Constraints on neutrino masses from Planck and Galaxy Clustering data
aa r X i v : . [ a s t r o - ph . C O ] J un Constraints on neutrino masses from Planck and Galaxy Clustering data
Elena Giusarma, Roland de Putter, Shirley Ho, and Olga Mena IFIC, Universidad de Valencia-CSIC, 46071, Valencia, Spain Jet Propulsion Laboratory, California Institute of Technology, Pasadena,CA 91109 & California Institute of Technology, Pasadena, CA 91125 McWilliams Center for Cosmology, Department of Physics,Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA 15213
We present here bounds on neutrino masses from the combination of recent Planck Cosmic Mi-crowave Background measurements and galaxy clustering information from the Baryon OscillationSpectroscopic Survey (BOSS), part of the Sloan Digital Sky Survey-III. We use the full shape ofeither the photometric angular clustering (Data Release 8) or the 3D spectroscopic clustering (DataRelease 9) power spectrum in different cosmological scenarios. In the ΛCDM scenario, spectroscopicgalaxy clustering measurements improve significantly the existing neutrino mass bounds from Planckdata. We find P m ν < .
39 eV at 95% confidence level for the combination of the 3D power spec-trum with Planck CMB data (with lensing included) and Wilkinson Microwave Anisoptropy Probe9-year polarization measurements. Therefore, robust neutrino mass constraints can be obtainedwithout the addition of the prior on the Hubble constant from HST.In extended cosmological scenarios with a dark energy fluid or with non flat geometries, galaxyclustering measurements are essential to pin down the neutrino mass bounds, providing in themajority of cases better results than those obtained from the associated measurement of the BaryonAcoustic Oscillation scale only. In the presence of a freely varying (constant) dark energy equation ofstate, we find P m ν < .
49 eV at 95% confidence level for the combination of the 3D power spectrumwith Planck CMB data (with lensing included) and Wilkinson Microwave Anisoptropy Probe 9-yearpolarization measurements. This same data combination in non flat geometries provides the neutrinomass bound P m ν < .
35 eV at 95% confidence level.
PACS numbers: 98.80.-k 95.85.Sz, 98.70.Vc, 98.80.Cq
I. INTRODUCTION
Massive neutrinos leave distinct imprints in the dif-ferent cosmological data sets. Concerning Cosmic Mi-crowave Background (CMB) anisotropies, the primaryeffect of neutrino masses is via the
Early Integrated SachsWolfe effect . The transition from the relativistic to thenon relativistic neutrino regime will affect the decaysof the gravitational potentials at the decoupling period,leading to a non negligible signature around the firstpeak. This has been, traditionally, the most relevantsignature from neutrino masses on the CMB [1]. How-ever, recent neutrino mass bounds from Planck data [2],seem to be driven by the massive neutrino signature ongravitational lensing. A non zero value of the neutrinomass will induce a higher expansion rate which will sup-press the clustering on scales smaller than the horizonwhile neutrinos turn non relativistic [3]. Regarding largescale structure, due to the large neutrino velocity disper-sion, the non-relativistic neutrino overdensities will onlycluster at wavelengths larger than their free streamingscale. Consequently, the growth of matter density per-turbations is reduced and the matter power spectrum issuppressed at small scales, see Ref. [4] and referencestherein. Therefore, cosmological data provide a uniquetool to test the neutrino masses, see Refs. [5–13] for neu-trino mass bounds before Planck CMB data release.The limits from Planck satellite, including lensing aswell as low- ℓ polarization measurements from WMAP 9- year data [14] (WP) are P m ν < .
11 eV at 95% CL. Theaddition of a prior on the Hubble constant H from theHubble Space Telescope [15] improves the constraint in avery significant way, P m ν < .
