Determine whether two-field early dark energy improves the cosmological fit

Determine whether distributing the early dark energy contribution between two axion fields improves the full joint CMB likelihood relative to a conventional single-field early-dark-energy model, after consistently evolving scalar and metric perturbations and accounting for the additional model parameters.

Background

The benchmark contains two third-power cosine axions whose energy-density peaks occur on opposite sides of matter–radiation equality. Their staggered contributions modify the expansion history over different intervals and may affect acoustic propagation, photon diffusion, gravitational-potential evolution, and CMB lensing differently from a single early-dark-energy field.

The paper provides only a homogeneous background evolution. A decisive comparison requires evolving the scalar and metric perturbations together with the ordinary cosmological components and implementing the model in a Boltzmann code such as CLASS or CAMB. The authors leave unresolved whether the additional temporal flexibility produces a statistically improved fit rather than merely reflecting the model’s greater parameter freedom.

References

Future work will test the model through quantitative comparisons with cosmological observations. It has two parts: a consistent BBN abundance calculation and a joint CMB, BAO, and supernova analysis of the early- and late-time fields. The central EDE question is whether distributing the contribution between two fields improves the full likelihood relative to conventional single-field EDE.

— A Multi-Axion Ladder Across Cosmic History: From Inflation, BBN, and Early Dark Energy to Late-Time Accelerated Expansion  (2609.11907 - Sengupta et al., 10 Sep 2026) in Section 5.2, “Single-field and two-field EDE in the CMB likelihood”; reiterated in Section 7, Discussion and conclusions