Constraining Perturbative Early Dark Energy with Current Observations

In this work, we study a class of early dark energy (EDE) models, in which, unlike in standard DE models, a substantial amount of DE exists in the matter-dominated era, self-consistently including DE perturbations. Our analysis shows that, marginalizing over the non DE parameters such as $Omega_m, H_0, n_s$, current CMB observations alone can constrain the scale factor of transition from early DE to late time DE to $a_t geq 0.44$ and width of transition to $Delta_t leq 0.37$. The equation of state at present is somewhat weakly constrained to $w_0 leq -0.6$, if we allow $H_0 < 60$ km/s/Mpc. Taken together with other observations, such as supernovae, HST, and SDSS LRGs, the constraints are tighter-- $w_0 leq -0.9, a_t leq 0.19, Delta_t leq 0.21$. The evolution of the equation of state for EDE models is thus close to $Lambda$CDM at low redshifts. Incorrectly assuming DE perturbations to be negligible leads to different constraints on the equation of state parameters, thus highlighting the necessity of self-consistently including DE perturbations in the analysis. If we allow the spatial curvature to be a free parameter, then the constraints are relaxed to $w_0 leq -0.77, a_t leq 0.35, Delta_t leq 0.35$ with $-0.014 < Omega_{kappa} < 0.031$ for CMB+other observations. For perturbed EDE models, the $2sigma$ lower limit on $sigma_8$ ($sigma_8 geq 0.59$) is much lower than that in $Lambda$CDM ($sigma_8 geq 0.72$), thus raising the interesting possibility of discriminating EDE from $Lambda$CDM using future observations such as halo mass functions or the Sunyaev-Zeldovich power spectrum.