The promising future of a rubust cosmological neutrino mass measurement

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The promising future of a rubust cosmological neutrino

mass measurement

Maria Archidiacono RWTH Aachen University

The quest for new physics, Valencia, 12 -14 December 2018

Archidiacono, Brinckmann, Lesgourgues, Poulin, JCAP (2017)

Sprenger, Archidiacono, Brinckmann, Clesse, Lesgourgues, submitted to JCAP (2018)

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Timeline

Temperature Process and Observables ν Constraints

T γ ∼ 1 MeV ν decoupling

T γ ∼ 0.8 MeV BBN Flavour, Number

T γ ∼ 1 eV CMB Number, (Mass)

T ν ∼ m ν / 3 ν nr transition

T γ ∼ 0.2 meV LSS Mass, (Number)

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•  Background effects (z eq , d A , z Λ ) è Correlation between M ν and H 0

•  Perturbation effects (early ISW)

Neutrino mass & CMB (TT, EE)

Archidiacono+ JCAP (2017 )

M ν ,ref = 60 meV M ν = 150 meV

Δh ≈ −0.09 Δ M ν 1eV

⎛

⎝ ⎜ ⎞

⎠ ⎟ Ω ν h 2 = ρ ν

ρ c = ∑ m ν 93.14eV

Planck 2018 TT + lowE

Planck 2018 TTTEEE + lowE m ν

∑ < 0.54 eV (95%c.l.)

m ν

∑ < 0.26 eV (95%c .l.)

CORE-like

CMB experiment

3

See talk of Lattanzi

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Synergy with CMB lensing

ℓ 4 C ℓ φφ ∝ A s ω m 3/2 h −1/2 M ν −α

•  Increase A s ✗

keeping A s exp(-2 τ reio ) fixed èNo correlation between M ν and τ reio

•  Increase ω cdm ✓

  keeping ω b and θ s fixed èCorrelation between M ν and ω cdm   èCMB data alone cannot measure M ν

M ν ,ref = 60 meV M ν = 150 meV Archidiacono+ JCAP (2017)

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Neutrino non-relativistic transition

When neutrinos become non-relativistic

z nr ≈ 1890 (m ν,i /1eV), they travel through the Universe with a thermal velocity

v th,i = <p>/m ν,i ≈ 3T ν,i /m ν,i ≈ 150 (1+z) (1eV/m ν,i ) km/s

Neutrinos cannot be confined below the characteristic free-streaming scale defined by v th,i .

k nr,i (z) ≡ H (z nr,i )

(1 + z nr,i ) = 0.0145Mpc −1 m ν ,i 1eV

⎛

⎝ ⎜ ⎞

⎠ ⎟

1/2

Ω 1/2 m h

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Synergy with LSS

P (k, z ) = δ m (k, z) 2 δ m = δρ m

ρ m

k 2

a 2 φ = −4 π G( δρ m ) ( δρ ν << δρ cdm )

H 2 = 8 π G

3 ( ρ γ + ρ b + ρ cdm + ρ ν + ρ Λ )

δ cdm ∝ a δ cdm ∝ a 1−3/5 f ν

only cold dark matter

in the presence of ν cdm+hdm=mdm

P m (k ) ν

P m (k ) ΛCDM ≈ 1 − 8 f ν

��

� [� �� -� ]

� / � Λ � ��

� = �

��

� ν = ��

/

Figure 1. Linear theory results in massive neutrino cosmologies. Left panel: Ratio of the total matter power spectrum to the CDM power spectrum at redshifts z = 0 (continuous curves) and z = 2 (dashed curves) for two di↵erent values of the sum of neutrino masses, ⌃ m ⌫ = 0.3 eV in red and ⌃ m ⌫ = 0.53 eV in green. Dotted lines denote the asymptotic value at small scales of (1 f ⌫ ) 2 . Right panel: ratio at z = 0 of the total matter power spectrum (continuous curves) and CDM power spectrum (dashed curves) for the same two cosmologies to the ⇤CDM prediction.

while from Eq. (2.8) and Eq. (2.5), it follows that the suppression for the CDM power spectrum, P cc , is given by a factor ⇠ (1 6f ⌫ ). The di↵erence in the suppression between the two power spectra is shown in the right panel of Figure 1.

