Unveiling ν secrets with cosmology

Sunny Vagnozzi

The Oskar Klein Centre for Cosmoparticle Physics, Stockholm University

Based on:

arXiv:1605.04320 [Phys. Rev. D94 (2016) 083522],arXiv:1610.08830 [Phys. Rev. D, in press],

arXiv:1701.08172

with Katherine Freese, Shirley Ho, Olga Mena,Martina Gerbino, Elena Giusarma, Massimiliano Lattanzi

Cosmology on Safari, Zulu Nyala, South Africa, February 2017

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Overview: Qs (& As)

Q: How constraining are the bounds on Mν from cosmology if webelieve some of the most recent datasets?A: VERY

Q: Within a flat ΛCDM background and with recent datasets, isshape [P(k)] or geometrical (BAO) information more constraining?A: GEOMETRICAL 1

Q: Can we say something quantitatively interesting and statisticallycorrect about the ν mass hierarchy?A: YES, WE CAN

Q: Do assumptions on the distribution of mass among the threeeigenstates matter?A: NOT MUCH

1with caveats2 / 18

Neutrino masses

Nobel Prize 2015: “for upptackten av neutrinooscillationer, som visar attneutriner har massa” (“for the discovery of neutrino oscillations, whichshows that neutrinos have mass”)

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Neutrino oscillationsSensitive to mass-squared differences∆m2

ij ≡ m2i − m2

j

Exploits quantum-mechanical effects

Currently not sensitive to the mass hierarchy

Beta decay

Sensitive to effective electron neutrino massm2

β ≡∑

i |Uei |2m2i

Exploits conservation of energy

Model-independent, but less tight bounds

Cosmology

Sensitive to sum of neutrino massesMν ≡

∑i mi

Exploits GR+Boltzmann equations

Tightest limits, but somewhat model-dependent

Neutrinoless double-beta decay

Sensitive to effective Majorana massmββ ≡

∑i |U

2eimi |

Exploits GR+Boltzmann equations

Limited by NME uncertainties and ν nature

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The CνB

Background of relic νs generic prediction of standard cosmological model:νs kept in thermal equilibrium with the plasma until T ∼ 1MeV (z ∼ 1010)Below T ∼ 1MeV νs free-stream keeping an equilibrium spectrum

Today Tν ' 1.9K, nν ' 113 cm−3, Neff = 3.046

Courtesy of Elena Giusarma5 / 18

How can cosmology measure ν masses?

Courtesy of Martina Gerbino; see Lyman’s talk6 / 18

Datasets: CMB temperature and polarization

0

1000

2000

3000

4000

5000

6000

DT

T`

[µK

2]

30 500 1000 1500 2000 2500`

-60-3003060

D

TT

`

2 10-600-300

0300600

0

20

40

60

80

100

CEE

`[1

05µK

2]

30 500 1000 1500 2000

`

-404

CE

E`

-140

-70

0

70

140

DT

E`

[µK

2]

30 500 1000 1500 2000

`

-100

10

D

TE

`

0.5

0

0.5

1

1.5

2

1 10 100 500 1000 2000

[L(L

+1)

]2C

L/2

[10

7]

L

Planck (2015)

Planck (2013)

SPTACT

TT TE

EE

φφ

Courtesy of Massimiliano Lattanzi; see Francois’ talk

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Datasets: galaxy power spectrum

BOSS DR12 CMASS P(k)

10-2 10-1102

103

104

105

P(k

)[h−

3M

pc

3]

Halofit Non Linear Matter Power, PHF

Non Linear Matter Power, PNL

(PNL-PHF)/PHF

DR9 data

DR12 data

10-2 10-1

k[h/Mpc]

0.20.00.20.40.60.8

∆P/P

Modelling of data and theory withinlikelihood:

Pgmeas(ki ) =

∑j

W (ki , kj)Pgtrue(kj)

Pgth(k, z) = b2

HFPmHFν(k , z) + Ps

HF

Power on small scales is affected by free-streaming of neutrinos:

∆P(k)

P(k)∼ −8fν , knr ' 0.018Ω

12m

( m

1 eV

) 12

h Mpc−1

Issues: (scale-dependent?) bias, non-linearities, redshift-spacedistortions, systematics

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Datasets: Baryon Acoustic Oscillations

Approximately constrain the quantityDv (zeff)/rs(zdrag), where:

Dv (z) =

[(1 + z)2DA(z)2 cz

H(z)

] 13

Several BAO measurements available(BOSS DR11/DR12CMASS/LOWZ, WiggleZ, 6dFGS)

Standard ruler: constrain expansion history and break degeneracies (mainlyinvolving Ωm and H0)

Substantially less affected by systematics (bias, non-linear evolution)

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Other “external” datasets

Consider other “external” datasets:

Optical depth to reionization τ = 0.055± 0.009 from Planck HFI

Direct measurements of the Hubble parameterH0 = 73.02± 1.79 km/s/Mpc

Planck SZ clusters

Each of them is important for resolving parameter degeneracies:

Degeneracy between Mν and τ in CMB and P(k): τ ↓ =⇒ Mν ↓Degeneracy between Mν and H0 with CMB, affects distance to lastscattering: H0 ↑ =⇒ Mν ↓ (careful with tensions see Adam’s talk )

Cluster mass function probes Ωm and σ8, important for fixing thenormalization of P(k)

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Results

Results reported assuming a spectrum of three massive degenerate νs

PlanckTT+lowP: Mν < 0.716 eV@95% C.L.

