This work presents an original equation of motion for a massive ultralight scalar field with nonlinear self-interactions that is directly sourced by an electromagnetic field. The model incorporates Hubble damping from cosmic expansion, spatial gradients, a stabilizing mass term, and higher-order nonlinearities including a distinctive self-interaction term αr(ṙ² − (∇r)²). The right-hand side introduces a coupling between the electromagnetic field φ and the scalar r, allowing electromagnetic energy to pump and influence the dark-matter-like scalar. This framework is proposed as a potential mechanism to address several tensions in the standard ΛCDM cosmological model while opening new possibilities for the interaction between the electromagnetic sector and the dark sector. The full equation is shown in the attached figure. This is an ongoing independent research effort.
Andre Swart Andre (2026) studied this question.