Constraining Warm Dark Matter candidates including sterile neutrinos and light gravitinos with WMAP and the Lyman-alpha forest

TL;DR

This work provides joint constraints on warm dark matter candidates by combining WMAP CMB data with a large, high-fidelity Lyman-$\alpha$ forest power spectrum. The authors model how WDM suppresses small-scale structure via a transfer function $T(k)$ and calibrate the relation between flux and matter power using state-of-the-art hydrodynamical simulations, applying a comprehensive account of systematics. They derive a 2$\sigma$ lower bound of $m_x \gtrsim 550$ eV for thermal relic WDM and $m_x \gtrsim 2.0$ keV for sterile neutrinos, while in a mixed CDM+warm component scenario they obtain an upper bound $m_x \lesssim 16$ eV tied to a maximal warm fraction $f_x \lesssim 0.12$; the gravitino case further yields $\Lambda_{\rm susy} \lesssim 260$ TeV. Collectively, the results place tight, model-dependent constraints on particle physics parameters (SUSY-breaking scale, sterile neutrino properties) and on the viability of WDM as a solution to small-scale structure issues, with implications for future cosmological and collider investigations.

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-alpha 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 sigma for early decoupled thermal relics and m_wdm > 2.0 keV (2 sigma) 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 sigma). This translates into a bound on the scale of supersymmetry breaking, Lambda_{susy} < 260 TeV, for models of supersymmetric gauge mediation in which the gravitino is the lightest supersymmetric particle.

Figures (5)

• Figure 1: The WDM transfer function $T(k)$ defined in equation (\ref{['transdef']}) for various models (all with the same cosmological parameters $\Omega_\mathrm{B}\!=\!0.05$, $\Omega_\mathrm{DM}\!=\!0.25$, $\Omega_{\Lambda}\!=\!0.70$). (a) Pure $\Lambda$WDM model with, from left to right, $T_x/T_{\nu}=0.5,0.3,0.25,0.226,0.2$, corresponding to $m_x = 92, 427, 738, 1000, 1441 \, \mathrm{eV}$. The solid curves are obtained numerically, the long--dashed curves (essentially indistinguishable from the solid curves) show the analytical fits based on equation (\ref{['fit']}), the short--dashed curves those based on Ref. bode. (b) Mixed $\Lambda$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 $\Omega_\mathrm{CDM}=0.25-\Omega_x$). The solid curves show the numerical results for $m_x=10,20,30,50,70,100\, \mathrm{eV}$, from top right to bottom left. At the top-axis we show the wavenumber scale in s/km (assuming the above cosmological model and $z=2.5$ intermediate between the two Lyman-$\alpha$ data sets analysed here). In both panels the double arrow indicates the range of wavenumbers used in our analysis.
• Figure 2: Fractional difference of the flux power spectrum for a hydro-dynamical simulation of a $\Lambda$WDM model and the flux power spectrum for a $\Lambda$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), 1 keV (thin dashed), 2 keV (thin dotted), 4 keV (thick dashed) and 8 keV (continuous). The diamonds show the results for a simulation with a WDM particle of mass 1keV when random oriented velocity dispersion drawn from a Fermi-Dirac distribution have been added in the initial conditions.
• 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: $\Lambda$CDM (diamonds) and $\Lambda$WDM (squares), with a (thermal WDM) particle mass $m_{\rm WDM} = 1$ keV. The simulation has a boxsize of 60 comoving $h^{-1}$Mpc and $2\times400^3$ (gas and dark matter) particles (see Section \ref{['hydro']} for further details on other simulation parameters). The shaded area indicates the range of wavenumbers used in our analysis.
• Figure 4: Results for the pure $\Lambda$WDM model. The top left panel shows the likelihood for the break scale $\alpha$. The other three panels show the 1$\sigma$ and 2$\sigma$ contours for ($m_x^{-1}$, $\omega_x$), ($m_x^{-1}$, $\sigma_8$) and ($m_x^{-1}$, $n_s$), repectively, 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.
• Figure 5: Results for the $\Lambda$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: $\sigma_8$, $n_s$ and $\omega_X$. 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.