Probing the Warm Dark Matter with High-z Quasar Luminosity Function
  In a warm dark matter (WDM) cosmology, the first objects to form at z>=20 are
one dimensional filaments with mean length on the order of the WDM
free-streaming scale. Gao and Theuns recently claimed by using high-resolution
hydrodynamic simulations that the eventual collapse of these WDM filaments
along their longest axes may seed the supermassive black holes that power
high-z quasars. In this picture, it is supposed that the high-z quasar
luminosity function should reflect how abundant the WDM filaments are in the
early universe. We derive analytically the mass function of early-universe
filaments with the help of the Zel'dovich approximation. Then, we determine the
rate of its decrease in the mass section corresponding to the free streaming
scale of a WDM particle of mass m_v. Adjusting the value of m_v, we fit the
slope of the analytic model to that of the high-z quasar luminosity function
measured from the Sloan Digital Sky Survey DR3. A new WDM constraint from this
feasibility study is found to be consistent with the lightest super-symmetric
partner.
