While second and higher order correlations of the light distribution have received extensive study , the lowest order probability distribution function ( PDF ) — the probability that a unit volume of space will emit a given amount of light — has received very little attention .
We estimate this function with the aid of hydrodynamic simulations of the \Lambda CDM model , finding it significantly different from the mass density PDF , and not simply related to it by linear bias or any of the other prescriptions commonly adopted .
If the optical light PDF is , in reality , similar to what we find in the simulations , then some measures of \Omega _ { m } based on mass-to-light ratio and the cosmic virial theorem will have significantly underestimated \Omega _ { m } .
Basically , the problem is one of selection bias , with galaxy forming regions being unrepresentative of the dark matter distribution in a way not described by linear bias .
Knowledge of the optical PDF and the plausible assumption of a log-normal distribution for the matter PDF will allow one to correct for these selection biases .
We find that this correction ( which amounts to 20 - 30 \% ) brings the values of \Omega _ { m } estimated by using the mass-to-light ratio and the cosmic virial theorem to the range \Omega _ { m } = 0.2 - 0.3 , in better agreement with the WMAP result than the uncorrected estimates .
In addition , the relation between mass and light PDFs gives us insight concerning the nature of the void phenomenon .
In particular our simulation indicates that 20 % of mass is distributed in voids , which occupy 85 % of volume in the universe .