21 eV. This is due to thestrong degeneracy between H and P m ν at 95% CL: ifthe sum of the neutrino masses is increased, the changeinduced in the distance to last scattering can be com-pensated by lowering H [8]. However, Planck and HSTmeasurements of the Hubble constant H show a 2 . σ tension and therefore, it is fortunate that datasets otherthan the HST prior may help in pinning down the boundon neutrino mass from CMB data alone.Baryon Acoustic Oscillation (BAO) data, as measuredby the Sloan Digital Sky Survey (SDSS) Data Release7 [16, 17], the WiggleZ survey [18], the Baryon Acous-tic Spectroscopic Survey (BOSS) SDSS-III Data Release9 [19] and 6dF [20], also significantly improve the con-straints, leading to P m ν < .
26 eV at 95% CL whencombined with Planck (with lensing) and WP data. How-ever, in non minimal scenarios with a curvature or witha more general dark energy component these constraintsare notably degraded and geometrical
BAO informationfrom galaxy clustering may not be as powerful as shape measurements of the matter power spectrum. Previousworks [6, 8] have noticed the advantages of using fullpower spectrum measurements in extended cosmologicalscenarios due to their ability of removing degeneracies.Here we combine recent Planck data with galaxy powerspectrum measurements from the BOSS experiment [21],one of the four surveys of the Sloan Digital Sky Sur-vey III, SDSS-III [22]. We consider first the 2D angu-lar power spectrum measurements [23] from the CMASSsample [24] of luminous galaxies of SDSS Data Release 8(DR8) [25]. We then explore as well the neutrino massconstraints from the full 3D power spectrum shape ofSDSS Data Release 9 (DR9) [26]. While DR8 containsthe full photometric CMASS sample, DR9 provides thegalaxy spectra of CMASS galaxies, the largest publiclyavailable set of galaxy spectra to date.The authors of Ref. [7], in the context of a ΛCDMmodel, found P m ν < .
36 eV ( P m ν < .
26 eV)at 95% CL with (without) shot noise-like parameterswhen combining WMAP 7 year data with DR8 2D angu-lar power spectrum measurements plus a HST prior on H . Exploiting DR9 3D power spectrum measurementsRef. [9] quotes the bound P m ν < .
34 eV at 95% CLafter combining with WMAP7, supernova data and ad-ditional BAO measurements within a ΛCDM model.We shall update here the constraints quoted above,quantifying the benefits from the improved CMB Planckdata. Our neutrino mass constraints are presented in dif-ferent fiducial cosmologies, namely, non flat and dynami-cal dark energy cosmologies. We also show the impact onour constraints of the underlying galaxy power spectrum,adopting different models to describe galaxy clustering.The structure of the paper is as follows. In Sec. IIwe describe the parameters used in the analysis. PlanckCMB and galaxy clustering data, plus galaxy clusteringmodeling are described in Sec. III. Section IV containsour results, and we draw our conclusions in Sec. V.
II. COSMOLOGICAL PARAMETERS
The standard, three massive neutrino scenario we ex-plore here is described by the following set of parameters: { ω b , ω c , Θ s , τ, n s , log[10 A s ] , X m ν } , (1) ω b ≡ Ω b h and ω c ≡ Ω c h being the physical baryon andcold dark matter energy densities, Θ s the ratio betweenthe sound horizon and the angular diameter distance atdecoupling, τ is the reionization optical depth, n s thescalar spectral index, A s the amplitude of the primordialspectrum and P m ν the sum of the masses of the threeactive neutrinos in eV. We assume a degenerate neutrinomass spectrum in the following. The former scenario isenlarged with w and Ω k in the case of extended models.Table I specifies the priors considered on the differentcosmological parameters. For our numerical analyses,we have used the Boltzmann CAMB code [27] and ex-tracted cosmological parameters from current data usinga Monte Carlo Markov Chain (MCMC) analysis basedon the publicly available MCMC package cosmomc [28]. Parameter PriorΩ b h . → . c h . → . s . → τ . → . n s . → . A s ) 2 . → P m ν (eV) 0 . → . Ω k − . → . w − → III. CMB AND GALAXY CLUSTERINGMEASUREMENTSA. Planck
We consider the high- ℓ TT likelihood, including mea-surements up to a maximum multipole number of ℓ max =2500, combined with the low- ℓ TT likelihood, includ-ing measurements up to ℓ = 49 and the low- ℓ WMAPTE,EE,BB likelihood including multipoles up to ℓ = 23.We include the lensing likelihood in all our Monte Carloanalyses. We refer to this data set as the PLANCK dataset.We also consider the effect of a gaussian prior on theHubble constant H = 73 . ± . Y p = 0 .
