Question Isn't expansion just a lorentz transformation through time?

[Greenlight]

the universe was 10^-35 meters a fraction of a second after the big bang, but isn't that a relative size? Relative to our current space/time reference frame? Time ran slower back then but if you were there you wouldn't know it, isn't it the same for space as well? isn't space static but we see it through a changing lorentz factor?

 

[Greenlight]

z = γ (1 + v/c) -1
we don't really know the velocity, its inferred by the redshift observation.
we do have the cosmic ladder so we have a better grasp on distance.
if redshift is proportional to distance can we not substitute distance for velocity?
we can do away with the inferred velocity its not necessary nor accurate, because it's not really a velocity.
A velocity infers a direction of movement. but with expansion no two locations will agree on its vector direction.

 

[Gibsense]

z = γ (1 + v/c) -1
we don't really know the velocity, its inferred by the redshift observation.
we do have the cosmic ladder so we have a better grasp on distance.
if redshift is proportional to distance can we not substitute distance for velocity?
we can do away with the inferred velocity its not necessary nor accurate, because it's not really a velocity.
A velocity infers a direction of movement. but with expansion no two locations will agree on its vector direction.

You seem to be differentiating between recessional speed due to expansion and a velocity through space in the context of 'Lorentz' i.e. for example, the reference to energy required. It would seem that, as no energy is involved in travelling through space to achieve the recessional speed of a galaxy (as a result of the expansion of the universe), the relevance of Lorentz is in doubt.

Your point about substituting distance for velocity is IMO appropriate depending on the context. I don't see why the direction of movement is important nor understand your comment that time ran slower 'back then'

But anyway maybe someone with more competence mathematically than I might comment
Also where are you going with this?