A Multi-Axion Ladder Across Cosmic History: From Inflation, BBN, and Early Dark Energy to Late-Time Accelerated Expansion

Abstract: What if dark energy is recurrent throughout cosmic history? In this picture, episodes of scalar-field dark energy become less surprising and more natural features of cosmic evolution. We construct a homogeneous multi-axion cosmology with a transient contribution during Big Bang nucleosynthesis, two early dark energy components before recombination, and a thawing field that supplies the present dark-energy density. As Hubble friction weakens, the fields begin to roll at successive epochs set by their potential-curvature scales. Their initial displacements affect the rolling delays and peak energy fractions. The transient fields have third-power cosine potentials, whose sextic minima allow faster-than-radiation dilution during rapid, small-amplitude oscillations. All four fields are evolved in a common Friedmann background, with their first roll and subsequent dynamics resolved numerically. With reference matter and radiation densities taken from Planck 2018, the benchmark has a nucleosynthesis-era peak fraction of approximately $0.99\%$ near $z=10<sup>9$. The two early dark energy fields peak near $z=7.9\times10<sup>3$ and $2.4\times10<sup>3$, with individual fractions of $8.6\%$ and $7.8\%$; their combined fraction reaches $9.7\%$. The late-time field is normalized to supply a present fraction of approximately $0.685$, while the three transients leave a combined fraction of approximately $6.0\times10<sup>{-7}$. An aligned two-axion example illustrates the enhanced field range available for an inflationary extension. We also outline how searches for transient contributions to the expansion rate at other epochs could constrain additional axion scales.