- Email: [email protected]
Neutrino physics after Planck
Available online at www.sciencedirect.com
Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55 www.elsevier.com/locate/nppp
Neutrino physics after Planck G. Polenta ASI Science Data Center, via del Politecnico, 00133 Roma, Italy INAF - Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
on behalf of the Planck Collaboration
Abstract We present constraints on neutrino physics derived from the 2013 Planck data release, which involves data collected during the first 15.5 months of observations. After a brief description of the effect of neutrino masses and number of relativistic species on CMB anisotropies, we present results obtained from Planck data alone and in combination with other astrophysical probes. In particular, Planck set constraints on the sum of neutrino masses is mν < 0.23 eV, and on the number of relativistic species of Neff = 3.30+0.54 −0.51 both at 95% C.L. Finally, we briefly discuss updated results from the Planck 2015 data release as well as future prospects for CMB experiments. Keywords: Cosmology, Cosmic Microwave Background, Cosmological parameters, Neutrinos
1. Introduction The Planck satellite1 [1] is a third generation Cosmic Microwave Background (CMB) experiment. It was launched on 14 May 2009 and observed the sky continuously from 12 August 2009 to 23 October 2013. Planck’s scientific payload contains detectors sensitive to nine frequency bands between 25 and 1000 GHz with angular resolution between 33 and 5 . The Low Frequency Instrument (LFI; [2]) covers bands centred at 30, 44, and 70 GHz using pseudo-correlation radiometers, while the High Frequency Instrument (HFI; [3]) is equipped with bolometers covering bands centred at 100, 143, 217, 353, 545, and 857 GHz. Planck imaged the whole sky with an unprecedented combination of Email address: [email protected] (G. Polenta) 1 Planck (http://www.esa.int/Planck) is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states and led by Principal Investigators from France and Italy, telescope reflectors provided through a collaboration between ESA and a scientific consortium led and funded by Denmark, and additional contributions from NASA (USA).
http://dx.doi.org/10.1016/j.nuclphysbps.2015.06.014 2405-6014/© 2015 Elsevier B.V. All rights reserved.
sensitivity, angular resolution, and frequency coverage. In January of 2011, the Planck Collaboration released a first set of scientific data, the Early Release Compact Source Catalogue (ERCSC; [4]) together with initial scientific results related to astrophysical foregrounds (A&A, Vol. 520, 2011). Since then, 34 Intermediate papers on foreground properties have been published. In March of 2013, the second release of scientific data took place, consisting mainly of temperature maps of the whole sky [5]; these products and associated scientific results are described in a special issue of A&A (Vol. 571, 2014). In February of 2015, the third data release has started and includes products and scientific results obtained using data collected throughout the entire mission in both temperature and polarisation [6]. In this paper we present how Planck 2013 data constrain neutrino physics, as extensively described in the Planck cosmological parameter paper [7], and we briefly discuss 2015 updates.
