I've been reading about the red-shift, the universe expanding, ect... And about the observation that the further a galaxy is from us, the faster it is moving away from us, accounting for an ever expanding universe. I'm also curious about the fact that the further the galaxy, the further 'in the past' the observation of the state of the galaxy is. Say a galaxy cluster is 500 million light years away from us, it is only telling us what the rate of expansion of the universe (in a broad sense) was 500 million years ago. I'm sure that is accounted for when deducing the current rate of expansion of the universe, but I was wondering if the fact that galaxies far away move faster and accelerate faster is only because we observe them as they were closer to the origin of the universe. So in term of a universe where the expansion is slowing down, it would make sense to see a closer, more 'up to date' galaxy be moving and expanding slower than a distant, 'younger' galaxy. Or is that 'time-shift' effect due to observation and the speed of light insignificant compared to the actual 'red-shift' observed?