I assume the rulers are not attached in any way. Then, if the rate of expansion is neither accelerating nor decelerating, the balls and rulers will remain exactly as they started. Because they had no relative motion to start, they will not develop any. Comoving observers move apart because they always were moving apart.

If the rate of expansion is accelerating, then the balls and rulers will separate from each other. If the rate of expansion is decelerating, the balls and rulers will develop pressure, over time.

One further thought is that a better SR analog of recession rate is to consider the growth of distance, in some inertial frame, of two oppositely moving bodies as a function of their proper time. This is really the way cosmological recession rate is defined. The result is that even in SR, there is no upper bound on this recession rate - it can easily be a trillion times c. Yet the relative velocity of the two bodies is always less than c. That is, comparing recession rate to c as a relative velocity limit is a nonsensical category error.

If the rate of expansion is accelerating, then the balls and rulers will separate from each other. If the rate of expansion is decelerating, the balls and rulers will develop pressure, over time.

One further thought is that a better SR analog of recession rate is to consider the growth of distance, in some inertial frame, of two oppositely moving bodies as a function of their proper time. This is really the way cosmological recession rate is defined. The result is that even in SR, there is no upper bound on this recession rate - it can easily be a trillion times c. Yet the relative velocity of the two bodies is always less than c. That is, comparing recession rate to c as a relative velocity limit is a nonsensical category error.

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