Persistent tensions in the Hubble parameter ($H_0$) and the matter clustering amplitude ($S_8$) motivate theoretical extensions beyond the non-interacting dark sector assumed in $\Lambda$CDM. From an effective field theory perspective, a non-zero Yukawa interaction between a scalar dark-energy field $\phi$ and fermionic dark matter $\psi$ is technically natural unless prohibited by symmetry. In this work, we construct a microphysically consistent framework in which such an interaction emerges dynamically rather than being imposed phenomenologically.
We model the dark sector as an open quantum system, in which the scalar field constitutes a reduced subsystem that exchanges energy and information with an environmental dark-matter bath. Unlike a closed (unitary) quantum system, tracing over the fermionic degrees of freedom induces irreversible effects captured by a Lindblad evolution equation for the scalar density matrix. The scalar potential undergoes spontaneous symmetry breaking once the dark-matter density falls below a critical scale, inducing a time-dependent vacuum expectation value. The resulting interaction kernel $Q(a)$ and coupling profile $\beta(a)$ are therefore not free parameters, but consequences of the underlying symmetry-breaking and dissipative microphysics.
The resulting phenomenology is distinctive: the expansion history remains close to $\Lambda$CDM, while structure growth is modified through a late-time activation of the coupling. We test this against current large-scale structure and background probes using RSD, BAO, SN Ia, and CMB priors. A dynamical analysis—which self-consistently evolves both the background and perturbations—favours a late transition ($a_c \simeq 0.47$) and ($\beta_0 \simeq 0.52$). The model naturally suppresses the growth amplitude to $\sigma_{8,0} \simeq 0.59$ while simultaneously raising the inferred Hubble constant to $H_0 \simeq 69.6\ \mathrm{km\,s^{-1}\,Mpc^{-1}}$, suggesting that the $H_0$ and $S_8$ discrepancies may trace distinct physical origins. This places observationally inferred coupling strengths in direct correspondence with radiative stability constraints, making the next generation of spectroscopic surveys a decisive test of this class of models.
