Neutrino mass from future large scale structure surveys

Available online at www.sciencedirect.com

Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 50–53 www.elsevier.com/locate/npbps

Neutrino mass from future large scale structure surveys Carmelita Carbonea,b,∗ a INAF-Osservatorio b INFN,

Astronomico di Bologna, Via Ranzani 1, Bologna I-40127, Italy Sezione di Bologna, Viale Berti Pichat, 6/2, Bologna I-40127, Italy

Abstract We examine whether future, nearly all-sky spectroscopic galaxy surveys and photometric galaxy-cluster catalogs, as the ESA Euclid satellite, in combination with CMB priors, will be able to detect the signature of the cosmic neutrino background and determine the absolute neutrino mass scale. We find that the sensitivity of such future surveys is well suited to span the entire range of neutrino masses allowed by neutrino oscillation experiments, and to yield a clear detection of non-zero neutrino mass. Keywords: absolute neutrino mass, cosmology, galaxies, galaxy-clusters

1. Introduction Future galaxy surveys, like the ESA Euclid satellite1 , promise to measure with unprecedented accuracy the parameters which characterise the underlying cosmology of the Universe, focusing, in particular, on the dark energy (DE) and dark matter (DM). In this respect, neutrinos are so far the only DM candidates that we actually know to exist, even if, due to their light masses, they represent only a tiny fraction of the total DM density in the Universe. Neutrino flavour oscillation experiments are particularly sensitive to measurements of the squared neutrino mass differences, but are not sensitive to their absolute masses. On the other hand, cosmological probes, as Cosmic Microwave Background (CMB) experiments or Large Scale Structure (LSS) surveys, are mostly blind to neutrino flavors, but can provide stringent constraints on the number Neff of relativistic  species and on the sum Mν = ν mν of neutrino masses. In fact, a thermal neutrino relic component in the Universe impacts both the expansion history and the growth of structures. Neutrinos with total mass Mν  0.6 eV become non-relativistic after the epoch of recombination probed by the CMB, and this mechanism allows

massive neutrinos to alter the matter-radiation equality for a fixed Ωm h2 . Moreover, neutrino’s radiation-like behaviour, at early times, changes the expansion rate, shifting the peak positions in the CMB angular power spectrum. WMAP72 alone constrains Mν < 1.3 eV and forecasts for the Planck satellite3 alone give Mν ∼ 0.2 − 0.4 eV. On the LSS side, massive neutrinos act directly on the cosmic structure formation. In fact, some time after recombination, they become non-relativistic and, therefore, start to contribute to the total matter density of the Universe (and no more to its radiation component). Nonetheless, due to their high thermal velocities, they do not cluster on scales k > knr , where 1/2 h/Mpc is the scale waveknr ∼ 0.018Ω1/2 m (mν /eV) number corresponding to the Hubble horizon size at redshift znr when a given neutrino species become nonrelativistic [1] (see §2 for further details on the parameter definitions). More specifically, since neutrino thermal velocities increase with z, there exists a so-called free-streaming scale, kfs (z) = 0.82/(1 + z)2 H(z)/H0 (mν /1eV)hMpc−1 , beyond which neutrino density perturbations are washed-out and do not con-

∗ [email protected]

2 http://map.gsfc.nasa.gov/news/

1 http://sci.esa.int/euclid

3 www.rssd.esa.int/index.php?project=planck

0920-5632/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nuclphysbps.2013.04.056

C. Carbone / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 50–53

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Figure 1: Left: Ratio T (k, z)/T (k, z = 0) of the linear matter transfer functions computed with a Boltzmann solver code at redshifts z = 0, 0.5, 1, 1.5, 2, for a fiducial cosmology with a total neutrino mass Mν = 0.3 eV and a degenerate mass spectrum [2]. Middle: Ratio T z=0 (k, Mν )/T z=0 (k, Mν = 0) between the transfer functions, computed with a Boltzmann solver code for the different Mν –cosmologies, and the transfer function obtained assuming massless neutrinos [2]. Right: The relative difference between the values of the theoretical linear redshiftspace distortion parameter β = f /b calculated in the ΛCDM+ν and ΛCDM cosmologies, normalised to the same σ8 [1]. Here b is the bias of the considered DM tracer.

Figure 2: Left: The relative difference between the values of the theoretical linear redshift-space distortion parameter β = f /b calculated in the ΛCDM+ν and ΛCDM cosmologies, normalised to the same σ8 [1]. Here b is the bias of the considered DM tracer. Right:Ratio between the halo mass functions (MF) from N-body simulations with and without neutrinos from [1]. The green triangles show the MF ratios of the FoF haloes, while yellow circles show the ones of the SUBFIND haloes. The lines represent the theoretically expected MF ratios: the black solid lines are the MF ratios predicted for Mν = 0.3 eV and Mν = 0.6 eV; the red dashed lines are the same ratios but assuming ρ¯ = ρc · (Ωm − Ων ) in the ST-MF formula; finally, the blue dotted lines are the ratios between the ST-MFs in two ΛCDM cosmologies, which differ for the σ8 normalisation, as explained in the text.

