So I was watching some videos. Over [here] Padmanabhan claims that in a zero cosmological constant universe setting $a =1 $ in the FLRW metric is quite non-trivial:
so there is a constant in the universe which you can determine
only if this $a_0$ is given but the Friedmann equations do not fix
$a_0$... Friedman equations with no extra physical input you will never
be able to figure this out
Sorkin makes a similar point [here]:
it has an arbitrary normalization; it no longer has a direct physical meaning. It's only the ratios of $a$, sort of $a$ at one time $τ_1$ to $a$ of $τ_2$ that have meaning.
I know while there were some solutions of General Relativity which are pathological from the initial value problem's formulation. I didn't think FLRW was one of them?
The initial value problem then consists of specifying initial data for
all fields on one such a spatial hypersurface, such that the
subsequent evolution forward in time is fully determined.
Like naively I'd think that the initial value data corresponded to something physical? I feel something is amiss? Because if I take limits and go to a Newtonian mechanical regime I've never heard someone make similar claims for a fluid?