  The formation of the Inner Oort Cloud (IOC) - a vast halo of icy bodies
residing far beyond Neptune's orbit - is an expected outcome of the solar
system's primordial evolution within a stellar cluster. Recent models have
shown that the process of early planetesimal capture within the trans-Neptunian
region may have been sufficiently high for the cumulative mass of the Cloud to
approach several Earth masses. In light of this, here we examine the dynamical
evolution of the IOC, driven by its own self-gravity. We show that the
collective gravitational potential of the IOC is adequately approximated by the
Miyamoto-Nagai model, and use a semi-analytic framework to demonstrate that the
resulting secular oscillations are akin to the von Zeipel-Lidov-Kozai
resonance. We verify our results with direct $N$-body calculations, and examine
the effects of IOC self-gravity on the long-term behavior of the solar system's
minor bodies using a detailed simulation. Cumulatively, we find that while the
modulation of perihelion distances and inclinations can occur within an
observationally relevant range, the associated timescales vastly surpass the
age of the sun, indicating that the influence of IOC self-gravity on the
architecture of the solar system is negligible.
