April 10, 2019; UT Particle and Astrophysics P599 Seminar Review of the paper 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 by Roy, Satyajit sroy14@vols.utk.edu /UTK Source paper: https://arxiv.org/abs/1703.10829
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 ( Σ m ν ) with recent cosmological data.
Standard neutrino cosmology • Neutrino properties leave detectable imprints on cosmological observations 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 of 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, Λ CDM, currently provides a good fit to most cosmological data sets.
Λ CDM 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.
Λ CDM 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 Λ CDM 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. • H o is derived in a non trivial way and • ∑m ν 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. • N eff = effective number of neutrino species (3). • Taking into account flavour oscillations, e-p annihilation and other effects, N eff = 3.045
Effect of N eff on the CMB and matter power spectrum Ratio of the CMB C TTℓ (left, including lensing effects) and matter power spectrum P(k) (right, computed for each model in units of (h − 1 Mpc) 3 ) for different values of Δ N eff ≡ N eff − 3.045 over those of a reference model with Δ N eff = 0. In order to minimize and better characterise the effect of N eff on the CMB, the parameters that are kept fixed are {z eq , z Λ , ω b , τ } and the primordial spectrum parameters. Fixing {z eq , z Λ } is equivalent to fixing the fractional density of total radiation, of total matter and of cosmological constant { Ω r , Ω m , Ω Λ } while increasing the Hubble parameter as a function of N eff . The statistical errors on the C ℓ are ∼ 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 Λ CDM model. Plank collaboration has done CMB analysis assuming two massless neutrinos and one massive neutrino, while fixing Σ m = 0.06 eV. For this paper, Based on the work of Capozzi et al.
Neutrino mass hierarchy • Individual neutrino masses as a Σ m ν function of for the two hierarchies (NH : plain line, IH dotted lines), under the assumptions given by equations 1 and 2-3. The vertical dashed lines outline 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 Σ m ν >0.25 eV • CMB and BAO data: we observe Σ m ν almost no difference in constraints when comparing results obtained 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 C TTℓ and matter power spectrum P(k) (computed for each model in units of (h − 1 Mpc) 3 ) for different values of Σ m ν over those of a reference model with massless neutrinos. In order to minimize and better characterise the effect of Σ m ν on the CMB, the parameters that are kept fixed are ω b , ω c , τ , the angular scale of the sound horizon θ s and the primordial spectrum parameters (solid lines). This implies that we are increasing the Hubble parameter h as a function of Σ m ν . 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 { ω m , ω b , Ω Λ } are kept fixed. For comparison, the error on P(k) is of the order of 5% with current observations, and the fractional C ℓ errors are of the order of 1/ √ℓ at low ℓ .
Constraints on Σ m ν and degeneracies • the impact of Σ m ν 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 Ω Λ • Σ m ν can impact the amplitude of the matter power spectrum and thus is directly correlated to A s (primordial spectral amplitude) • The addition of lensing distortions, the amplitude of which is proportional to A s , 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 θ i 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 of θ and its associated uncertainty.
Profile likelihoods • the likelihoods that are used here-after for the derivation of the results on Σ m ν
νΛ CDM(3 ν ) model • Figure illustrates that the behaviour of the as a function of Σ m ν 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 Σ m ν profile likelihoods obtained when combining hlpTT+lowTEB with VHL data in green: An apparent minimum shows up, around Σ m ν 0.7 eV
Adding BAO and SN1a data
νΛ CDM(3 ν ) +A L model • CMB data tend to favour a value of A L greater than one • A L is not fully compatible with the νΛ CDM model • open up the parameter space to νΛ CDM(3 ν ) +A L
Combining with CMB lensing • Another way of tackling the A L problem is to add the lensing Planck likelihood to the combination. This allows us to obtain a lower A L value; the A L value extracted from the data is fully compatible with the CDM model, allowing us to derive a limit on Σ m ν together with a coherent A L value.
Constraint on the neutrino mass hierarchy
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