We work out an effective theory of accelerated expansion for the background to describe general phenomena of inflation and acceleration (dark energy) in the universe. Our aim is to determine from theoretical grounds, in a physically motivated and model-independent way, which and how many (free) parameters are needed to broadly capture the physics of a theory describing the background of cosmic acceleration. Our goal is to make as much transparent as possible the physical interpretation of the parameters describing the expansion. We show that, at leading order, there are five independent parameters, of which one can be constrained via general relativity tests. The other four parameters need to be determined by observing and measuring the cosmic expansion rate only, H(z). Therefore, we suggest that future cosmology surveys focus on obtaining an accurate value as possible measurement of H(z) to constrain the nature of accelerated expansion.