The expansion of the universe is proportional to t^(2/3) in a matter dominated universe and t^(1/2) in a radiation dominated universe. Both have power less than 1, so the universe is decelerating.

In a dark energy dominated universe, the expansion is proportional to e^t, so it's exponentially growing, and exponentially accelerating.

https://en.m.wikipedia.org/wiki/Friedmann_equations

In the current universe (which is mostly dark energy, but has still a lot of matter), it's slowly accelerating.

Those equations come from general relativity and are harder to understand and follow though.

To understand the principle, it's best to think of the universe from an observer point of view with newtonian gravity.