24 and the lens-ing spectrum normalization to A L = 1. We marginalizeover all foregrounds parameters as described in [2]. B. DR8 Angular Power Spectrum
1. DR8 Data
We exploit the stellar mass-limited DR8 CMASS sam-ple of luminous galaxies, detailed in [24], divided into fourphotometric redshift bins, z = 0 . − . − . − . − . σ z ( z ) = 0 . − .
06, increasing from low to high red-shift, see Refs. [23, 29]. The calculation of the angu-lar power spectrum for each bin is described in detailin Ref. [23]. The expectation value of the power spec-trum is a convolution of the true power spectrum with awindow function, see [30] for examples on these windowfunctions. When fitting the data to the underlying the-oretical model, we always apply these window functionsto the theoretical power spectra before calculating thelikelihood relative to the data. To avoid large system-atic uncertainties [23, 29] we do not consider bands with ℓ <
30 in our analysis.
DR8 parameters Prior b i . → a i − → z =0 . − . − . − . − .
65 used in the DR8 clustering dataanalyses.
2. DR8 Clustering model
In order to describe the theoretical angular power spec-trum, we follow here the simple linear scale independentbias model described in Ref. [7], characterized by fourfree bias parameters b i (i.e. one per each redshift bin).In addition to these bias parameters, we also considershot noise-like parameters a i C ( ii ) ℓ = b i π Z k dk P m ( k, z = 0) × (cid:16) ∆ ( i ) ℓ ( k ) + ∆ RSD , ( i ) ℓ ( k ) (cid:17) + a i , (2)where the a i parameters mimic the effects of a scale-dependent galaxy bias as well as the effect of potentialinsufficient shot noise subtraction. Table II denotes thepriors adopted on the bias and shot noise parameters ineach of the four redshift bins exploited here. The neu-trino mass bounds presented in the next section will bederived by default including the shot noise parameters a i in the next section, although we shall mention onsome cases the bounds without shot noise. In Eq. (2), P m ( k, z = 0) is the matter power spectrum at redshiftzero after applying the HaloFit prescription [31, 32] toaccount for non-linear effects and∆ ( i ) ℓ ( k ) = Z dz g i ( z ) T ( k, z ) j ℓ ( k d ( z )) . (3)Here, g i ( z ) is the normalized redshift distribution ofgalaxies in bin i , j ℓ is the spherical Bessel function, d ( z )is the comoving distance to redshift z and T ( k, z ) thematter transfer function relative to redshift zero. The Although the revisited version of the HaloFit model [32] accountsfor a constant, w = − −
10% discrepancy with simulations even inthe simplest case of a flat ΛCDM scheme, (see e.g. Ref. [34] andreferences therein), we neglect here the extra corrections in theHaloFit description in not flat cosmologies. contribution due to redshift space distortions is∆
RSD , ( i ) l ( k ) = β i Z dz g i ( z ) T ( k, z ) × (cid:20) (2 l + 2 l − l + 3)(2 l − j l ( kd ( z )) − l ( l − l − l + 1) j l − ( kd ( z )) − ( l + 1)( l + 2)(2 l + 1)(2 l + 3) j l +2 ( kd ( z )) (cid:21) , (4)where β i ( z ) = f ( z ) /b i is the redshift distortion parame-ter and f ( z ) ≡ d ln D ( z ) d ln a (5)is the growth factor (with D ( z ) the linear growth func-tion). When massive neutrinos are an additional ingre-dient in the universe’s mass energy-density, the growthfunction is scale-dependent. Following Ref. [7], we shallignore the scale dependent growth in β ( z ) since it is asmall ( ≪ ℓ >
30 in our data analyses. Weconsider ℓ max = 200, value which ensures the suppressionof the uncertainties from non-linear corrections to themodeled angular power spectra [7]. For the likelihoodfunction, we use 17 data points per redshift slice. C. DR9 Power Spectrum
DR9 parameters Prior S − → b HF . → P sHF → b Q . → Q . → b HF and P sHF respectively, in the case of theHaloFit prescription for the galaxy power spectrum as wellas for b Q and Q , free parameters of the model of Ref. [43].We explore the neutrino mass constraints for these two galaxyclustering models in the case of the DR9 3D power spectrum.
