My biggest obstacle so far to derive MOND from FLRW in a completely satisfactory manner, is that from (flat) FLRW metric
dvdtnull=−cHϵ(t),
whereas for MOND to work, I need
dvdtnull=−12iπcHϵ(t).
Currently one of my few ideas is:
ω=H(t).
Recall that ω=˙θ, and that
H(t)=ddtlogϵ(t),
so
dθdt=ddtlogϵ(t),
yielding
ϵ=ϵ0eθ.
Applying the condition that
ϵ(t0)=1,
and allowing θ∈C, yields
θ0=2inπ−logϵ0, n∈Z.
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