+P(k): < 0.299 eV

+P(k)+BAO: < 0.246 eV

+P(k)+BAO+τ : < 0.205 eV

+P(k)+BAO+SZ: < 0.239 eV

+P(k)+BAO+H0: < 0.164 eV

+P(k)+BAO+H0+τ :< 0.140 eV

+P(k)+BAO+H0+τ+SZ:< 0.136 eV

PlanckTT+lowP+TTTEEEE :Mν < 0.485 eV @95% C.L.

+P(k): < 0.275 eV

+P(k)+BAO: < 0.215 eV

+P(k)+BAO+τ : < 0.177 eV

+P(k)+BAO+SZ: < 0.208 eV

+P(k)+BAO+H0: < 0.132 eV

+P(k)+BAO+H0+τ :< 0.109 eV

+P(k)+BAO+H0+τ+SZ:< 0.117 eV

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Shape vs geometry

What’s more constraining: shape [P(k)] or geometrical (BAO)information? To answer this question we replace the DR12 CMASS P(k)by the DR11 CMASS BAO information

PlanckTT+lowP+BAO:Mν < 0.186 eV @95% C.L.

+τ : < 0.151 eV

+H0: < 0.148 eV

+H0+τ : < 0.115 eV

+H0+τ+SZ: < 0.114 eV

PlanckTT+lowP+TTTEEEE :Mν < 0.153 eV @95% C.L.

+τ : < 0.118 eV

+H0: < 0.113 eV

+H0+τ : < 0.094 eV

+H0+τ+SZ: < 0.093 eV

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Shape vs geometry

Mν posteriors: compare shape information (solid) with geometricalinformation (dashed), for a given color

Without small-scale polarization

0.0 0.1 0.2 0.3 0.4

Mν [eV]

0.0

0.2

0.4

0.6

0.8

1.0

P/

Pm

ax

basePK

baseBAO

basePK+τ0p055

baseBAO+τ0p055

basePK+H073p02+τ0p055

baseBAO+H073p02+τ0p055

With small-scale polarization

0.0 0.1 0.2 0.3 0.4

Mν [eV]

0.0

0.2

0.4

0.6

0.8

1.0

P/

Pm

ax

basepolPK

basepolBAO

basepolPK+τ0p055

basepolBAO+τ0p055

basepolPK+H073p02+τ0p055

basepolBAO+H073p02+τ0p055

Geometrical information more constraining than shape (win-win, as BAOalso less prone to systematics), BUT:

true within the assumption of a background flat ΛCDMlimit of our analysis methodology (e.g. we don’t know the bias)

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What about the mass hierarchy?

For each mass hierarchy, there exists a minimal allowed value for Mν

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Sensitivity to the mass hierarchy

Current cosmological data is mainly sensitive to Mν

Sensitivity to the mass hierarchy is only due to volume effects

We are approaching region of parameter space where these effects areimportant

Current data cannot distinguish between the two mass orderings,futuristic data might be able to measure individual neutrino massesthrough their free-streaming imprint on P(k) and on the EISW

In the most optimistic case, need a sensitivity of 0.02 eV todistinguish between NH and IH at 2σ (reachable withCMB-S4/COrE+DESI BAO) through volume effects alone

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Model comparison for mass hierarchies

Probability for a given mass hierarchy H = N, I given data:

pH =p(H)

∫∞0 dm0 L(D|m0,H)

p(N)∫∞

0 dm0 L(D|m0,N) + p(I )∫∞

0 dm0 L(D|m0, I )

Can then report posterior odds for NH vs IH, or exclusion C.L. for IHCLIH = 1− pI ( 6= C.L. at which we exclude the minimal mass in the IH,0.1 eV, CL0.1). Examples:

PlanckTT+lowP+BAO+τ : Mν < 0.151 eV @95% C.L.pN/pI = 1.8 : 1, CLIH = 64%, CL0.1 = 82%

+TTTEEE Mν < 0.118 eV @95% C.L.pN/pI = 2.4 : 1, CLIH = 71%, CL0.1 = 91%

+H0+SZ: Mν < 0.093 eV @95% C.L.pN/pI = 3.3 : 1, CLIH = 77%, CL0.1 = 96%

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Assumptions on the neutrino mass spectrum

Bounds derived assuming 3 massive degenerate νs spectrum (3deg)Compare results when considering 1 massive + 2 massless νs (1mass)1mass more constrained than 3deg when not using high-`polarization, less constraining otherwise (O(0.1)σ shifts)

0.00 0.08 0.16 0.24 0.32 0.40

Mν [eV]

0.0

0.2

0.4

0.6

0.8

1.0

P/

Pm

ax

basepol : 3deg

basepol : 1mass

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Conclusions

Cosmology provides tightest constraints on ν masses (Mν < 0.093 eV)

Geometrical surpasses shape information in constraining power

Data are starting to put the inverted hierarchy under pressure

Model comparison excludes inverted hierarchy at most @77% C.L.

Weak dependence on assumptions about ν mass spectrum

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