Linear cosmological structure limits on warm dark matter

I consider constraints from observations on a cutoff scale in clustering due to free streaming of the dark matter in a warm dark matter cosmological model with a cosmological constant. The limits are derived in the framework of a sterile neutrino warm dark matter universe, but can be applied to gravitinos and other models with small-scale suppression in the linear matter power spectrum. With freedom in all cosmological parameters including the free streaming scale of the sterile neutrino dark matter, limits are derived using observations of the fluctuations in the cosmic microwave background, the 3D clustering of galaxies and 1D clustering of gas in the Lyman-alpha ($\mathrm{Ly}\alpha$) forest in the Sloan Digital Sky Survey (SDSS), as well as the $\mathrm{Ly}\alpha$ forest in high-resolution spectroscopic observations. In the most conservative case, using only the SDSS main-galaxy 3D power-spectrum shape, the limit is $m_s>0.11\mathrm{keV}$; including the SDSS $\mathrm{Ly}\alpha$ forest, this limit improves to $m_s>1.7\mathrm{keV}$. More stringent constraints may be placed from the inferred matter power spectrum from high-resolution $\mathrm{Ly}\alpha$ forest observations, which has significant systematic uncertainties; in this case, the limit improves to $m_s>3.0\mathrm{keV}$ (all at 95% CL).