The impact of early dark energy on non-linear structure formation

We study non-linear structure formation in high-resolution simulations of early dark energy (EDE) cosmologies and compare their evolution with the standard Lambda cold dark matter (Lambda CDM) model. In EDE models, the impact on structure formation is expected to be particularly strong because of the presence of a non-negligible dark energy component even at very high redshift, unlike in standard models that behave like matter-dominated universes at early times. In fact, extensions of the spherical top-hat collapse model predict that the virial overdensity and linear threshold density for collapse should be modified in EDE model, yielding significant modifications in the expected halo mass function. Here, we present numerical simulations that directly test these expectations. Interestingly, we find that the Sheth & Tormen formalism for estimating the abundance of dark matter haloes continues to work very well in its standard form for the EDE cosmologies, contrary to analytic predictions. The residuals are even slightly smaller than for Lambda CDM. We also study the virial relationship between mass and dark matter velocity dispersion in different dark energy cosmologies, finding excellent agreement with the normalization for Lambda CDM as calibrated by Evrard et al. The earlier growth of structure in EDE models relative to Lambda CDM produces large differences in the mass functions at high redshift. This could be measured directly by counting groups as a function of the line-of-sight velocity dispersion, skirting the ambiguous problem of assigning amass to the halo. Using dark matter substructures as a proxy for member galaxies, we demonstrate that even with three to five members sufficiently accurate measurements of the halo velocity dispersion function are possible. Finally, we determine the concentration-mass relationship for our EDE cosmologies. Consistent with the earlier formation time, the EDE haloes show higher concentrations at a given halo mass. We find that the magnitude of the difference in concentration is well described by the prescription of Eke, Navarro & Steinmetz for estimating halo concentrations.