1. DR9 Data
Here we use the DR9 CMASS sample of galax-ies [26] which contains 264 283 massive galaxies covering3275 deg with redshifts 0 . < z < . z eff = 0 . P meas ( k ) is the one used in Refs. [9, 19, 35–40], which is obtained using the standard Fourier tech-nique [41], see [42] for details. This galaxy power spec-trum was the one used to fit the Baryon Acoustic Oscil-lations [19].On large scales, we are affected by systematic effectsfrom stars or seeing of the survey. On small scales, weare affected by observational effects such as redshift fail-ures and fiber collisions. A conservative approach hasbeen provided by Refs. [39, 40], which add an extra freeparameter in the measured power spectrum P meas ( k ) = P meas , w ( k ) − S [ P meas , nw ( k ) − P meas , w ( k )] , (6)where P meas , w ( k ) refers to the measured power spectrumafter applying the weights for stellar density, which rep-resent the main source of systematic errors, P meas , nw ( k )is the measured power spectrum without these weightsand S is an extra nuisance parameter to be marginalizedover, see Tab. III. The expectation value of the matterpower spectrum is a convolution of the true matter powerspectrum with the window functions, which account forthe correlation of data at different scales k due the sur-vey geometry. Therefore, the theoretical power spectra P g th ( k ) (to be computed in the following section) needsto be convolved with a window matrix before compar-ing it to P meas ( k ). In order to avoid non linearities, weadopt the conservative choice of a maximum wavenumberof k max = 0 . h /Mpc, region which is safe against largenon linear corrections in the modeled theoretical spectra,that we discuss below. We use therefore 22 points in therange 0 . h /Mpc < k < . h /Mpc from the total 74points of the DR9 power spectrum.
2. DR9 Clustering model
We follow here two different approaches to modelthe theoretical power spectrum in the weakly nonlinearregime explored here ( k max = 0 . h /Mpc). These twomodels are among the three ones considered in Ref. [9],where it was checked that the neutrino mass bounds showa very mild dependence on the galaxy clustering modelsconsidered in their analyses. The first approach we con-sider for DR9 is the HaloFit prescription (HF) [31, 32].The final theoretical galaxy power spectrum to be con-volved with the window functions reads P g th ( k, z ) = b P mHF ν ( k ; z ) + P sHF , (7)where b HF and P sHF are the bias and the shot contribu-tion respectively, considered to be constant. The priorsadopted in the the former two parameters are depicted inTab. III. The model given above by Eq. (7) with a biasand a shot noise parameter is equivalent to that used be-fore for modeling the theoretical angular power spectraofr DR8 data analyses, see Eq. (2). The second approach adopted here for galaxy cluster-ing modeling is that of Ref. [43]: P g th ( k, z ) = b Qk . k P m , linear ( k, z ) , (8)where k is the wavenumber in units of h/Mpc and P m , linear is the linear matter power spectrum. The freeparameters of this model are b Q and Q , which mimicthe scale dependence of the power spectrum at smallscales. These two parameters are considered here con-stants with priors specified in Tab. III. In the followingsection we shall comment on the dependence of the neu-trino mass constraints on the underlying galaxy powerspectrum model. IV. RESULTS
Here we present the constraints from current cosmo-logical data sets on the sum of the three active neutrinomasses P m ν in different scenarios and with differentcombinations of data sets. A. Standard Cosmology plus massive neutrinos
Throughout this section we shall assume a ΛCDM cos-mology, and compute the bounds on the sum of the threeactive neutrino masses arising from the different cosmo-logical data sets considered here. Table IV shows the95% CL upper bounds on the total neutrino mass forPLANCK, PLANCK plus DR8 and PLANCK plus DR9data sets, with and without the HST prior on the Hubbleconstant. These limits include the shot noise additionalparameters in the case of DR8 and the systematic effects,in the case of DR9. Notice first that the constraints fromthe PLANCK data set described before (which includethe Planck lensing likelihood as well as WMAP 9 yeardata polarization measurements) are not very promis-ing, since in this case P m ν < .
