CMB acoustic scale in the entropic-like accelerating universe

We consider generalizations of the entropic accelerating universe recently proposed in [D. A. Easson, P. H. Frampton, and G. F. Smoot, Phys. Lett. B 696, 273 (2011).] and [D. A. Easson, P. H. Frampton, and G. F. Smoot, arXiv:1003.1528.] and show that their background equations can be made equivalent to a model with a dark energy component with a constant parameter of state wX=-1+2γ/3, where γ is related to the coefficients of the new terms in the Friedmann equations. After discussing all the Friedmann equations for an arbitrary γ, we show how to recover the standard scalings for dust and radiation. The acoustic scale ℓA, related to the peak positions in the pattern of the angular power spectrum of the cosmic microwave background anisotropies, is also computed and yields the stringent bound |γ|≪1. We then argue that future data might be able to distinguish this model from pure ΛCDM (corresponding to γ=0).