Since gravity contracts space, I wondered how the local increase in density of matter and energy due to the current galactic mergers with the Milky Way affects our perception of the universe.

Basically if we have black holes coming closer to us, then our space contraction should make it look like the rest of the universe is expanding, due to the local gravitational red shift.

I'm sure I'm not the first to think of this but I wonder how well it's been studied, what the magnitude of that effect would be, and also how we would even know if some dark matter were creating a dense gravitational field around the earth.