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Sunday, 23 July 2023

The pesky 2iπ of MOND-FLRW

 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 θC, yields

θ0=2inπlogϵ0,  nZ.

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