Based on the Lambda-CDM cosmological model, our universe is not only expanding, but is accelerating in its expansion. However, the Equivalence Principle would suggest that inertia manifests itself in non-inertial reference frames as a pseudo-force, a body force similar to gravity but anti-parallel to the direction of acceleration. If this is in fact the case—with seemingly no reference frame being truly un-accelerated (due to the expansion of the universe)—why can't I feel it? Is it because the acceleration is too weak? Or is it because I have never not known the presence of this pseudo-force (so I am just used to it)? And if there is a small apparent force, what direction is it in given the isotropy of the expansion?
Is it because the acceleration is too weak?
It is too weak with respect to the four forces we measure. The fact that the four known forces are so much stronger means that agglomerates of particles, up to the scale of galaxies are not internally affected, they keep their structure intact, like the famous raisins in the rising bread. It is only at the level of clusters of galaxies that the expansion and the acceleration can be observed.
And if there is a small apparent force, what direction is it in?
A cluster of galaxies sees expansion in all three space dimensions. The balloon surface analogy, blowing up the balloon with a gnat on it, might give an insight. The gnat sees the surface expanding away from it in both surface directions.