Dark Matter Translation

[petrushkagoogol]

1. Does dark matter move in tandem with regular matter as the Universe expands ?

Is there any method using spectroscopy that we can measure the equivalent of red-shift for dark matter ? 

[sanctus]

1) Gravitationally bound to each other, so why not?

2) Since dark matter does not emit EM radiation, there is no direct application of spectroscopy. But if you consider standard "detection" of dark matter via graviational lensing then indirectly spectroscopy is used.