These equations are sometimes simplified by replacing ρ ρ → → ρ ρ − − Λ Λ c 2 8 π π G p → → p + Λ Λ c 4 8 π π G to give: H 2 = ( a ˙ ˙ a ) 2 = 8 π π G 3 ρ ρ − − k c 2 a 2 H ˙ ˙ + H 2 = a ¨ ¨ a = − − 4 π π G 3 ( ρ ρ + 3 p c 2 ) .