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.