3 Simulations

The DEMNUni simulations have been conceived for the testing of di↵erent probes, including galaxy surveys, CMB lensing, and their cross-correlations, in the presence of massive neutrinos. To this aim, this set of simulations is characterised by a volume big enough to include the very large-scale perturbation modes, and, at the same time, by a good mass resolution to investigate small-scales nonlinearity and neutrino free streaming. Moreover, for the accurate reconstruction of the light-cone back to the starting redshift of the simulations, it has been used an output-time spacing small enough that possible systematic errors, due to the interpolation between neighbouring redshifts along the line of sight, result to be negligible.

The simulations have been performed using the tree particle mesh-smoothed particle hydrody- namics (TreePM-SPH) code gadget-3, an improved version of the code described in [37], specifically modified in [38] to account for the presence of massive neutrinos. This version of gadget-3 follows the evolution of CDM and neutrino particles, treating them as two distinct sets of collisionless particles. For the specific case of the DEMNUni simulations, a gadget-3 version, modified for OpenMP parallelism and for memory efficiency, has been used to smoothly run on the BG/Q Fermi cluster.

Given the relatively high velocity dispersion, neutrinos have a characteristic clustering scale larger than the CDM one. This allows to save computational time by neglecting the calculation of the short- range tree-force induced by the neutrino component. This results in a di↵erent scale resolution for the two components, which for neutrinos is fixed by the PM grid (chosen with a number of cells eight times larger than the number of particles), while for CDM particles is larger and given by the tree-force (for more details see [38] ). This choice does not a↵ect the scales we are interested in; in fact, the tree-force acts below the PM-grid scale, which, for the DEMNUni simulations is ⇠ 0.5h/Mpc (PMGRID=4096 and L box = 2 h 1 Gpc), and, as discussed also in [39], this corresponds to wavenumbers which are at least two orders of magnitude smaller than the zero-redshift free-streaming lengths for the neutrino masses considered in our runs. This means that for z > 0, neutrino overdensities are completely

– 4 – Castorina+ JCAP (2015)

P c (k ) ν

P c (k ) ΛCDM ≈ 1− 6 f ν

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Synergy with LSS

Galaxy surveys

BAO Cosmic shear Galaxy clustering

Tegmark+ PRD(2006)

SDSS-DR12

KiDS Giblin+ MNRAS(2018)

7

8 Giblin et al.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

s

= 6.6 arcmin,

e

= 0.28

c= 0.015 c= 0.010 c= 0.005

CDM Unclipped

0.2 0.4 0.6 0.8 1.0 1.2 1.4

0.0 0.5 1.0 1.5 2.0 2.5 3.0

✓⇠

+

⇥ 10

4

[arcmin]

c

= 0.010,

e

= 0.28

s= 8.8 arcmin s= 6.6 arcmin s= 4.4 arcmin

0.2 0.4 0.6 0.8 1.0 1.2 1.4

⇠

+

/ ⇠

unclip +

10

⁰

10

¹

10

²

✓ [arcmin]

0.0 0.5 1.0 1.5 2.0 2.5 3.0

s

= 6.6 arcmin,

^c

= 0.010

e= 0 e= 0.28 e= 0.40

10

⁰

10

¹

10

²

✓ [arcmin]

0.2 0.4 0.6 0.8 1.0 1.2 1.4

Figure 4.The mean unclipped (solid grey) and clipped (other solid colours)⇠+correlation functions measured from the SLICS realisations. The dashed black line is the theoretical unclipped prediction from equation13. The left hand panels display✓⇠+, the right hand the measurements normalised to the unclipped statistic from SLICS. The annotation in the lower right hand corner of each panel specifies which of the parameters are held constant in the calculations. The upper panel is concerned with variations in the clipping threshold,^c, with fixed smoothing scale, s, and shape noise characteristics, e. The middle and lower panels present variations in the smoothing scale and shape noise respectively. The magenta line in all cases depicts the measurement for the fiducial parameters:^c= 0.010,s= 6.6arcmin and e= 0.28. The error bars are the error on the mean measurement.

