Mechanism of Dark Matter Generation via Cosmic Expansion

Cosmic space is undergoing expansion. Hypothetically, if celestial bodies possessed no inertia, the expansion distance of the bodies, $d$, would equal the expansion distance of space, $r$. However, celestial bodies possess inertia, which is determined solely by their mass. This inertia provides a resistance to cosmic expansion, preventing celestial bodies from expanding synchronously with space. Consequently, at any given time $t$, the separation between bodies $d$ is less than the spatial separation $r$. While the purely spatial distance $r$ is unobservable, it can be conceptualized as the distance bodies would occupy in the absence of inertia. Let $X$ denote the comoving coordinate distance corresponding to $r$, and $x$ denote the comoving coordinate distance corresponding to $d$. Defining the lag as $\Delta x = X - x$, it follows that $\Delta x > 0$. The comoving coordinates $X$, $x$, and the difference $\Delta x$ are time-invariant. Since the masses $m_1$ and $m_2$ of any pair of celestial bodies differ, their inertial properties differ, resulting in a unique comoving coordinate difference $\Delta x$ for each pair. This analysis suggests that $\Delta x$ is the fundamental physical origin of the gravitational effects attributed to dark matter.