Will the Universe eventually stop expanding Sorry if this is a naive question, not being even a part qualified physicist in any way shape or form.
I've read that the universe is expanding and the rate of expansion is increasing. The assumption being that it will continue expanding indefinitely.
However isn't there another possibility.
Let me illustrate my question prior to posing it.
If I throw a ball in the air.. it accelerates away from my hand and keeps accelerating, until momentum is lost and it starts to slow down, eventually falling back to my hand. 
Is it possible that the expanding universe is also in the throws (excuse the pun) of an initial acceleration phase, prior to that acceleration slowing and eventually the universe compressing?
Again sorry if its a stupid observation!
 A: The ball, in fact, is always accelerating downward, even though it is moving up for the first part of its trip.  A ball that kept accelerating upward would just fly up out of the atmosphere.  
A: Carroll (2004) introducing the standard Friedmann-Lemaitre-Robertson-Walker model, shows that this will become clear in a formula that sheds light on the fate of the cosmos:

To determine the dividing line between perpetual expansion and eventual recollapse, note 
  that collapse requires the Hubble parameter to pass through zero as it changes from positive to negative. The scale factor $a_{*}$ at which this turnaround occurs can be found by setting $H=0$ in the Friedmann equation.

Which after rearranging gives 

$\Omega_{\Lambda0}a_{*}^3+(1-\Omega_{M0}-\Omega_{\Lambda})a_{*}+\Omega_{M0}=0$

Where $\Omega's$ are the density parameters associated with vacuum energy and matter in the cosmos defined as $\frac {8 \pi G \rho}{3H^2}.$ 
The cubic equation in terms of $a_{*}$, the scale factor, gives us predictive power. 
If there is no real positive solution to it then we have to expect “perpetual” expansion. 
And the current experimental data indeed favor such an open ended cosmic future. 