An additional test of whether the chosen(^c, s)combination is suitable comes from inspection of the clipped and unclipped correlation functions. The optimal choices for these parameters will facilitate clipping of the non-linear regions exclusively, leaving the linear signal untouched. In this case, the unclipped and clipped⇠+ should converge on the larger, linear angular scales. In Figure4, we present how the⇠^clip+ measured from the SLICS are affected by variations in the clipping threshold, smoothing scale and the galaxy shape noise. Similar trends are seen for the⇠^clipstatistic at higher angular scales (we refer the reader to Section4). The left hand panels in this figure display✓⇠+, where⇠+is the mean unclipped (in solid grey) or clipped (other colours) correlation function measured from the SLICS realisations. The right hand panels display the various correlation functions normalised to that of the unclipped. In calculating the error on the ratios, we take into account the cross-covariance between the clipped and unclipped statistics. The magenta line on all panels is the same and corresponds to^c= 0.010, s= 6.6arcmin with KiDS-450 level shape noise.

The upper panel of Figure4illustrates the effect of increasing the clipping threshold from^c= 0.005to 0.010 to 0.015, whilst the smoothing scale is fixed to 6.6 arcmin and the shape noise is fixed to the KiDS-450 level. On average,26±3%of the area of the field is clipped in the case of the most aggressive clipping threshold,^c= 0.005, and3±1%is clipped in the case of the least aggressive,^c= 0.015. We see that when adopting^c= 0.005, the clipped signal exhibits a large reduction in power at angular scales

around 6 arcmin and a failure to converge with the unclipped at the larger angular scales. The power deprecation is caused by overly aggressive clipping; subtracting too much of the shear signal en- genders anticorrelations in the⇠+^clip. The excess power at large✓ is caused by the smoothing transferring small-scale power to larger scales. This effect is illustrated by considering the convolution of a single -function with a Gaussian smoothing kernel; the signal is spread by an extent given by the width of the Gaussian. This panel suggests that^c= 0.010and 0.015 are more appropriate thresh- olds as they better recover the large scale behaviour of the⇠+^unclip. The variations in the⇠^clip+ when the smoothing scale is altered, whilst^cis fixed to 0.010 and the shape noise is fixed to KiDS- 450 level, are shown in the middle panel of Figure4. We note the lack of convergence between the unclipped and the clipped signal with s= 4.4arcmin, indicating over-clipping of the convergence field. We also see that the angular scale at which the loss of power in the⇠^clip+ is maximised translates right with increasing smoothing scale. This is due to the loss of signal incurred from smoothing over features of this angular size. The upper and middle panels of Figure 4illustrate the importance of identifying a clipping threshold and smoothing scale which are high enough to diminish the clipping of pure noise features, but low enough to avoid smoothing out the cosmological content in the clipped statistic.

The lower panel of Figure4illustrates the sensitivity of the

⇠^clip+ to the shape noise, whilst^cand sare fixed to0.010and 6.6 arcmin respectively. Wheree>0the shape noise is sampled from MNRAS000, 000–000 (0000)

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Synergy with BAO

Current DESI

D V (z) = ⎡⎣ z / H(z )(1+ z) 2 d A 2 (z) ⎤⎦ 1/3

•  BAO data alone can bound M ν , but not with great accuracy

•  The strong degeneracy between M ν and H 0 observed in the CMB cannot exist with BAO

•  There exists, however, a correlation among M ν , H 0 , ω cdm with BAO but along different angles than CMB

è CMB+BAO: Correlation between M ν and A s , τ reio

θ s constant

8

Archidiacono+ JCAP (2017)

CMB

BAO

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Synergy with GC & CS

•  The CMB M ν , H 0 degeneracy is lifted in GC (and CS in the high z bins)

•  GC and CS induce a correlation between M ν and the primordial power spectrum parameters

è CMB+GC+CS: Correlation between M ν and A s , τ reio

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Archidiacono+ JCAP (2017)

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Synergy with SKA ( τ rei o )

0.0505 0.0561 0.0616 0.0672 0.0728

⌧ reio

0.0243 0.0437 0.0631 0.0825 0.102

M ⌫ [eV]

