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 Omegaₘ, H₀, nₛ, current CMB observations alone can constrain the scale factor of transition from early DE to late time DE to aₜ ≥ 0.44 and width of transition to Deltaₜ ≤ 0.37. The equation of state at present is somewhat weakly constrained to w₀ ≤ -0.6, if we allow H₀ < 60 km/s/Mpc. Taken together with other observations, such as supernovae, HST, and SDSS LRGs, the constraints are tighter-- w₀ ≤ -0.9, aₜ ≤ 0.19, Δₜ ≤ 0.21. The evolution of the equation of state for EDE models is thus close to ΛCDM 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 w₀ ≤ -0.77, aₜ ≤ 0.35, Δₜ ≤ 0.35 with -0.014 < Ωκ < 0.031 for CMB+other observations. For perturbed EDE models, the 2σ lower limit on σ₈ (σ₈ ≥ 0.59) is much lower than that in ΛCDM (σ₈ ≥ 0.72), thus raising the interesting possibility of discriminating EDE from ΛCDM using future observations such as halo mass functions or the Sunyaev-Zeldovich power spectrum.