11 eV at 95% CL. Thefact that CMB alone does not provide very significantconstraints on the sum of the neutrino masses has beenalready discussed in the literature (see, for instance [8]).Indeed, without the H prior, the change induced in theCMB temperature anisotropies caused by an increase in P m ν can be compensated by a decrease in the Hubbleconstant H . An increase in P m ν will induce a shift inthe distance to last scattering . While the acoustic peakstructure of the CMB data does not leave much freedomin ω c and ω b , the change in distance to last scatteringcould be compensated by lowering H . The presence ofthe HST prior on the Hubble parameter will break this r θ ( z rec ) ∝ R z rec dz (cid:2) ω r a − + ω m a − + (1 − ω m /h ) (cid:3) − / , with ω m = ω b + ω c + ω ν strong degeneracy, setting a 95% CL bound of 0 .
22 eV inthe sum of the three active neutrino masses.However, and as discussed in the introductory section,HST and Planck data sets show a tension of ∼ . σ intheir measured value of the Hubble constant H . It istherefore mandatory to explore whether other data setscould also strengthen the constraint on P m ν from thePLANCK data set alone. DR8 angular power spectrummeasurements, if combined with the PLANCK data set,provide an upper limit of P m ν < .
98 eV at 95% CLwith the shot noise parameters included in the analy-sis. If we consider instead the DR8 BAO angular di-ameter distance constraint D A ( z ) = 1411 ±
65 Mpc at z = 0 .
54 [30] and combine this measurement with thePLANCK data set, the bound is P m ν < .
85 eV at95% CL. The neutrino mass bound from DR8 BAO-onlyis mildly stronger than the one obtained with the fullshape of the DR8 galaxy clustering matter spectrum dueto the larger value of ℓ max = 300 used in the analysis ofRef. [30] to extact the angular BAO signature.When considering the DR9 data set combined withPLANCK, we achieve a bound of P m ν < .
39 eV at95% CL. The former limit is obtained in the case inwhich the theoretical power spectrum for DR9 is givenby Eq. (7) which uses the HF prescription. Very similarbounds are obtained if we use for the theoretical DR9spectrum the approach given by Eq. (8).If instead of using the full shape information fromBOSS DR9 we use the DR9 BAO signature [19], the neu-trino mass limit is P m ν < .
40 eV at 95% CL. Note thatthe bound on P m ν arising from the geometrical BAODR9 geometrical information is very similar to that ob-tained using the full shape of the DR9 3D clustering mea-surements. While in the context of the minimal ΛCDMmodel, BAO measurements and galaxy clustering datashould provide similar constraints, the BAO DR9 sig-nal is extracted using the matter power spectrum in therange 0 . h /Mpc < k < . h /Mpc [19], a much widerrange than the one considered in the full power spectrumcase.To summarize, galaxy clustering data, and, especially,DR9 3D power spectrum data, helps enormously in im-proving the neutrino mass constraints, arriving at m ν < .
39 eV at 95% CL without the addition of the mea-surement of H from the HST experiment. The formerbound is not as tight as the value quoted by the Planckcollaboration P m ν < .
