Dynamical Dark Sector: A Joint Two-Scalar-Field Model for Dark Matter and Quintessence

The physical nature of dark matter and dark energy remains one of the most pressing questions in modern cosmology. This work presents a phenomenological model where the entire dark sector is described by two minimally coupled scalar fields within General Rela-tivity. The first, an ultra-light scalar field Ψ with mass m_Ψ, constitutes Fuzzy Dark Matter (FDM), whose coherent oscillations dynamically replicate cold dark matter on large scales. The second, a quintessence field ϕ, evolves under an axion-like potential and serves as the dark energy component. We demonstrate that this framework can successfully reproduce the canonical cosmic history while offering a physical mechanism to address the S₈ tension. By exploring the model’s parameter space, we show that the suppression of small-scale structure is a direct function of the FDM mass. For a benchmark mass of m_Ψ = 10⁻²² eV, chosen to illustrate the potential impact, we show that the model can produce a value of S₈ σ₈(Ω_m/0.3)^0.5 of approximately 0.79, significantly alleviating the tension between early and late-universe probes [1,9,10]. Concurrently, the model predicts a “thawing” behavior for dark energy, with a present-day equation of state, w_ϕ,0, that depends on the potential’s parameters, yielding w_ϕ,0 0.92 in our benchmark case—a value distinguishably different from the cosmological constant’s w_Λ = 1. We acknowledge that the FDM mass required to affect the S₈ tension creates a testable conflict with some Lyman-alpha forest constraints [16], a point we discuss as a key feature for the model’s falsifiability. By connecting cos-mic acceleration, dark matter, and the S₈ tension, this self-consistent framework offers a compelling and highly testable alternative to the ΛCDM model, motivating a full statistical analysis.