We consider a minimal scale-invariant extension of the standard model of particle physics combined with unimodular gravity formulated in [M. Shaposhnikov and D. Zenhausern, Phys. Lett. B 671, 187 (2009).]. This theory is able to describe not only an inflationary stage, related to the standard model Higgs field, but also a late period of dark-energy domination, associated with an almost massless dilaton. A number of parameters can be fixed by inflationary physics, allowing us to make specific predictions for any subsequent period. In particular, we derive a relation between the tilt of the primordial spectrum of scalar fluctuations, n(s), and the present value of the equation of state parameter of dark energy (DE), w(DE)(0). We find bounds for the scalar tilt, n(s) < 0: 97, the associated running, -0.0006 < dlnn(s) = dlnk less than or similar to -0.000 15, and for the scalar-to-tensor ratio, 0.0009 less than or similar to r < 0.0033, which will be critically tested by the results of the Planck mission. For the equation of state of dark energy, the model predicts w(DE)(0) > -1. The relation between n(s) and w(DE)(0) allows us to use the current observational bounds on n(s) to further constrain the dark-energy equation of state to 0 < 1 + w(DE)(0) < 0: 02, which is to be confronted with future dark-energy surveys.