Cosmologists see a mismatch between different ways of measuring the universe. Measurements of the cosmic microwave background (CMB), the pattern of galaxies called baryon acoustic oscillations (BAO), and supernovae (SN) give slightly different answers for the same basic numbers. One example is the current expansion rate, H0, where the CMB-based value under the standard model (ΛCDM) is about 67.24 km s−1 Mpc−1 while local distance measurements report about 73.5 km s−1 Mpc−1. The paper shows that treating a change in the early universe and a change at late times separately can reduce these disagreements without invoking a theoretically problematic “phantom” dark energy component.

The authors study an “early dark energy” (EDE) component that briefly speeds up the expansion before recombination, the time when the CMB was released. In their main model EDE is like an axion-like field that sits still early on, then rolls and quickly dilutes. This short burst shrinks the sound horizon, the standard ruler used by BAO, and so changes how BAO data are calibrated against the CMB. They find that EDE improves the fit to CMB+BAO data with a change in the goodness-of-fit statistic Δχ2 = −9.4 compared with ΛCDM, and it raises the CMB-inferred H0 to about 70.87 km s−1 Mpc−1.

EDE by itself does not make all datasets agree. The supernova distance measurements probe the late-time expansion and do not respond to the short-lived EDE change. To address the remaining mismatch the authors add a late-time, non-phantom dark energy component called thawing quintessence. Thawing quintessence is a stable scalar-field model that starts nearly static and then slowly rolls, giving an equation of state w(a) that stays above −1 (the non-phantom side). Combining EDE with a thawing quintessence model yields Δχ2 = −12.6 relative to ΛCDM without crossing into the phantom regime. For comparison, the common w0–wa parametrization that does cross the phantom divide gives a somewhat larger improvement, Δχ2 = −15.8, but at the cost of involving w < −1 which can cause theoretical instabilities.