0.0505 0.0561 0.0616 0.0672 0.0728

⌧ reio

CMB-S4+Euclid ...+LiteBird

...+SKA1-IM+ ⌧ reio prior Brinckmann, Hooper, Archidiacono+ (2018)

Liu+ PRD (2016) σ(τ reio )=0.001

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…but

²  Theoretical errors: non-linear scales

²  Systematic effects: neutrino bias

²  Degeneracies in extended models

More than 3 σ detection of a non-zero neutrino mass

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1 2 3 4 5 6 k [h/Mpc]

0.6 0.4 0.2 0.0 0.2 0.4 0.6

e ↵ /P [%]

z = 1, µ = 0 sensitivity obs. error th. error

The Matter Power with Neutrinos 7

Figure 4. The e↵ect of massive neutrinos on the matter power spectrum for a neutrino mass of M ⌫ = 0.3 eV. Solid lines show the ratio between simulations with and without massive neutrinos, for both L30 (red), with a 512 Mpc h 1 box and S30 (orange), with a 150 Mpc h 1 box. Initial redshift was 49. The blue dashed line shows the estimated ratio using HALOFIT , while the black dashed line shows the prediction from linear theory.

HALOFIT clearly over-predicts the suppression of the matter power spectrum due to massive neutrinos in the non- linear regime. The cause is similar to that discussed in Sec- tion 3.1; HALOFIT includes massive neutrinos only through the linear theory neutrinos suppression on the non-linear scale, and thus neglects any back-reaction from the dark matter. This interpretation is supported by the good agree- ment of HALOFIT with the Fourier-space simulations.

The largest discrepancy, around 10% of the total suppression, occurs at k ⇠ 1 hMpc 1 . The location of the maximal suppression in the numerical simulation moves to larger scales at lower redshifts, an e↵ect which is again not captured by HALOFIT , although it was present to some extent in our Fourier-space simulations. Furthermore, the ampli- tude of the suppression decreases with redshift, which is to be expected from our discussion in 3.1; as non-linear growth occurs in the dark matter more neutrinos fall into the grav- ity wells. A cross-over redshift occurs at z = 1; on very small scales the suppression here is equal to that of linear theory, while at lower redshifts it is less. Note also that in the quasilinear regime, 0.05 < k < 0.2 hMpc 1 , the simulations clearly agree much better with HALOFIT rather than linear theory The dependence of our results on M ⌫ is well described by a linear relation, with the maximal suppression

for a given redshift being proportional to f ⌫ , although the redshift dependence is more complicated.

HALOFIT over-predicts the e↵ect of neutrinos on the smallest scales. This is not due to neutrino physics, but is a discrepancy induced because, as found by Hilbert et al.

(2009), HALOFIT under-predicts the growth of non-linear power for k > 2 hMpc 1 in a ⇤CDM universe by up to a factor of two. We corrected this by re-fitting the HALOFIT pa- rameter that controls the small-scale power using our ⇤CDM simulations, after which we could reproduce the asymptotic neutrino e↵ect. We detail our modifications in Appendix A.

Note that HALOFIT also has reduced accuracy at z = 3 4, with errors of 15 20%, compared to 5 10% at z = 0 2.

Because of this, it fails to accurately predict the location of the peak non-linear suppression at z > 2. We did not correct this e↵ect, as our attempts were found to negatively impact accuracy at lower redshifts.

We have also performed some simulations varying the cosmological parameters from our fiducial values, as described in Section 2.3. The results of these simulations were similar to those for our fiducial cosmology, and agree with the results discussed in Viel et al. (2010). The dependence of the non-linear suppression on cosmology is largely captured c 2011 RAS, MNRAS 000, 1–12

Non-linear scales

Bird+ MNRAS (2012)

•  Implementation of massive neutrinos in cosmological simulations:

DEMNUni Carbone+ (2015)

Hybrid methods:

Brandbyge & Hannestad (2009/10)

Semi-linear methods:

Ali-Haimoud & Bird (2012)

•  Baryonic feedback Parimbelli+ (2018)

Sprenger, Archidiacono+ (2018)

Euclid GC

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See talk of Parimbelli

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Neutrino Bias

“Bias from neutrino bias: to worry or not to worry?”

