The Role of Energy Density Diffusion in Galactic Dynamics and Cosmic Expansion: A Unified Theory for MOND and Dark Energy

The galactic rotation curve anomaly and the universe's accelerated expansion remain the most compelling evidence for physics beyond standard models. This paper presents a unified mechanism explaining both phenomena without dark matter or dark energy postulates. Building on a wave-based paradigm where matter constitutes trapped standing waves in a dynamic medium, we demonstrate that energy released from mass conversion events—from primordial matter-antimatter annihilation to stellar nucleosynthesis—is injected into and diffuses through the fabric of space. This diffusion process is central to our model: it creates extended energy density fields with a characteristic $\rho_{\text{diff}}(r) \propto 1/r$ profile. We demonstrate that this profile directly influences gravitational dynamics through the constitutive law $a(r) \propto |\nabla \rho(r)| / \rho(r)$, naturally producing flat rotation curves without dark matter. Crucially, order-of-magnitude calculations reveal that the total gravitational potential energy of the observable universe ($|U| \approx 8.36 \times 10^{70}$ J) matches the energy released from primordial mass conversion ($E_{\text{thermal}} \approx 2.6 \times 10^{70}$ J), suggesting a common mechanism operating across cosmic and galactic scales. This model provides a physical foundation for Modified Newtonian Dynamics (MOND) by identifying the MONDian regime as the domain where diffused energy density dominates, and explains the recent acceleration of cosmic expansion through the condensation of accumulated low-energy neutrinos, offering a physical alternative to the dual dark matter and dark energy hypotheses.