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LCDM cosmological models with Early Dark Energy (EDE) have been proposed toresolve tensions between the Hubble constant H0 = 100h km/s/Mpc measuredlocally, giving h ~ 0.73, and H0 deduced from Planck cosmic microwavebackground (CMB) and other early universe measurements plus LCDM, giving h ~0.67. EDE models do this by adding a scalar field that temporarily adds darkenergy equal to about 10% of the cosmological energy density at the end of theradiation-dominated era at redshift z ~ 3500. Here we compare linear andnonlinear predictions of a Planck-normalized LCDM model including EDE giving h= 0.728 with those of standard Planck-normalized LCDM with h = 0.678. We findthat nonlinear evolution reduces the differences between power spectra offluctuations at low redshifts. As a result, at z = 0 the halo mass functions ongalactic scales are nearly the same, with differences only 1-2%. However, thedifferences dramatically increase at high redshifts. The EDE model predicts 50%more massive clusters at z = 1 and twice more galaxy-mass halos at z = 4. Evengreater increases in abundances of galaxy-mass halos at higher redshifts maymake it easier to reionize the universe with EDE. Predicted galaxy abundancesand clustering will soon be tested by JWST observations. Positions of baryonicacoustic oscillations (BAOs) and correlation functions differ by about 2%between the models -- an effect that is not washed out by nonlinearities. Bothstandard LCDM and the EDE model studied here agree well with presentlyavailable acoustic-scale observations, but DESI and Euclid measurements willprovide stringent new tests.

Clustering and Halo Abundances in Early Dark Energy Cosmological Models