Raccanelli+ MNRAS (2018)

“Bias due to neutrinos must not uncorrect’d go”

Vagnozzi, Brinckmann, Archidiacono, Freese, Gerbino, Lesgourgues, Sprenger, JCAP (2018)

25% shift in best-fit and in σ P g (k, z) = b cb 2 (k, z )P cb (k, z)

b cb (k, z ) = P hh (k, z) P cb (k, z )

Because of their large thermal velocities neutrinos do not cluster within the dark matter halos.

13

��

� [� ��

^-�

]

� / �

Λ��

� = �

��

�

_ν

= ��

�

_ν

= ��

� / �

Figure 1. Linear theory results in massive neutrino cosmologies. Left panel: Ratio of the total matter power spectrum to the CDM power spectrum at redshifts z = 0 (continuous curves) and z = 2 (dashed curves) for two di↵erent values of the sum of neutrino masses, ⌃ m ⌫ = 0.3 eV in red and ⌃ m ⌫ = 0.53 eV in green. Dotted lines denote the asymptotic value at small scales of (1 f ⌫ ) 2 . Right panel: ratio at z = 0 of the total matter power spectrum (continuous curves) and CDM power spectrum (dashed curves) for the same two cosmologies to the ⇤CDM prediction.

while from Eq. (2.8) and Eq. (2.5), it follows that the suppression for the CDM power spectrum, P cc , is given by a factor ⇠ (1 6f ⌫ ). The di↵erence in the suppression between the two power spectra is shown in the right panel of Figure 1.

3 Simulations

The DEMNUni simulations have been conceived for the testing of di↵erent probes, including galaxy surveys, CMB lensing, and their cross-correlations, in the presence of massive neutrinos. To this aim, this set of simulations is characterised by a volume big enough to include the very large-scale perturbation modes, and, at the same time, by a good mass resolution to investigate small-scales nonlinearity and neutrino free streaming. Moreover, for the accurate reconstruction of the light-cone back to the starting redshift of the simulations, it has been used an output-time spacing small enough that possible systematic errors, due to the interpolation between neighbouring redshifts along the line of sight, result to be negligible.

The simulations have been performed using the tree particle mesh-smoothed particle hydrody- namics (TreePM-SPH) code gadget-3, an improved version of the code described in [37], specifically modified in [38] to account for the presence of massive neutrinos. This version of gadget-3 follows the evolution of CDM and neutrino particles, treating them as two distinct sets of collisionless particles. For the specific case of the DEMNUni simulations, a gadget-3 version, modified for OpenMP parallelism and for memory efficiency, has been used to smoothly run on the BG/Q Fermi cluster.

Given the relatively high velocity dispersion, neutrinos have a characteristic clustering scale larger than the CDM one. This allows to save computational time by neglecting the calculation of the short- range tree-force induced by the neutrino component. This results in a di↵erent scale resolution for the two components, which for neutrinos is fixed by the PM grid (chosen with a number of cells eight times larger than the number of particles), while for CDM particles is larger and given by the tree-force (for more details see [38] ). This choice does not a↵ect the scales we are interested in; in fact, the tree-force acts below the PM-grid scale, which, for the DEMNUni simulations is ⇠ 0.5h/Mpc (PMGRID=4096 and L box = 2 h 1 Gpc), and, as discussed also in [39], this corresponds to wavenumbers which are at least two orders of magnitude smaller than the zero-redshift free-streaming lengths for the neutrino masses considered in our runs. This means that for z > 0, neutrino overdensities are completely

– 4 –

Castorina+ JCAP (2015)

The relative effect that

we can actually see

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Degeneracies

Brinckmann, Hooper, Archidiacono+ (2018)

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Conclusions

•  Cosmology is a powerful tool to constrain neutrino physics, but the results have to be taken with a grain of salt (theoretical erros & systematics)

•  Future galaxy and hydrogen surveys will be able to pin down the neutrino mass sum in the minimal extension of the Λ CDM and having systematics under control.

•  Caveats:

²  Non-linearities & Baryonic feedback

²  Neutrino bias

²  Degeneracies in extended models

•  Final remark: synergies with ground-based neutrino experiments

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See talk of Oldengott

The promising future of a rubust cosmological neutrino mass measurement