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C. Carbone / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 50–53

Table 1: σ(Mν ) and σ(Neff ) marginalised errors from a Euclid-like spectroscopic galaxy survey combined with Planck

fiducial→ Mν =0.3 eVa Mν =0.2 eVa Euclid+Planck 0.035 0.043

General cosmology Mν =0.125 eVb Mν =0.125 eVc Mν =0.05 eVb Neff =3.04d

0.031

0.044

0.053

0.086

0.021

0.021

0.023

ΛCDM cosmology Euclid+Planck a

0.017

0.019

0.017

for degenerate spectrum: m1 ≈ m2 ≈ m3 ; b for normal hierarchy: m3  0, m1 ≈ m2 ≈ 0 inverted hierarchy: m1 ≈ m2 , m3 ≈ 0; d fiducial cosmology with massless neutrinos

c for

tribute to the total matter density perturbations, damping, in this way, the structure formation with respect to a cosmological model where neutrinos are assumed massless. This effect modifies the matter transfer function which becomes also redshift dependent T (k, z) (see Fig. 1), the growth rate of DM structures f (see the left panel of Fig. 2), and the galaxy-cluster abundances (see the right panel of Fig. 2). Therefore, much more stringent constraints can be obtained by combining CMB data with LSS observations, and, indeed, the forecast sensitivity of future Euclid-like experiments, when combined with Planck priors, indicates that observations should soon allow to measure the neutrino mass even in the case of the minimum mass expected by neutrino oscillation experiments, i.e. Mν ∼ 0.05 eV [2]. 2. Method and results In order to forecast neutrino constraints from future LSS probes, we apply a Fisher matrix approach to both clustering and abundance observables. Including redshift-space distortions and the geometrical effects due to the incorrect assumption of the reference cosmology with respect to the true one, the observed power spectrum of galaxies or galaxy-clusters can be written as Pobs (kref⊥ , kref , z)

=

DA (z)2ref H(z) P(kref⊥ , kref , z) DA (z)2 H(z)ref (1) +Pshot ,

Here, H(z) and DA (z) are the Hubble parameter and the angular diameter distance, respectively, and the prefactor (DA (z)2ref H(z))/(DA (z)2 H(z)ref ) encapsulates the geometrical distortions due to the so-called “AlcockPaczynski effect”. Their values in the reference cosmology are distinguished by the subscript ‘ref’, while those in the true cosmology have no subscript. k⊥ and k are the wave-numbers across and along the line of sight in the true cosmology, and they are related to the wavenumbers calculated assuming the reference cosmology by kref⊥ = k⊥ DA (z)/DA (z)ref and kref = k H(z)ref /H(z).

P(kref⊥ , kref , z) is the redshift dependent power spectrum of the LSS tracers, and, finally, Pshot represents the unknown white shot noise that remains even after the conventional shot noise of inverse number density has been subtracted, and which could arise from clustering bias even on large scales due to local bias (see [2, 3] for further details). The Fisher matrix associated to Pobs can be approximated as 

P

Fi jobs

=

kmin

 =

kmax

1 −1



dk ∂ ln Pobs (k) ∂ ln Pobs (k) Veff (k) ∂q˜ α ∂q˜ β 2(2π)3 kmax

kmin

Veff (k, μ)

∂ ln Pobs (k, μ) ∂ ln Pobs (k, μ) × ∂q˜ α ∂q˜ β

2πk2 dkdμ , 2(2π)3

(2)

where the derivatives are evaluated at the cosmological parameter values q˜ α of the assumed fiducial model, and Veff (k, μ) ≡ [n(z)P(k, μ)]2 /[n(z)P(k, μ) + 1]2 Vsurvey is the effective volume of the survey. Here we have assumed that the comoving number density of the DM tracers n is constant in position. In order to consider only the contribution from the power spectrum shape and the positions of the Baryon Acoustic Oscillations (BAO), we do not include information from the amplitude and the redshift space distortions, i.e. we marginalise over these variables and also over Pishot . Concerning the galaxy-cluster abundance, the Fisher matrix for the number of clusters, Ni , within the i-th redshift bin of the survey (with sky coverage ΔΩ) and mass M > Mmin (z), can be written as N Fαβ

 zi+1  ∂Ni ∂Ni 1 dV = , Ni ≡ ΔΩ dz n(z). ∂ q ˜ ∂ q ˜ N dzdΩ α β i zi i

(3)

