η ϕ( ˆn) = dη χ(η ) χ(η) 0 LS (ϕ +ψ ) Deflec6on η LS χ(η)χ(η LS ) The free streaming nature of the neutrino suppresses the power spectrum and the lensing poten6al that depends on the gravita6onal poten6al. (Ade et al 13 Planck Collaboration )