26 eV at 95% CL, obtained af-ter combining Planck measurements (including lensing)with WP and BAO data. The reason for the differenceamong these two 95% CL neutrino mass bounds (i.e. P m ν < .
39 eV versus P m ν < .
26 eV) is due tothe fact that here we are considering exclusively BAOinformation from DR9 SDSS data, while in the Planckanalysis other available BAO measurements have beenconsidered as well.
B. Dark energy and massive neutrinos
In this section we explore the bounds on the sum ofneutrino masses if the dark energy equation of state w is allowed to vary, ( w CDM model). There exists astrong and very well known degeneracy in the P m ν − w plane [44]. If the neutrino mass is allowed to freely vary,the amount of cold dark matter is required to increasein order to leave the matter power spectrum unchanged.This change of Ω m can also occurr if w is allowed tofreely vary as well. Consequently, cosmological neutrinomass bounds will become weaker if the dark energy equa-tion of state is included as a free parameter. Table Vpresents the galaxy clustering limits on the sum of neu-trino masses and on the dark energy equation of state w within the w CDM scenario. For the sake of compari-son, we depict as well the constraints from the PLANCKdata set alone. The addition of HST data to the ba-sic PLANCK CMB data set barely changes the 95% CLconstraint of P m ν < , the addition of theDR9 3D power spectrum measurements sets a 95% CLlimit of P m ν < .
48 eV. This limit is much better thanthe one provided by the combination of DR9 BAO in-formation [19] and the PLANCK data set in a w CDMuniverse, which is P m ν < .
71 eV at 95% CL.Concerning w , the mean values and the 95% CL associ-ated errors depicted in Tab. V show that the combinationof galaxy clustering measurements with the PLANCKCMB data set is not able to extract w with high pre-cision: the constraints we obtained from this data com-bination for w are rather weak but perfectly consistentwith a ΛCDM model. The addition of Supernovae Ia lu-minosity distance measurements from the 3 year Super-nova Legacy Survey (SNLS3) [45] reduces significantlythe errors on the dark energy equation of state: the com-bination of PLANCK plus SNLS3 provides a mean valueand 95% CL errors on the dark energy equation of stateparameter of w = − . +0 . − . . If DR9 galaxy clusteringdata is also added in the analysis, w = − . +0 . − . .Figure 1, left panel, shows the 68% and 95% CL al-lowed regions in the ( P m ν , w ) plane from the PLANCKdata set described in Sec. III, and also from the combina-tion of the former data set with DR9 BAO geometricalinformation and with DR9 galaxy clustering (i.e. fullshape) measurements. Notice that the neutrino masslimits using the galaxy clustering information are bet-ter than those obtained using the BAO signature alone.Indeed, DR9 BAO measurements show a mild prefer- Without shot noise parameters the addition of DR8 angularpower spectrum to Planck data results in a much better con-straint than the one quoted in Tab. V, being P m ν < .
77 eVat 95% CL.
Planck+WP+lensing Planck+WP +lensing Planck+WP+lensing(+HST) +DR8 (+HST) +DR9 (+HST)Σ m ν [ eV ] < .
11 (0 . < .
98 (0 . < .
