Cosmological constraints on the neutrino mass including systematic - - PowerPoint PPT Presentation

Cosmological constraints on the neutrino mass including systematic uncertainties

• F. Couchot1, S. Henrot-Versillé?1, O. Perdereau1, S. Plaszczynski1,
• B. Rouillé d’Orfeuil1, M. Spinelli1;2, and M. Tristram1

Source paper: https://arxiv.org/abs/1703.10829

Review of the paper

by Roy, Satyajit sroy14@vols.utk.edu /UTK April 10, 2019; UT Particle and Astrophysics P599 Seminar

Abstract

• When combining cosmological and oscillations results to constrain

the neutrino sector, the question of the propagation of systematic uncertainties is often raised. We address this issue in the context of the derivation of an upper bound on the sum of the neutrino masses (Σmν) with recent cosmological data.

Standard neutrino cosmology

• Neutrino properties leave detectable imprints on cosmological
• bservations that can then be used to constrain neutrino properties.
• Present cosmological data are already providing constraints on

neutrino properties not only complementary but also competitive with terrestrial experiments; for instance, upper bounds on the total neutrino mass have shrinked by a factor of about 10 in the past 15 years.

Cosmic neutrino background

• A relic neutrino background pervading the Universe is a generic prediction
• f the standard hot Big Bang model. It has been indirectly confirmed by the

accurate agreement of predictions and observations of

• the primordial abundance of light elements,
• the power spectrum of Cosmic Microwave Background (CMB)

anisotropies,

• the large scale clustering of cosmological structures.

Within the hot Big Bang model such good agreement would fail dramatically without a CνB with properties matching closely those predicted by the standard neutrino decoupling process.

Standard neutrino cosmology

cosmology is sensitive to the following neutrino properties:

• their density, related to the number of active neutrino species,
• their masses.

The minimal cosmological model, ΛCDM, currently provides a good fit to most cosmological data sets.

ΛCDM model

• Observations:85% of the universe is dark matter. Small fraction is

Baryonic matter that composes stars, planets and living organisms.

• Cold: dark matter moves slowly compared to light.
• Dark: interacts very weakly with ordinary matter and electromagnetic

radiations.

• Structure grows hierarchically:
• Small objects collapse due to self gravity
• Merging in a continuous way to form larger massive objects.
• Agrees with the observations of the cosmological large scale

structures.

ΛCDM model

• Geometry Euclidean – no curvature. its constituents are dominated today by a cosmological constant Λ, associated with dark

energy, and cold dark matter; it also includes radiation, baryonic matter and three neutrinos. Density anisotropies are assumed to result from the evolution of primordial power spectra, and only purely adiabatic scalar modes are assumed.

• Minimal ΛCDM model has 6 parameters
• assumes that the only massless or light

(sub-keV) relic particles since the Big Bang Nucleosynthesis (BBN) epoch are photons and active neutrinos.

• Ho is derived in a non trivial way and
• ∑mν is usually fixed to 0.06 eV based on oscillation constraints

Neutrino decoupling

• the three active neutrino types thermalize in the early Universe, with a

negligible leptonic asymmetry. Then they can be viewed as three propagating mass eigenstates sharing the same temperature and identical Fermi-Dirac distributions, thus with no visible effects of flavour oscillations. Neutrinos decouple gradually from the thermal plasma at temperatures T ∼ 2MeV.

• Neff = effective number of neutrino species (3).
• Taking into account flavour oscillations, e-p annihilation and other effects,

Neff = 3.045

Effect of Neff on the CMB and matter power spectrum

Ratio of the CMB CTTℓ(left, including lensing effects) and matter power spectrum P(k) (right, computed for each model in units of (h−1Mpc)3) for different values of ΔNeff≡ Neff− 3.045 over those of a reference model with Δ Neff = 0. In order to minimize and better characterise the effect of Neffon the CMB, the parameters that are kept fixed are {zeq, zΛ, ωb, τ} and the primordial spectrum parameters. Fixing {zeq, zΛ} is equivalent to fixing the fractional density of total radiation, of total matter and of cosmological constant {Ωr, Ωm, ΩΛ} while increasing the Hubble parameter as a function of Neff. The statistical errors on the Cℓare ∼ 1% for a band power of Δ ℓ = 30 at ℓ ∼

• 1000. The error on P(k) is estimated to be of the order of 5%.

Neutrino mass hierarchy

• we have to choose a neutrino mass splitting scenario to define the

ΛCDM model. Plank collaboration has done CMB analysis assuming two massless neutrinos and one massive neutrino, while fixing Σm = 0.06 eV. For this paper, Based on the work of Capozzi et al.

