Dark Energy as a Modification of the Friedmann Equation

Abstract

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 $(1-Ω_M)H^α/H_0^{α-2}$, we explore the phenomenology and detectability of such. We show that: (i) $α$ must be $\la 1$; (ii) such a correction behaves like dark energy with equation-of-state $w_{\rm eff} = -1 + {α\over 2}$ 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) $w_{\rm eff}$ 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 $σ_w$, could determine $α$ to precision $σ_α\approx 2 σ_w$.