53
G. Polenta / Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55
In the standard scenario for the thermal history of the Universe, massless neutrinos are in thermal equilibrium with the primeval plasma through weak interactions until the temperature drops below T dec ≈ 1 Mev [8]. Thus, neutrinos are not reheated by e± annihilations favoured when the Universe becomes colder than the electron mass, and resulting in a background of cosmological neutrinos with a present temperature T ν ≈ 1.9 K, corresponding to ∼ 0.2 eV at the last scattering surface. As a consequence, CMB primary anisotropies cannot probe neutrinos with masses below mν ≈ 1 eV, since they are relativistic at CMB decoupling, and the effect on the background cosmology can be compensated by changes in the Hubble constant H0 . For larger values of the mass, changing mν impacts on matter-radiation ratio and equality, leading to variations in the gravitational potential that are visible at angular scales around the first CMB acoustic peak (early Integrated SachsWolfe effect; ISW). Moreover, neutrino masses also impact the early ISW at perturbation level through neutrino free streaming. It is important to note that increas ing mν suppresses clustering, thus reducing the lensing potential affecting CMB photons at small angular scales. Thanks to its angular resolution, Planck is sensitive to gravitational lensing, and can therefore overcome the limit of ≈ 1 eV on the sum of neutrino masses. The number of relativistic species Neff reflects the energy density of neutrinos: ρν = Neff (7/8) (4/11)4/3 ργ . This parameter actually accounts for the energy density of all relativistic components but photons, i.e. it includes also possible forms of dark radiation. In the standard model with 3 families of neutrinos, detailed calculations provide Neff = 3.046 [9]. Increasing Neff increases the expansion rate before recombination, leading to an increase of the diffusion angular scale θd that reduces the power in the damping tale of the CMB power spectrum. 3. Results from the Planck 2013 data release 3.1. Constraints on
mν
When constraining the sum of neutrino masses we assume 3 degenerate massive neutrinos. This approximation is accurate enough given the Planck sensitivity. As discussed in [10, 7], we combine: Planck temperature power spectrum (labelled Planck; [10]); Planck lensing likelihood derived from lensing 4-point correlation function [11]; WMAP low- polarisation (labelled WP;
[12]); data coming from high-resolution CMB experiments (labelled HighL), namely the Atacama Cosmology Telescope [13] and the South Pole Telescope [14], whose primary role is to improve modelling of unresolved foreground components. Results are shown in Fig. 1. Corresponding 95% upper limits are mν < 0.66 eV Planck+WP+HighL, mν < 0.85 eV Planck+lensing+WP+HighL, thus confirming that Planck entered a new regime thanks to its sensitivity to gravitational lensing. It is interesting to note that adding the Planck lensing likelihood weakens the upper limit. In fact, Planck tem-
1.0
Planck+WP+highL Planck+lensing+WP+highL
0.8
Planck+WP+highL (AL ) Planck−lowL+highL+τ prior
P/Pmax
2. CMB and neutrinos
0.6
Planck−lowL+lensing+highL+τ prior Planck−lowL+τ prior
0.4 0.2 0.0 0.0
0.4
0.8
1.2 Σmν [eV]
1.6
Figure 1: Marginalised posterior distributions of data combinations (from [7]).
2.0
mν for different
perature power spectrum favours a slightly higher lensing amplitude to add more lensing smoothing than predicted in ΛCDM. Neutrino mass acts in the opposite way, i.e. increasing mν reduces the predicted smoothing even further. On the other hand, lensing likelihood directly probes the lensing power with a mild preference for a lensing amplitude slightly below (but consistent with) ΛCDM predictions. Therefore combining Planck temperature power spectrum with lensing likelihood pulls the sum of neutrino masses towards higher values. This is even more evident when we remove low data and add a prior for the optical depth τ (labelled -lowL+τprior), which results in a best-fit value away from zero. Baryon acoustic oscillations (BAO) in the matter power spectrum have proven to be very useful in constraining neutrino masses, because these are basically geometric measurements that are sensitive to the evolution of the angular-diameter distance and the Hubble
54
G. Polenta / Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55
parameter. Adding BAO data from SDSS DR7 [15, 16], WiggleZ [17], BOSS DR9 [18], and 6dF Galaxy Survey [19], the constraint on neutrino masses tightens significantly to mν < 0.23 eV 95%, Planck+WP+HighL+BAO, which can be regarded as our best limit on mν . Since Planck 2013 data release, several authors suggested a preference for massive neutrinos in the Planck data. However, this is mainly due to an attempt to reduce tensions between Planck and external datasets in the amplitude of matter density perturbation σ8 : in creasing mν decreases the amplitude of late-time fluctuations σ8 through the effect of neutrino free streaming on structure formation. However, larger masses also imply lower values of the Hubble constant that are in strong tension with direct measurements of H0 .
