Can we distinguish early dark energy from a cosmological constant?

Early dark energy (EDE) models are a class of quintessence dark energy with a dynamically evolving scalar field which display a small but non-negligible amount of dark energy at the epoch of matter-radiation equality. Compared with a cosmological constant, the presence of dark energy at early times changes the cosmic expansion history and consequently the shape of the linear theory power spectrum and potentially other observables. We constrain the cosmological parameters in the EDE cosmology using recent measurements of the cosmic microwave background and baryon acoustic oscillations. The best-fitting models favour no EDE; here we consider extreme examples which are in mild tension with current observations in order to explore the observational consequences of a maximally allowed amount of EDE. We study the non-linear evolution of cosmic structure in EDE cosmologies using large volume N-body simulations. Many large-scale structure statistics are found to be very similar between the $\Lambda$ cold dark matter ($\Lambda$CDM) and EDE models. We find that the most promising way to distinguish EDE from $\Lambda$CDM is to measure the power spectrum on large scales, where differences of up to 15% are expected.