Accelerating universe explained by constant expansion?

[RussB]

Why is the accelerating expansion of the universe not explained simply by the perspective of acceleration caused by a constant (non accelerating) universal expansion? Let's take two particles (X,Y) in a 1d expanding universe where it expands universally by 1 unit per per unit time. O represents empty space.

T=0: XY
T=1: XOY
T=2: XOOOY
T=3: XOOOOOOOOOY

Even though the universe is expanding in a completely constant way, any given particle would perceive every other particle (not bound by some sufficiently strong force) to be accelerating away.

 

[Orodruin]

What you are describing is constant expansion rate, not constant expansion. Accelerating expansion means that the second derivative of the scale factor is positive. Constant expansion rate (Hubble parameter) means that the scale factor grows exponentially and hence corresponds to an accelerated expansion - as you have deduced. In a non accelerating expansion (coasting universe), the scale factor grows linearly and the Hubble parameter is decreasing with time.