As I understand it the de Sitter model is a model of the Universe with: rho = matter density = rho = 0 p = pressure = 0 k = spatial curvature = 0 cosmological constant = Lambda = non zero Putting these values in the Friedmann equations one finds the solution for the scale factor a(t) is: a(t) = exp( sqrt(Lambda c^2/3) * t) This describes an accelerating empty universe with a non-zero cosmological constant. Although this model has the right deceleration parameter q = -1 it is contrary to observations as we know there is matter in the Universe. Now consider the following model: p = - rho c^2 k = 0 Plugging these values into the Friedmann equations we find we are left with the following equation for the scale factor a: a'^2 = a a'' This also has the solution: a(t) = exp(H * t) where H^2 = 8 Pi G rho' / 3 where rho' = rho + Lambda c^2 Now this model describes a matter-filled accelerating Universe with no explicit cosmological constant provided that the equation of state of the matter is: p = -rho c^2 Is this right? Does this latter model describe the present Universe provided that p = -rho c^2 holds for present day matter? In this model the negative pressure is associated with the particles of matter themselves rather than having a cosmological constant that is associated with the background space. Perhaps the negative pressure is a zero-point energy phenomenon holding the individual particles of matter together (in the same manner as the Casimir effect pushes conducting plates together).