On the construction of quintessential inflation models

Attention has been recently drawn towards models in which inflation and quintessence schemes are unified. In such 'quintessential inflation' models, a unique scalar field is required to play both the role of the inflaton and of the late-time dynamical cosmological constant. We address the issue of the initial conditions for quintessence in this context and find that, in the two explicit examples provided, inflation can uniquely fix them to be in the allowed range for a present day tracking.