Dark Energy as a Modification of the Friedmann Equation

Dark energy could actually be the manifestation of a modification to the Friedmann equation arising from new physics (e.g., extra dimensions). Writing the correction as $(1-{\mathrm{\Omega }}_M)H^{\alpha }\mathrm{/}{H}_0^{\alpha -2}$, we explore the phenomenology and detectability of such. We show that: (i) $\alpha$ must be $\text{la}1$; (ii) such a correction behaves like dark energy with equation-of-state $w_{\mathrm{e}\mathrm{f}\mathrm{f}}=-1+\frac{\alpha }{2}$ in the recent past (${10}^4>z\gg 1$) and $w=-1$ in the distant future and can mimic $w<-1$ without violating the weak-energy condition; (iii) $w_{\mathrm{e}\mathrm{f}\mathrm{f}}$ changes, $dz/dw|_{z\sim 0.5} \sim {\cal O}(0.2)$, which is likely detectable; and (iv) a future supernova experiment like SNAP that can determine $w$ with precision ${\sigma }_w$, could determine $\alpha$ to precision ${\sigma }_{\alpha }\approx 2{\sigma }_w$.