Hi Roger.

I have done some calcs on those earliest galaxies that you PM'd me about. They possibly formed in the epoch z ~ 19 to z ~ 9, or roughly 200 to 500 million years after the BB. At 200 My age, it was probably just a dark matter halo that formed (including some matter particles that would later form stars). If I take that halo as having the total mass of our MW galaxy (with dark matter included), it comes to some M ~ 3 x 10⁴² kg, with a halo radius of some 10 thousand light years, or r ~ 10²⁰ meters (20% of the MW, according to the article).

A single particle orbiting just outside such a halo would experience a gravitational acceleration of order 10^-9 g (one nano-g). The cosmic tidal acceleration during that epoch would have been inward, enhancing gravity, but its magnitude worked out to only ~ 10^-13 g (100 femto-g), hence negligible compared to gravity.

A question that you asked is: would this tiny force, operating over millions of years not have compacted the galaxies? The paper that I referred you to (http://arxiv.org/abs/gr-qc/0602098) states that all that will happen is that the angular orbit velocity will be increased to compensate for the additional contracting force. The increase ratio is given as:

(ω₀ - ω)/ω = √[1 - sign(a''/a) (r/r_crit)³]

where a is the expansion factor, a'' the (negative) acceleration of expansion of that period, r the orbital radius and r_crit the radius where the gravitational and cosmic tidal forces are of equal magnitude for that mass.

Taking the worst case, at z~19 (when the dark matter is reckoned to have formed), a''/a ~ -112 Gy^-1. The crucial value is however r/r_crit ~ 0.03, meaning that it is only at ~ 30 times the radius of the galactic halo that cosmic tidal forces equal gravity. This gives the utterly negligible order of magnitude: (ω₀ - ω)/ω ~ 10^-5.

Hence, any notion that cosmic tidal forces could have caused those stars to whiz around the galaxy at more than twice the velocity of the solar system's velocity is false. Likewise, cosmic tidal forces do not contribute to the compactness of early galaxies.

-J