Constraints on the number of relativistic species are derived assuming that the extra degrees of freedom are massless. Posterior distributions for Neff are shown in Fig. 2, and correspond to
Neff =
3.30+0.54 −0.51
95%, Planck+WP+HighL, 95%, Planck+WP+HighL+BAO.
Hence, Planck data are consistent with standard model predictions but do not completely rule out Neff = 4. Adding BAO observations helps in further reducing possible evidences for extra relativistic degrees of freedom. Planck+WP+highL +BAO +H0 0.8 +BAO+H0
P/Pmax
1.0
−0.52
As we can see, constraints are not much degraded by the joint analysis as these parameters affect different regions of the CMB power spectrum, and are therefore almost uncorrelated. The inclusion of sterile neutrino is motivated by recent works that aim to explain some anomalies arising, for instance, from the MiniBoone experiment [20]. In the following, we assume normal hierarchy for the active sector plus a massive sterile neutrino whose distribution is either a thermal one or proportional to those of the active sector (Dodelson-Widrow scenario). These two cases are practically identical from the point of view of the analysis that uses the effective mass meff ν, sterile as parameter, while they differ only when moving to the interpretation of the physical mass mthermal sterile . Results for < 10 eV are mthermal sterile ⎫ ⎪ mν < 0.42 eV ⎪ ⎬ 95%, PlanckTT+WP+HighL+BAO, ⎪ ⎪ ⎭ N < 3.80 eff
0.6
thus only marginally compatible with a fully thermaleff ized sterile neutrino with mthermal sterile ≈ mν, sterile < 0.5 eV. For Neff ∼ 3 the physical mass of neutrinos becomes so large that they become non-relativistic well before recombination, and therefore they are hidden within the overall cold dark matter budget.
0.4 0.2 0.0 2.0
3.3. Joint constraints on Neff and either mν or eff mν, sterile Since extra relics could have a mass themselves or coexist with massive neutrinos, it is interesting to derive joint constraints on these parameters. When considering extra relics plus massive neutrinos we obtain ⎫ mν < 0.28 eV ⎪ ⎪ ⎬ 95%, PlanckTT+WP+HighL+BAO. ⎪ +0.54 ⎪ ⎭ N = 3.32 eff
3.2. Constraints on Neff
Neff = 3.36+0.68 −0.64
It is important to note that Neff is positively correlated with the expansion rate H(z). Hence, when combining Planck with direct measurements of H0 , the slight tension between the two observations pulls Neff high, thus favouring the presence for extra neutrinos at ∼ 2σ level. However, at the same time this also increases σ8 , therefore producing a strong tension with weak lensing and cluster abundance observations that favour lower σ8 compared to Planck.
2.5
3.0
3.5
Neff
4.0
4.5
5.0
Figure 2: Marginalised posterior distributions of Neff for different data combinations (from [7]).
