An accelerating universe

As mentioned I'm re-reading the Infinite Book and one topic that came up was with regards to the expansion of the universe. The logic presented in simple fashion goes like this:

The universe initially expanded (accelerated), however with no additional force gravity should 'instantly' start to cause everything to collapse.

In everyday terms if I throw a ball into the air as soon as the initial force of my hand is removed and the ball leaves my hand gravity takes over and 'removes' that force from the ball; until there's none left and the only force remaining is gravity and down comes the ball.

Looking at the universe parts are accelerating. That's like throwing a ball in the air and having its speed increase. Explanations are many and the book seems to settle on dark energy/dark matter etc. which are gravitationally repulsive. Spit-balling I threw some other concepts together and asked what if the acceleration is an illusion?


Consider two circles that touch each other at one point. Each circle is 10 light years in diameter and both are collapsing at a steady rate of 1 light year/year. If the centres remain unmoving relative to a third point it would appear that the two circles are moving away from each other. After 1 year they'd be 2 light-years apart after 2 years they'd be 4 light years etc. every year the gap would increase by 2 light-years. The rate of change of distance is 0 (always 2 light-years/year) so it's a steady speed with no acceleration.

Consider however living inside one of the circles. Measure to the 'edge' at the start and it's 10 light-years, after a year it's 9 light-years. Easy to see what's happening, but what if everything in the circle was collapsing at the same rate? Measure to an edge and it's 10 light-years measure again in one year's time and it's still 10 light-years because your measuring tools have also shrunk. What would the distances between our two circles now look like?

After 1 year a distance of 2.2 light-years
... 2 years ... 5 light-years
... 3 years ... 8.5 light-years
... 4 years ... 13.3 light-years

The distance is increasing and the rate of distance is also increasing; our two circles are 'accelerating' away from each other.

Of course I've simplified a lot here. How do we define the two centres as being fixed? What happens to time (as a property of space) within the collapsing circles? A whole host of concerns that need to be taken into account. I just thought it was an interesting thought experiment.