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Quantum gravity computations suggest the existence of an ultraviolet and aninfrared fixed point where quantum scale invariance emerges as an exactsymmetry. We discuss a particular variable gravity model for the crossoverbetween these fixed points which can naturally account for inflation and darkenergy, using a single scalar field. In the Einstein-frame formulation thepotential can be expressed in terms of Lambert functions, interpolating betweena power-law inflationary potential and a mixed-quintessence potential. For twonatural heating scenarios, the transition between inflation and radiationdomination proceeds through a "graceful reheating" stage. The radiationtemperature significantly exceeds the temperature of big bang nucleosynthesis.For this type of model, the observable consequences of the heating process canbe summarized in a single parameter, the heating efficiency. Our quantitativeanalysis of compatibility with cosmological observations reveals the existenceof realistic models able to describe the whole history of the Universe usingonly a single metric and scalar field and involving just a small number oforder one parameters.

Emergent scale symmetry: Connecting inflation and dark energy