39 (0 . m ν in a ΛCDM model from the different data combinations considered here, with(without) the HST prior on the Hubble constant H . The results with DR8 (DR9) data sets include the shot noise (thesystematic corrections) parameters. Σ m ν w Σ m ν Ω k FIG. 1: Left panel: the red contours show the 68% and 95% CL allowed regions from the PLANCK data set in the ( P m ν , w ) plane, while the blue and green contours show the impact of the addition of the DR9 BAO signature and the full shapeof DR9 galaxy clustering measurements respectively. The magenta contours depict the combination of PLANCK with DR9galaxy clustering data and SNLS3 measurements. Right panel: as in the left panel but in the ( P m ν , Ω k ) plane (note theabsence of the case with SNLS3 data in the analyses presented in this figure). ence for w < −
1, allowing therefore for a larger neutrinomass. We also investigate the impact of adding Super-novae Ia luminosity distance constraints to the combina-tion of PLANCK and DR9 galaxy clustering data sets:while the impact on the sum of the neutrino mass boundis negligible, the errors on the dark energy equation ofstate parameter w are reduced by a factor of three. C. Curvature and massive neutrinos
We present here the constraints on neutrino massesin the context of a non flat universe, allowing for a nonnegligible curvature component, see Tab. I for the priorsadopted in the curvature component. Table VI shows ourconstraints for the PLANCK data set, PLANCK plusDR8 angular power spectrum data and PLANCK plusDR9 galaxy clustering measurements with and withouta prior on the Hubble constant H from HST. In this nonflat model, DR8 angular clustering measurements com-bined with PLANCK reduce the constraint on P m ν ,from P m ν < .
36 eV to P m ν < .
92 eV (both at95% CL). This constraint is very similar to the one ob-tained if the BAO DR8 geometrical information is used, P m ν < .
80 eV. Adding the HST prior to DR8 angularpower spectrum measurements improves significantly theconstraints: the 95% CL upper limit is P m ν < .
33 eV.DR9 3D power spectrum measurements greatly im-prove the results from the PLANCK data set: whencombined with our basic PLANCK dataset, the 95% CLbounds without the HST prior are P m ν < .
35 eVwith systematic uncertainties. If HST data is includedas well in the analysis, the former 95% CL bound trans-lates into P m ν < .
26 eV. These limits are better thanthose obtained from the combination of the PLANCKdata set with the DR9 BAO measurement, which is P m ν < .
47 eV without the HST prior. Therefore,this non flat model, together with the w CDM one, is aworking example in which constraints from full shape 3Dpower-spectrum measurements provide significant extrainformation than those from BAO signature alone.Figure 1, right panel, shows the 68% and 95% CLallowed regions in the ( P m ν , Ω k ) plane from thePLANCK data set described in Sec. III, and from thecombination of the former data set with DR9 BAO mea-surements, and DR9 galaxy clustering information. No-tice that the neutrino mass constraint arising from theclustering measurements is more powerful than those ob- Planck+WP +lensing Planck+WP +lensing Planck+WP +lensing(+HST) +DR8 (+HST) +DR9 (+HST)Σ m ν [ eV ] < .
01 (0 . < .
02 (0 . < .
48 (0 . w − . +0 . − . − . +0 . − . − . +0 . − . ( − . +0 . − . ) ( − . − . − . ) ( − . +0 . − . )TABLE V: 95% CL upper bounds on Σ m ν from the different data combinations considered here within a w CDM model,with (without) the HST prior on the Hubble constant H . We show as well the mean value of w together with its 95% CLerrors. The results with DR8 (DR9) data sets refer to the case in which the full-shape of the angular (3D) power spectrumis considered, including shot noise parameters (systematic corrections) in the analyses. The constraint from the full shape ofDR9 galaxy clustering measurements is highly superior to that arising from the combination of DR9 BAO information [19] andthe PLANCK data set in a w CDM universe, which is P m ν < .
