Question about LIGO theory (for the physicists out there)

This is not an easy question to answer. It turns out that the meaning of phrases such as 'the distance between the arms' and 'the wavelength of the light' depends upon the coordinate system choosen by the observer making these statements. Depending upon the choice of the coordinate system, it might be that the distance between the test masses remains fixed and the laser wavelength changes, or vice versa. However the thing that does NOT change and is independent of the choice of coordinates is the behavior of the light at the instrument's 'output' which is the antisymmetric port of the beamsplitter. This does reflect the effects of any gravitational waves.

A good place to look at the extensive literature on gravitational waves is this scientific literature catalog. (See the section at the bottom on gravitational waves.)

Two books on the subject are by Schutz and by Saulson. Note that both Schutz and Saulson are early Einstein@home members and actively accumulating credits!

An out of date but worthwhile set of slides by Peter Saulson is here .