where t is time, x (i =1,2,3) are the spatial coordinates and a (t) is the scale factor. Along a timeline geodesic x i = constant, we can consider the universe to be filled with comoving particles. For an observer with proper time τ following the world line x (τ), has a 4-momentum P μ μ = m d x μ μ / d τ τ = ( E , p ) , where E = p 2 + m 2 is the energy, m is the mass and p =| p | the magnitude of the 3-momentum.