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

Abstract

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), ${w}_{\mathrm{DE}}^{0}$. We find bounds for the scalar tilt, ${n}_{s}<0.97$, the associated running, $\ensuremath{-}0.0006<d\mathrm{ln}{n}_{s}/d\mathrm{ln}k\ensuremath{\lesssim}\ensuremath{-}0.000\text{ }15$, and for the scalar-to-tensor ratio, $0.0009\ensuremath{\lesssim}r<0.0033$, which will be critically tested by the results of the Planck mission. For the equation of state of dark energy, the model predicts ${w}_{\mathrm{DE}}^{0}>\ensuremath{-}1$. The relation between ${n}_{s}$ and ${w}_{\mathrm{DE}}^{0}$ allows us to use the current observational bounds on ${n}_{s}$ to further constrain the dark-energy equation of state to $0<1+{w}_{\mathrm{DE}}^{0}<0.02$, which is to be confronted with future dark-energy surveys.