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 \cite{Shaposhnikov:2008xb}. 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 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, $ω_{DE}^0$. We find bounds for the scalar tilt, $n_s<0.97$, the associated running, $-0.0006 -1$. The relation between $n_s$ and $ω_{DE}^0$ allows us to use the current observational bounds on $n_s$ to further constrain the dark energy equation of state to $0< 1+ω_{DE}^0< 0.02$, which is to be confronted with future dark energy surveys.