Higgs-dilaton cosmology: From the early to the late Universe

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, nₛ, and the present value of the equation of state parameter of dark energy (DE), wDE⁰. We find bounds for the scalar tilt, nₛ<0.97, the associated running, -0.0006<dlnnₛ/dlnk-0.000 15, and for the scalar-to-tensor ratio, 0.0009r<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 wDE⁰>-1. The relation between nₛ and wDE⁰ allows us to use the current observational bounds on nₛ to further constrain the dark-energy equation of state to 0<1+wDE⁰<0.02, which is to be confronted with future dark-energy surveys.