4. Planck 2015 results and future prospects On February 5, 2015, the Planck Collaboration published its third data release [6]. The updated constraints
G. Polenta / Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55
on neutrino physics are [21] ⎫ ⎪ mν < 0.21 eV 95% ⎪ ⎬ ⎪ ⎪ PlanckTT+LowP+BAO, N = 3.15 ± 0.23 68% ⎭ eff
where LowP labels the Planck temperature and polarisation likelihood at large angular scales. The im provement on mν with respect to 2013 is small because Planck had almost saturated the sensitivity limit of CMB temperature power spectrum already in 2013. The 2015 best-fit value of Neff is closer to the standard model prediction of 3.046. Including high- polarisation tightens the limits based on Planck data alone and gives consistent results in ruling out Neff = 4 at over 3σ. However, models with thermalized extra relativistic species predicting ΔNeff 0.5 are still compatible with current data. Interestingly, when combining Planck with external data the inclusion of Planck high- polarisation has only a minor effect on mν , however when considering Planck alone it gives [21] mν < 0.50 eV 95%, PlanckTT+TE+EE+LowP, which is already tighter than the KATRIN2 mass limit. Future high-resolution CMB polarisation experiments, such as the COrE+ proposal 3 , are targeted to accurately reconstruct the lensing potential. Hence, when combined with future BAO observations from the Euclid satellite [22], they will probe lower mass scales allowing to distinguish between normal and inverted mass hierarchies. Acknowledgements. The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/planckcollaboration. GP would like to thank the organisers and the conveners for their kind invitation. 2 http://www.katrin.kit.edu 3 https://hangar.iasfbo.inaf.it/core/
55
References [1] Planck Collaboration I, Planck early results. I. The Planck mission, A&A 536 (2011) A1. [2] A. Mennella, et al, Planck early results. III. First assessment of the Low Frequency Instrument in-flight performance, A&A 536 (2011) A3. [3] Planck HFI Core Team, Planck early results, IV. First assessment of the High Frequency Instrument in-flight performance, A&A 536 (2011) A4. [4] Planck Collaboration VII, Planck early results. VII. The Early Release Compact Source Catalogue, A&A 536 (2011) A7. [5] Planck Collaboration I, Planck 2013 results: Overview of Planck Products and Scientific Results, A&A 571 (2014) A1. [6] Planck Collaboration I, Planck 2015 results. I. Overview of products and results, submitted to A&A. [7] Planck Collaboration XVI, Planck 2013 results. XVI. Cosmological parameters, A&A 571 (2014) A16. [8] J. Lesgourgues, S. Pastor, Massive neutrinos and cosmology, Phys.Rept. 429 (2006) 307–379. [9] G. Mangano, et al, A Precision calculation of the effective number of cosmological neutrinos, Phys.Lett. B534 (2002) 8. [10] Planck Collaboration XV, Planck 2013 results. XV. CMB power spectra and likelihood, A&A 571 (2014) A15. [11] Planck Collaboration XVII, Planck 2013 results. XVII. Gravitational lensing by large-scale structure, A&A 571 (2014) A17. [12] C. L. Bennett, et al, Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, ApJS 208 (2013) 20. [13] S. Das, et al, The Atacama Cosmology Telescope: temperature and gravitational lensing power spectrum measurements from three seasons of data, JCAP 4 (2014) 14. [14] C. L. Reichardt, et al, A Measurement of Secondary Cosmic Microwave Background Anisotropies with Two Years of South Pole Telescope Observations, ApJ 755 (2012) 70. [15] W. J. Percival, et al, Baryon acoustic oscillations in the Sloan Digital Sky Survey Data Release 7 galaxy sample, MNRAS 401 (2010) 2148–2168. [16] N. Padmanabhan, et al, A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillations - I. Methods and application to the Sloan Digital Sky Survey, MNRAS 427 (2012) 2132–2145. [17] C. Blake, et al, The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations, MNRAS 418 (2011) 1707–1724. [18] L. Anderson, et al, The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Release 9 spectroscopic galaxy sample, MNRAS 427 (2012) 3435–3467. [19] F. Beutler, et al, The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant, MNRAS 416 (2011) 3017–3032. [20] A. Aguilar-Arevalo, et al, A Combined νμ → νe and ν¯ μ → ν¯ e Oscillation Analysis of the MiniBooNE Excesses, FERMILABPUB-12-394-AD-PPD, LA-UR-12-23041. [21] Planck Collaboration XIII, Planck 2015 results. XIII. Cosmological parameters, submitted to A&A. [22] R. Laureijs, et al, Euclid Definition Study Report, ESA/SRE(2011)12.
Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55 www.elsevier.com/locate/nppp
Neutrino physics after Planck G. Polenta ASI Science Data Center, via del Politecnico, 00133 Roma, Italy INAF - Osservatorio Astronomico di Roma, via di Frascati 33, 00040 Monte Porzio Catone, Italy
on behalf of the Planck Collaboration
Abstract We present constraints on neutrino physics derived from the 2013 Planck data release, which involves data collected during the first 15.5 months of observations. After a brief description of the effect of neutrino masses and number of relativistic species on CMB anisotropies, we present results obtained from Planck data alone and in combination with other astrophysical probes. In particular, Planck set constraints on the sum of neutrino masses is mν < 0.23 eV, and on the number of relativistic species of Neff = 3.30+0.54 −0.51 both at 95% C.L. Finally, we briefly discuss updated results from the Planck 2015 data release as well as future prospects for CMB experiments. Keywords: Cosmology, Cosmic Microwave Background, Cosmological parameters, Neutrinos
1. Introduction The Planck satellite1 [1] is a third generation Cosmic Microwave Background (CMB) experiment. It was launched on 14 May 2009 and observed the sky continuously from 12 August 2009 to 23 October 2013. Planck’s scientific payload contains detectors sensitive to nine frequency bands between 25 and 1000 GHz with angular resolution between 33 and 5 . The Low Frequency Instrument (LFI; [2]) covers bands centred at 30, 44, and 70 GHz using pseudo-correlation radiometers, while the High Frequency Instrument (HFI; [3]) is equipped with bolometers covering bands centred at 100, 143, 217, 353, 545, and 857 GHz. Planck imaged the whole sky with an unprecedented combination of Email address: [email protected] (G. Polenta) 1 Planck (http://www.esa.int/Planck) is a project of the European Space Agency (ESA) with instruments provided by two scientific consortia funded by ESA member states and led by Principal Investigators from France and Italy, telescope reflectors provided through a collaboration between ESA and a scientific consortium led and funded by Denmark, and additional contributions from NASA (USA).
http://dx.doi.org/10.1016/j.nuclphysbps.2015.06.014 2405-6014/© 2015 Elsevier B.V. All rights reserved.
sensitivity, angular resolution, and frequency coverage. In January of 2011, the Planck Collaboration released a first set of scientific data, the Early Release Compact Source Catalogue (ERCSC; [4]) together with initial scientific results related to astrophysical foregrounds (A&A, Vol. 520, 2011). Since then, 34 Intermediate papers on foreground properties have been published. In March of 2013, the second release of scientific data took place, consisting mainly of temperature maps of the whole sky [5]; these products and associated scientific results are described in a special issue of A&A (Vol. 571, 2014). In February of 2015, the third data release has started and includes products and scientific results obtained using data collected throughout the entire mission in both temperature and polarisation [6]. In this paper we present how Planck 2013 data constrain neutrino physics, as extensively described in the Planck cosmological parameter paper [7], and we briefly discuss 2015 updates.
53
G. Polenta / Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55
In the standard scenario for the thermal history of the Universe, massless neutrinos are in thermal equilibrium with the primeval plasma through weak interactions until the temperature drops below T dec ≈ 1 Mev [8]. Thus, neutrinos are not reheated by e± annihilations favoured when the Universe becomes colder than the electron mass, and resulting in a background of cosmological neutrinos with a present temperature T ν ≈ 1.9 K, corresponding to ∼ 0.2 eV at the last scattering surface. As a consequence, CMB primary anisotropies cannot probe neutrinos with masses below mν ≈ 1 eV, since they are relativistic at CMB decoupling, and the effect on the background cosmology can be compensated by changes in the Hubble constant H0 . For larger values of the mass, changing mν impacts on matter-radiation ratio and equality, leading to variations in the gravitational potential that are visible at angular scales around the first CMB acoustic peak (early Integrated SachsWolfe effect; ISW). Moreover, neutrino