On the construction of quintessential inflation models

Attention has been recently drawn towards models in which inflation and qui ntessence 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 t he initial conditions for quintessence in this context and find that, in th e two explicit examples provided, inflation can uniquely fix them to be in the allowed range for a present day tracking.