Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-$\ensuremath{\alpha}$ forest

Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman- $α$ forest

Matteo Viel, Julien Lesgourgues, Martin G. Haehnelt, Sabino Matarrese, and Antonio Riotto

Phys. Rev. D 71, 063534 – Published 31 March 2005

Abstract

The matter power spectrum at comoving scales of $(1 - 40) h^{- 1} Mpc$ is very sensitive to the presence of Warm Dark Matter (WDM) particles with large free-streaming lengths. We present constraints on the mass of WDM particles from a combined analysis of the matter power spectrum inferred from the large samples of high-resolution high signal-to-noise Lyman- $α$ forest data of Kim et al. (2004) and Croft et al. (2002) and the cosmic microwave background data of WMAP. We obtain a lower limit of $m_{WDM} ≳ 550 eV$ ( $2 σ$ ) for early decoupled thermal relics and $m_{WDM} ≳ 2.0 keV$ ( $2 σ$ ) for sterile neutrinos. We also investigate the case where in addition to cold dark matter a light thermal gravitino with fixed effective temperature contributes significantly to the matter density. In that case the gravitino density is proportional to its mass, and we find an upper limit $m_{3 / 2} ≲ 16 eV$ ( $2 σ$ ). This translates into a bound on the scale of supersymmetry breaking, $Λ_{susy} ≲ 260 TeV$ , for models of supersymmetric gauge mediation in which the gravitino is the lightest supersymmetric particle.

Received 28 January 2005

DOI:https://doi.org/10.1103/PhysRevD.71.063534

Authors & Affiliations

Matteo Viel¹, Julien Lesgourgues^2,3, Martin G. Haehnelt¹, Sabino Matarrese^4,3, and Antonio Riotto³

¹Institute of Astronomy, Madingley Road, Cambridge CB3 0HA, United Kingdom
²Laboratoire de Physique Théorique LAPTH, F-74941 Annecy-le-Vieux Cedex, France
³INFN, Sezione di Padova, Via Marzolo 8, I-35131 Padova, Italy
⁴Dipartimento di Fisica “G. Galilei,” Università di Padova, Via Marzolo 8, I-35131 Padova, Italy

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Vol. 71, Iss. 6 — 15 March 2005

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Figure 1
The WDM transfer function $T (k)$ defined in Eq. (4) for various models (all with the same cosmological parameters $Ω_{B} = 0.05$ , $Ω_{DM} = 0.25$ , $Ω_{Λ} = 0.70$ ). (a) Pure $Λ$ WDM model with, from left to right, $T_{x} / T_{ν} = 0.5$ , 0.3, 0.25, 0.226, 0.2, corresponding to $m_{x} = 92$ , 427, 738, 1000, 1441 eV. The solid curves are obtained numerically, the long-dashed curves (essentially indistinguishable from the solid curves) show the analytical fits based on Eq. (7), the short-dashed curves those based on Ref. 7. (b) Mixed $Λ$ CWDM model for a warm component which decoupled when $g_{*} (T_{D}) = 100$ , like e.g. a light gravitino (with mass proportional to density and $Ω_{CDM} = 0.25 - Ω_{x}$ ). The solid curves show the numerical results for $m_{x} = 10$ , 20, 30, 50, 70, 100 eV, from top right to bottom left. At the top axis we show the wave number scale in s/km (assuming the above cosmological model and $z = 2.5$ intermediate between the two Lyman- $α$ data sets analyzed here). In both panels the double arrow indicates the range of wave numbers used in our analysis.Reuse & Permissions
Figure 2
Fractional difference of the flux power spectrum for a hydrodynamical simulation of a $Λ$ WDM model and the flux power spectrum for a $Λ$ CDM model. The simulations have a box size of $30 h^{- 1} Mpc$ and $200^{3}$ gas and $200^{3}$ dark matter particles. The results are for three different redshifts ( $z = 4$ , 3, 2.5, respectively, from left to right) and for five different values of the (thermal WDM) particle mass: 0.5 keV (thick dotted line), 1 keV (thin dashed line), 2 keV (thin dotted line), 4 keV (thick dashed line), and 8 keV (continuous line). The diamonds show the results for a simulation with a WDM particle of mass 1 keV when random oriented velocity dispersion drawn from a Fermi-Dirac distribution have been added in the initial conditions.Reuse & Permissions
Figure 3
Bias function $b^{2} (k)$ between the flux power spectrum and the linear dark matter power spectrum, $P_{F} (k) = b^{2} (k) P (k)$ , for two cosmological models: $Λ$ CDM (diamonds) and $Λ$ WDM (squares), with a (thermal WDM) particle mass $m_{WDM} = 1 keV$ . The simulation has a box size of 60 comoving $h^{- 1} Mpc$ and $2 \times 400^{3}$ (gas and dark matter) particles (see Section 3b for further details on other simulation parameters). The shaded area indicates the range of wave numbers used in our analysis.Reuse & Permissions
Figure 4
Results for the pure $Λ$ WDM model. The top left panel shows the likelihood for the break scale $α$ . The other three panels show the $1 σ$ and $2 σ$ contours for ( $m_{x}^{- 1}$ , $ω_{x}$ ), ( $m_{x}^{- 1}$ , $σ_{8}$ ), and ( $m_{x}^{- 1}$ , $n_{s}$ ), respectively, where $m_{x}$ is the mass of a thermal WDM particle. The solid curves correspond to the full marginalized likelihoods, while the dashed curves and color/shade levels show the mean likelihood of the samples in the Markov chains.Reuse & Permissions
Figure 5
Results for the $Λ$ CWDM model with a light gravitino (or a particle decoupling when $g_{*} = 100$ ). The top left panel shows the likelihood for the WDM density fraction $f_{x}$ . Other panels show the two-dimensional contours for the gravitino mass $m_{x}$ and the most correlated variables: $σ_{8}$ , $n_{s}$ , and $ω_{X}$ . The solid curves correspond to the full marginalized likelihoods, while the dashed curves and color/shade levels show the mean likelihood of the samples in the Markov chains.Reuse & Permissions

Physical Review D

covering particles, fields, gravitation, and cosmology

Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman- $α$ forest

Matteo Viel, Julien Lesgourgues, Martin G. Haehnelt, Sabino Matarrese, and Antonio Riotto

Phys. Rev. D 71, 063534 – Published 31 March 2005

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Physical Review D

covering particles, fields, gravitation, and cosmology

Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-α forest

Matteo Viel, Julien Lesgourgues, Martin G. Haehnelt, Sabino Matarrese, and Antonio Riotto

Phys. Rev. D 71, 063534 – Published 31 March 2005

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Constraining warm dark matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman- $α$ forest