masses also impact the early ISW at perturbation level through neutrino free streaming. It is important to note that increas ing mν suppresses clustering, thus reducing the lensing potential affecting CMB photons at small angular scales. Thanks to its angular resolution, Planck is sensitive to gravitational lensing, and can therefore overcome the limit of ≈ 1 eV on the sum of neutrino masses. The number of relativistic species Neff reflects the energy density of neutrinos: ρν = Neff (7/8) (4/11)4/3 ργ . This parameter actually accounts for the energy density of all relativistic components but photons, i.e. it includes also possible forms of dark radiation. In the standard model with 3 families of neutrinos, detailed calculations provide Neff = 3.046 [9]. Increasing Neff increases the expansion rate before recombination, leading to an increase of the diffusion angular scale θd that reduces the power in the damping tale of the CMB power spectrum. 3. Results from the Planck 2013 data release 3.1. Constraints on
mν
When constraining the sum of neutrino masses we assume 3 degenerate massive neutrinos. This approximation is accurate enough given the Planck sensitivity. As discussed in [10, 7], we combine: Planck temperature power spectrum (labelled Planck; [10]); Planck lensing likelihood derived from lensing 4-point correlation function [11]; WMAP low- polarisation (labelled WP;
[12]); data coming from high-resolution CMB experiments (labelled HighL), namely the Atacama Cosmology Telescope [13] and the South Pole Telescope [14], whose primary role is to improve modelling of unresolved foreground components. Results are shown in Fig. 1. Corresponding 95% upper limits are mν < 0.66 eV Planck+WP+HighL, mν < 0.85 eV Planck+lensing+WP+HighL, thus confirming that Planck entered a new regime thanks to its sensitivity to gravitational lensing. It is interesting to note that adding the Planck lensing likelihood weakens the upper limit. In fact, Planck tem-
1.0
Planck+WP+highL Planck+lensing+WP+highL
0.8
Planck+WP+highL (AL ) Planck−lowL+highL+τ prior
P/Pmax
2. CMB and neutrinos
0.6
Planck−lowL+lensing+highL+τ prior Planck−lowL+τ prior
0.4 0.2 0.0 0.0
0.4
0.8
1.2 Σmν [eV]
1.6
Figure 1: Marginalised posterior distributions of data combinations (from [7]).
2.0
mν for different
perature power spectrum favours a slightly higher lensing amplitude to add more lensing smoothing than predicted in ΛCDM. Neutrino mass acts in the opposite way, i.e. increasing mν reduces the predicted smoothing even further. On the other hand, lensing likelihood directly probes the lensing power with a mild preference for a lensing amplitude slightly below (but consistent with) ΛCDM predictions. Therefore combining Planck temperature power spectrum with lensing likelihood pulls the sum of neutrino masses towards higher values. This is even more evident when we remove low data and add a prior for the optical depth τ (labelled -lowL+τprior), which results in a best-fit value away from zero. Baryon acoustic oscillations (BAO) in the matter power spectrum have proven to be very useful in constraining neutrino masses, because these are basically geometric measurements that are sensitive to the evolution of the angular-diameter distance and the Hubble
54
G. Polenta / Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55
parameter. Adding BAO data from SDSS DR7 [15, 16], WiggleZ [17], BOSS DR9 [18], and 6dF Galaxy Survey [19], the constraint on neutrino masses tightens significantly to mν < 0.23 eV 95%, Planck+WP+HighL+BAO, which can be regarded as our best limit on mν . Since Planck 2013 data release, several authors suggested a preference for massive neutrinos in the Planck data. However, this is mainly due to an attempt to reduce tensions between Planck and external datasets in the amplitude of matter density perturbation σ8 : in creasing mν decreases the amplitude of late-time fluctuations σ8 through the effect of neutrino free streaming on structure formation. However, larger masses also imply lower values of the Hubble constant that are in strong tension with direct measurements of H0 .
Constraints on the number of relativistic species are derived assuming that the extra degrees of freedom are massless. Posterior distributions for Neff are shown in Fig. 2, and correspond to
Neff =
3.30+0.54 −0.51
95%, Planck+WP+HighL, 95%, Planck+WP+HighL+BAO.
