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ComaBerenices

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I just have a few questions about how the universe expands and whether some proportions are legit.

Firstly, say you have two gravitationally attracted points in space that are expanding away from each other:

http://geometry.freehomeworkmathhelp.com/Geometry_Main_0/geometry_homework_help_line_segment.GIF

Because I have heard that DE does not affect the actual motion of galaxies in space, but simply expands the space between them, would these objects continually accelerate 'towards' each other until they reach the distance where a signal cannot be communicated between them due to the increasing expansion between them? If so, if the two objects were within the range where gravitation and expansion balance out, would the two objects soon come together due to acceleration of velocity because of gravity?

Secondly, in an expanding, homogeneous universe, as distances grow, so does gravitational potential energy, as the curvature of space becomes less steep, the gravitational potential energy grows more slowly. This has seemed to correlate with a decreasing Hubble rate of expansion over time, however it is currently decreasing at a decelerated rate. I find this proportion curious so I was wondering whether any cosmologist has looked into this.

Regards,