It's evident and well known that light traveling across an expanding FLRW universe is redshifted via an equation: $$\frac{\lambda_{arriving}}{\lambda_{emitted}}=\frac{a_{now}}{a_{then}}$$ Where $a$ is the cosmological scale factor when the light is emitted and observed (denoted then and now respectively).
Let's say the light was traveling through a waveguide over that same distance. Calculations shouldn't be effected, and the redshift would follow the same equation.
If we now take that same waveguide and make it a large circle of the same total length, would that effect the redshift equation? I don't see how, but maybe someone here knows better.
If light is still redshifted the same it seems we can shrink the size of the waveguide arbitrarily down to a small local system. Does cosmological redshift happen locally? I've found arguments that energy isn't lost to bound systems lacking.
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