71 eV at 95% CL. tained exploiting the BAO signature.Concerning Ω k , the mean value and the associated95% CL errors are not significantly changed when galaxyclustering measurements are included. V. CONCLUSIONS
Cosmology provides an independent laboratory to testphysical properties of fundamental particles. Neutrinomasses affect the different cosmological observables in dif-ferent ways, and therefore it is possible to derive strongconstraints on the sum of their masses by combining dif-ferent cosmological data sets. Cosmic Microwave Back-ground physics is affected by the presence of massive neu-trinos via the
Early Integrated Sachs Wolfe effect , sincethe transition from the relativistic to the non relativis-tic neutrino regime will induce a non trivial evolutionof the metric perturbations. Massive neutrinos will alsosuppress the lensing potential.Large scale structure measurements of the galaxypower spectrum are affected by massive neutrinos, sincethey are hot relics with large velocity dispersion which,at a given redshift, erase the growth of matter perturba-tions on spatial scales smaller than the typical neutrinofree streaming scale. Recent measurements of the PlanckCMB experiment do not provide a strong bound on thesum of the neutrino masses. The addition of a prior onthe Hubble constant from the Hubble Space Telescopeimproves the results in a very significant way since itbreaks the strong degeneracy between the neutrino massand the Hubble constant. However, Planck and HSTdata sets show some tension in the measurement of theHubble parameter. While Baryon Acoustic Oscillationmeasurements also improve the neutrino mass boundswhen combined with Planck data, it is crucial to ex-plore if measurements using the full shape of the matterpower spectrum can further improve the neutrino masslimits, in particular, in non minimal cosmological scenar-ios with a curvature or with a dark energy equation of state w = − P m ν < .
39 eV at 95% confidence level for thecombination of the DR9 3D power spectrum with PlanckCMB data (with lensing included) and Wilkinson Mi-crowave Anisoptropy Probe 9-year polarization measure-ments. Similar results are obtained with the DR9 BAOgeometrical signature. Therefore, the 95% confidencelevel constraint of P m ν < . P m ν < .
49 eV at 95%confidence level for the combination of the DR9 3D powerspectrum with Planck CMB data (with lensing included)and Wilkinson Microwave Anisoptropy Probe 9-year po-larization measurements, making this constraint highlysuperior to that obtained when replacing galaxy cluster-ing data by the HST prior.In non flat geometries, the combination of the DR9 3Dpower spectrum with Planck CMB data (with lensingincluded) and Wilkinson Microwave Anisoptropy Probe9-year polarization measurements provides the neutrinomass bound P m ν < .
35 eV at 95% confidence level.If we use instead the associated DR9 BAO geometricalinfo, the 95% confidence level neutrino mass bounds inthe w CDM and non flat cosmologies are P m ν < .
71 eV
Planck+WP+lensing Planck+WP+lensing Planck+WP+lensing(+HST) +DR8 (+HST) +DR9 (+HST)Σ m ν [ eV ] < .
36 (0 . < .
92 (0 . < .
35 (0 . k − . +0 . − . − . +0 . − . . +0 . − . . +0 . − . (0 . +0 . − . ) (0 . +0 . − . )TABLE VI: 95% CL upper bounds on Σ m ν in a non-flat model from the different data combinations considered here, with(without) the HST prior on the Hubble constant H . We depict as well the mean value and the 95% CL errors for thecurvature energy density Ω k . The results with DR8 (DR9) data sets refer to the case in which the full-shape of the angular(3D) power spectrum is considered, including shot noise parameters (systematic corrections) in the analyses. The neutrinomass bound extracted from the full shape measurements of BOSS DR9 are better than the one obtained using the DR9 BAOmeasurement [19], which is P m ν < .
47 eV at 95% CL without the HST prior. and P m ν < .
46 eV, respectively. Consequently, in ex-tended cosmological scenarios with a free dark energyequation of state or with a curvature component, mea-surements of the full shape of the galaxy power spectramare extremely helpful, providing better results than thoseobtained with the associated Baryon Acoustic Oscillationsignature only.While we were completing this study, a new analy-sis [46] combining Planck data, galaxy clustering mea-surements from the WiggleZ Dark Energy Survey andother external data sets has appeared in the literature.The bound is P m ν < .
24 eV at 95% confidence levelwhen combining Planck with WiggleZ power spectrummeasurements, setting k max = 0 . h /Mpc. The analy-ses presented here are however penalized by our largesystematic uncertainties: as a comparison, when we ne-glect in our analyses systematic uncertainties, we get P m ν < .
25 eV at 95% confidence level after com-bining Planck with DR9 galaxy clustering measurements (with a shot noise nuisance parameter included and set-ting k max = 0 . h /Mpc). VI. ACKNOWLEDGMENTS
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