8 can complete the Friedmann-Lemaˆıtre acceleration equation This is remarkably like the surface term order of magnitude estimate except for the 3 / 2 π factor. With the Hawking temperature description the coefficient would have been 1/2. There is some freedom here and we chose the value that leads to nice equations in the two limiting cases. It is easy to show that if the H 2 is highly dominant over the 4 πG 3 ( ρ + 3 P/c $^{2}$), the solution to the equation is simply a de Sitter space with scale factor a ( t ) = a ( t$_{o}$ ) e H ( t − t$_{0}$ $^{)}$. The alternate equation may provide a better fit to the data (see § IV A) or a rigorous derivation but does not have the simplicity of Eq. (16). In order to adopt a broader approach, we generalized our discussion by considering where we anticipate the coefficients to be bounded by 3 2 π < ∼ C$_{H}$ ≤ 1 and 0 ≤ C ˙ H < ∼ 3 4 $_{π}$. We conclude with a demonstration that the entropic acceleration mechanism inspired by surface terms can provide a surprisingly remarkable fit the supernova data, assuming the simple form for the acceleration equation (17). Because we are using a metric theory of gravity, we may use the standard formula for the luminosity distance: ¨ a a = − 4 πG 3 ( ρ + 3 P c 2 ) + H $^{2}$. (16) ¨ a a = − 4 πG 3 ( ρ + 3 P c 2 ) + 3 2 π H 2 + 3 4 π ˙ H (17) ¨ a a = − 4 πG 3 ( ρ + 3 P c 2 ) + C$_{H}$H 2 + C ˙ H ˙ H (18) d$_{L}$ ( z ; H ( z ) , H$_{0}$ ) = c (1 + z ) H$_{0}$ ∫ z 0 dz ′ H ( z $^{′}$) , (19) A. Comparison with supernova data