  Quantum gravity computations suggest the existence of an ultraviolet and an
infrared fixed point where quantum scale invariance emerges as an exact
symmetry. We discuss a particular variable gravity model for the crossover
between these fixed points which can naturally account for inflation and dark
energy, using a single scalar field. In the Einstein-frame formulation the
potential can be expressed in terms of Lambert functions, interpolating between
a power-law inflationary potential and a mixed-quintessence potential. For two
natural heating scenarios, the transition between inflation and radiation
domination proceeds through a "graceful reheating" stage. The radiation
temperature significantly exceeds the temperature of big bang nucleosynthesis.
For this type of model, the observable consequences of the heating process can
be summarized in a single parameter, the heating efficiency. Our quantitative
analysis of compatibility with cosmological observations reveals the existence
of realistic models able to describe the whole history of the Universe using
only a single metric and scalar field and involving just a small number of
order one parameters.
