If you are interested in learning about "Moving Dimensions Theory" take
a look at my work on the Hypergeometrical Universe Theory. It proposes
that the Universe is a 4-D Shock Wave, thus the metric has a
Cosmological Time dependence (Cosmological Time is an Absolute Time).
Lorentz transformations relate different inertial frames within this
Shock-Wave, thus the theory is fully relativistic.

Expansion is quantized by de Broglie (Compton) steps of the
Hyperspherical Shock Wave Expansion. This makes the theory a Quantum
Theory, that is, capable of replicating Quantum Mechanics.

The expansion speed is clearly defined, as it should be, and equal to
the speed of light... the one and only speed we are able to travel.

The theory is not written in terms of metrics and geodesics because,
geodesics are not friendly for Quantum Mechanics and because there is
an introduction of a new Quantum Lagrangian Principle, thus making
equations that describe continuous motion unusable.

Have fun and feel free to ask questions.