Hence, Planck data are consistent with standard model predictions but do not completely rule out Neff = 4. Adding BAO observations helps in further reducing possible evidences for extra relativistic degrees of freedom. Planck+WP+highL +BAO +H0 0.8 +BAO+H0
P/Pmax
1.0
−0.52
As we can see, constraints are not much degraded by the joint analysis as these parameters affect different regions of the CMB power spectrum, and are therefore almost uncorrelated. The inclusion of sterile neutrino is motivated by recent works that aim to explain some anomalies arising, for instance, from the MiniBoone experiment [20]. In the following, we assume normal hierarchy for the active sector plus a massive sterile neutrino whose distribution is either a thermal one or proportional to those of the active sector (Dodelson-Widrow scenario). These two cases are practically identical from the point of view of the analysis that uses the effective mass meff ν, sterile as parameter, while they differ only when moving to the interpretation of the physical mass mthermal sterile . Results for < 10 eV are mthermal sterile ⎫ ⎪ mν < 0.42 eV ⎪ ⎬ 95%, PlanckTT+WP+HighL+BAO, ⎪ ⎪ ⎭ N < 3.80 eff
0.6
thus only marginally compatible with a fully thermaleff ized sterile neutrino with mthermal sterile ≈ mν, sterile < 0.5 eV. For Neff ∼ 3 the physical mass of neutrinos becomes so large that they become non-relativistic well before recombination, and therefore they are hidden within the overall cold dark matter budget.
0.4 0.2 0.0 2.0
3.3. Joint constraints on Neff and either mν or eff mν, sterile Since extra relics could have a mass themselves or coexist with massive neutrinos, it is interesting to derive joint constraints on these parameters. When considering extra relics plus massive neutrinos we obtain ⎫ mν < 0.28 eV ⎪ ⎪ ⎬ 95%, PlanckTT+WP+HighL+BAO. ⎪ +0.54 ⎪ ⎭ N = 3.32 eff
3.2. Constraints on Neff
Neff = 3.36+0.68 −0.64
It is important to note that Neff is positively correlated with the expansion rate H(z). Hence, when combining Planck with direct measurements of H0 , the slight tension between the two observations pulls Neff high, thus favouring the presence for extra neutrinos at ∼ 2σ level. However, at the same time this also increases σ8 , therefore producing a strong tension with weak lensing and cluster abundance observations that favour lower σ8 compared to Planck.
2.5
3.0
3.5
Neff
4.0
4.5
5.0
Figure 2: Marginalised posterior distributions of Neff for different data combinations (from [7]).
4. Planck 2015 results and future prospects On February 5, 2015, the Planck Collaboration published its third data release [6]. The updated constraints
G. Polenta / Nuclear and Particle Physics Proceedings 265–266 (2015) 52–55
on neutrino physics are [21] ⎫ ⎪ mν < 0.21 eV 95% ⎪ ⎬ ⎪ ⎪ PlanckTT+LowP+BAO, N = 3.15 ± 0.23 68% ⎭ eff
where LowP labels the Planck temperature and polarisation likelihood at large angular scales. The im provement on mν with respect to 2013 is small because Planck had almost saturated the sensitivity limit of CMB temperature power spectrum already in 2013. The 2015 best-fit value of Neff is closer to the standard model prediction of 3.046. Including high- polarisation tightens the limits based on Planck data alone and gives consistent results in ruling out Neff = 4 at over 3σ. However, models with thermalized extra relativistic species predicting ΔNeff 0.5 are still compatible with current data. Interestingly, when combining Planck with external data the inclusion of Planck high- polarisation has only a minor effect on mν , however when considering Planck alone it gives [21] mν < 0.50 eV 95%, PlanckTT+TE+EE+LowP, which is already tighter than the KATRIN2 mass limit. Future high-resolution CMB polarisation