In order to combine the forecasts from LSS with CMB priors, we also compute the Planck Fisher matrix, following Ref. [2, 3]. Therefore, the final 1–σ error on the parameter q α , marginalised over the other parameters, is σ(qα ) = (F −1 )αα , where F is the sum of the Fisher matrices of the single probes, and  the so-called correlation coefficients are r ≡ (F −1 )αβ / (F −1 )αα (F −1 )ββ . As final set of cosmological parameters we choose   q = Ωm , ΩK , Ωb , h, ζ, n s , w0 , wa , log(1010 A s ) ,

(4)

C. Carbone / Nuclear Physics B (Proc. Suppl.) 237–238 (2013) 50–53

with ζ = Neff , Mν . According to the latest observations, we assume the following fiducial cosmological model: Ωm = 0.271, ΩΛ = 1−Ωm , h = 0.703, A s = 2.502×10−9 , Ωb = 0.045, n s = 0.966, w0 = −0.95, wa = 0, where the total neutrino mass Mν can assume the fiducial values shown in Table 1. Here Ωm and Ωb are, respectively, the total matter and baryon present-day energy densities, in units of the critical energy density of the Universe, h is given by H0 = 100h km s−1 Mpc−1 , where H0 is the Hubble constant, A s represents the dimensionless amplitude of the primordial curvature perturbations evaluated at the pivot scale k0 = 0.002/Mpc, and n s is the scalar spectral index of the primordial matter power spectrum, assumed to be a power-law. In Table 1 we summarise the dependence of the Mν – and Neff –errors on the model cosmology, obtained combining CMB data and BAO+Pobs (k)-shape measurements from a Euclid-like spectroscopic galaxy survey. From the amplitude of the 1–σ errors we can infer that, if Mν is > 0.1 eV, this survey will be able to determine the neutrino mass scale independently of the model cosmology assumed (i.e., curvature and DE equation of state). If Mν is < 0.1 eV, the sum of neutrino masses, and in particular the neutrino mass lowest limit established by neutrino oscillation experiments, can be measured only in the context of a ΛCDM model. This means that future spectroscopic galaxy surveys, such as Euclid, will be able to cover the entire parameter space for neutrino mass allowed by oscillations experiments [2]. On the other hand, in Table 2 we consider the total combination of CMB priors with galaxy-cluster counts and BAO+Pobs (k)-shape measurements from a Euclid-like photometric galaxy-cluster catalog. Specifically, for the total neutrino mass error in a general cosmology we find σ(Mν ) = 0.18 eV, which reduces to σ(Mν ) = 0.076 eV in a ΛCDM Universe [3]. The latter value is only 1.5 times the minimum neutrino mass admitted by neutrino oscillation experiments. 3. Conclusions We conclude that future nearly all-sky spectroscopic Euclid-like galaxy surveys will detect the cosmological neutrino background at high statistical significance, and provide a measurement of the neutrino mass scale, giving crucial insights into neutrino properties, highly complementary to future particle physics experiments. On the other hand, also a photometric Euclid-like galaxy-cluster catalogs can provide competitive constraints on the total neutrino mass, for a ΛCDM cosmology in particular. This means that, even if the galaxy clustering constraining power is undoubtedly superior

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Table 2: marginalised 1–σ errors and corresponding correlations from a Euclid-like galaxy-cluster catalog combined with Planck, for Mν |fid = 0.05 eV.

BAO+COUNTS+CMB General cosmology ΛCDM σ r σ r Ωm 0.0106 0.4046 0.0036 -0.8361 ΩK 0.0039 0.3854 – – Ωb 0.0016 0.0125 0.0009 -0.7042 h 0.0125 -0.0380 0.0068 0.7796 Mν 0.1853 1.0000 0.0758 1.0000 ns 0.0024 -0.0297 0.0023 0.2220 w0 0.2133 0.0020 – – wa 0.7218 -0.2123 – – log(1010 A s ) 0.0222 0.8878 0.0138 0.7522

to the galaxy-cluster one, the two probes are complementary and their combination with CMB data could greatly help to improve constraints on all the cosmological parameters, including the neutrino mass. References [1] “Effects of Massive Neutrinos on the Large-Scale Structure of the Universe”, F. Marulli, C. Carbone, M. Viel, L. Moscardini, A. Cimatti, Mon. Not. R. Astron. Soc.418 (2011) 346–356. [2] “Neutrino constraints from future nearly all-sky spectroscopic galaxy surveys”, C. Carbone, L. Verde, Y. Wang, A. Cimatti, J. Cosm. Astro-Particle Phys.3 (2011) 30. [3] “Measuring the neutrino mass from future wide galaxy cluster catalogues”, C. Carbone, C. Fedeli, L. Moscardini, A. Cimatti, J. Cosm. Astro-Particle Phys.3 (2012) 23.