Neutrino mass hierarchy

• Individual neutrino masses as a

function

• f

Σmν for the two hierarchies (NH : plain line, IH dotted lines), under the assumptions given by equations 1 and 2-3. The vertical dashed lines

• utline

the minimal m value allowed in each case (corresponding to one massless neutrino generation). The log vertical axis prevents from the difference between m1 and m2 to be resolved in IH.

Neutrino mass hierarchy

• given the oscillation constraints,

neutrino masses are nearly degenerate for Σmν>0.25 eV

• CMB and BAO data: we observe

almost no difference in Σmν constraints when comparing results

• btained with one of the two

hierarchies with the case with three mass-degenerate neutrinos

• This is the model used in this

paper.

Effect of neutrino masses on the CMB and matter power spectrum

Ratio of the CMB CTTℓ and matter power spectrum P(k) (computed for each model in units of (h−1Mpc)3) for different values of Σmν over those of a reference model with massless neutrinos. In order to minimize and better characterise the effect of Σmνon the CMB, the parameters that are kept fixed are ωb, ωc, τ , the angular scale of the sound horizon θs and the primordial spectrum parameters (solid lines). This implies that we are increasing the Hubble parameter h as a function of Σmν. For the matter power spectrum, in order to single out the effect of neutrino free-streaming on P(k), the dashed lines show the spectrum ratio when {ωm, ωb,ΩΛ} are kept fixed. For comparison, the error on P(k) is of the order of 5% with current observations, and the fractional Cℓerrors are of the order of 1/√ℓ at low ℓ.

Constraints on Σmν and degeneracies

• the impact of Σmν on the CMB temperature power spectrum is partly

degenerated with that of some of the six other parameters.

• the impact of neutrino masses on the angular-diameter distance to

last scattering surface is degenerated with ΩΛ

• Σmν can impact the amplitude of the matter power spectrum and

thus is directly correlated to As (primordial spectral amplitude)

• The addition of lensing distortions, the amplitude of which is

proportional to As, helps to break this degeneracy.

Profile likelihoods

• The results described in this paper were obtained from profile likelihood analyses

performed with the CAMEL software.

• this method aims at measuring a parameter θ through the maximisation of the

likelihood function L(θ; μ)

• where μ is the full set of cosmological and nuisance parameters excluding θ.
• For different, fixed θi values, a multidimensional minimisation of the function
• The absolute minimum, , of the resulting curve is by construction the

(invariant) global minimum of the problem.

• From -

curve, the so-called profile likelihood, one can derive an estimate

• f θ and its associated uncertainty.

Profile likelihoods

• the likelihoods that are used here-after for the derivation of the

results on Σmν

νΛCDM(3ν) model

• Figure illustrates that the behaviour of the as a function of Σmν is almost independent of the choice of the likelihood
• Still, the spread of the profile likelihoods gives an indication of the systematic uncertainties linked to this choice.

Impact of VHL data

• Fig. 5 shows the Σmν profile likelihoods obtained when combining

hlpTT+lowTEB with VHL data in green: An apparent minimum shows up, around Σmν 0.7 eV

Adding BAO and SN1a data

νΛCDM(3ν) +AL model

• CMB data tend to favour a value
• f AL greater than one
• AL is not fully compatible with

the νΛCDM model

• open up the parameter space to

νΛCDM(3ν) +AL

Combining with CMB lensing

• Another way of tackling the AL problem is to add the lensing Planck

likelihood to the combination. This allows us to obtain a lower AL value; the AL value extracted from the data is fully compatible with the CDM model, allowing us to derive a limit on Σmν together with a coherent AL value.

Constraint on the neutrino mass hierarchy

Conclusion

• the propagation of foreground systematics on the determination of

the sum of the neutrino masses through extensive comparison.

• How νΛCDM(3ν) model leads to the same results as those obtained

when considering normal or inverted hierarchy.

• the details of the foreground residuals modelling play a non-negligible

role in the Σmν determination.

• In neutrino hierarchy, profile likelihoods are identical in the normal

and inverted hierarchies, proving that the current data are not sensitive to the details of the mass repartition.

• Combining the latest results gives Σmν < 0.17 eV at 95% CL

Conclusion

As far as cosmology is concerned, the uncertainty on the neutrino mass will be improved in the future: It could be reduced by a factor ' 5 if one refers, for instance, to the forecasts on the combination of next- generation ‘Stage 4’ B-mode CMB experiments with BAO and clustering measurements from DESI

References

• Cosmological constraints on the neutrino mass including systematic

uncertainties - F. Couchot et al

• Neutrinos in Cosmology – by J. Lesgourgues (RWTH Aachen U.)

and L. Verde (U. of Barcelona & ICREA) at pdg.lbl.gov