experiments, such as the COrE+ proposal 3 , are targeted to accurately reconstruct the lensing potential. Hence, when combined with future BAO observations from the Euclid satellite [22], they will probe lower mass scales allowing to distinguish between normal and inverted mass hierarchies. Acknowledgements. The Planck Collaboration acknowledges the support of: ESA; CNES and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, JA, and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). A description of the Planck Collaboration and a list of its members, indicating which technical or scientific activities they have been involved in, can be found at http://www.cosmos.esa.int/web/planck/planckcollaboration. GP would like to thank the organisers and the conveners for their kind invitation. 2 http://www.katrin.kit.edu 3 https://hangar.iasfbo.inaf.it/core/
55
References [1] Planck Collaboration I, Planck early results. I. The Planck mission, A&A 536 (2011) A1. [2] A. Mennella, et al, Planck early results. III. First assessment of the Low Frequency Instrument in-flight performance, A&A 536 (2011) A3. [3] Planck HFI Core Team, Planck early results, IV. First assessment of the High Frequency Instrument in-flight performance, A&A 536 (2011) A4. [4] Planck Collaboration VII, Planck early results. VII. The Early Release Compact Source Catalogue, A&A 536 (2011) A7. [5] Planck Collaboration I, Planck 2013 results: Overview of Planck Products and Scientific Results, A&A 571 (2014) A1. [6] Planck Collaboration I, Planck 2015 results. I. Overview of products and results, submitted to A&A. [7] Planck Collaboration XVI, Planck 2013 results. XVI. Cosmological parameters, A&A 571 (2014) A16. [8] J. Lesgourgues, S. Pastor, Massive neutrinos and cosmology, Phys.Rept. 429 (2006) 307–379. [9] G. Mangano, et al, A Precision calculation of the effective number of cosmological neutrinos, Phys.Lett. B534 (2002) 8. [10] Planck Collaboration XV, Planck 2013 results. XV. CMB power spectra and likelihood, A&A 571 (2014) A15. [11] Planck Collaboration XVII, Planck 2013 results. XVII. Gravitational lensing by large-scale structure, A&A 571 (2014) A17. [12] C. L. Bennett, et al, Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results, ApJS 208 (2013) 20. [13] S. Das, et al, The Atacama Cosmology Telescope: temperature and gravitational lensing power spectrum measurements from three seasons of data, JCAP 4 (2014) 14. [14] C. L. Reichardt, et al, A Measurement of Secondary Cosmic Microwave Background Anisotropies with Two Years of South Pole Telescope Observations, ApJ 755 (2012) 70. [15] W. J. Percival, et al, Baryon acoustic oscillations in the Sloan Digital Sky Survey Data Release 7 galaxy sample, MNRAS 401 (2010) 2148–2168. [16] N. Padmanabhan, et al, A 2 per cent distance to z = 0.35 by reconstructing baryon acoustic oscillations - I. Methods and application to the Sloan Digital Sky Survey, MNRAS 427 (2012) 2132–2145. [17] C. Blake, et al, The WiggleZ Dark Energy Survey: mapping the distance-redshift relation with baryon acoustic oscillations, MNRAS 418 (2011) 1707–1724. [18] L. Anderson, et al, The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: baryon acoustic oscillations in the Data Release 9 spectroscopic galaxy sample, MNRAS 427 (2012) 3435–3467. [19] F. Beutler, et al, The 6dF Galaxy Survey: baryon acoustic oscillations and the local Hubble constant, MNRAS 416 (2011) 3017–3032. [20] A. Aguilar-Arevalo, et al, A Combined νμ → νe and ν¯ μ → ν¯ e Oscillation Analysis of the MiniBooNE Excesses, FERMILABPUB-12-394-AD-PPD, LA-UR-12-23041. [21] Planck Collaboration XIII, Planck 2015 results. XIII. Cosmological parameters, submitted to A&A. [22] R. Laureijs, et al, Euclid Definition Study Report, ESA/SRE(2011)12.