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CMB acoustic scale in the entropic-like accelerating universe

We consider generalizations of the entropic accelerating universe recently proposed in Ref. [4,5] and show that their background equations can be made equivalent to a model with a dark energy component with constant parameter of state $w_{X} = -1 + 2\, γ/3$, where $γ$ is related to the coefficients of the new terms in the Friedman equations. After discussing all the Friedman equations for an arbitrary $γ$, we show how to recover the standard scalings for dust and radiation. The acoustic scale $\ell_A$, 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 $|γ|\ll 1$. We then argue that future data might be able to distinguish this model from pure $Λ$CDM (corresponding to $γ=0$).