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,
$\omega_{DE}^0$. We find bounds for the scalar tilt, $n_s<0.97$, the associated
running, $-0.0006<d\ln n_s/d\ln k\lesssim-0.00015$, and for the
scalar-to-tensor ratio, $0.0009\lesssim r<0.0033$, which will be critically
tested by the results of the Planck mission. For the equation of state of dark
energy, the model predicts $\omega_{DE}^0>-1$. The relation between $n_s$ and
$\omega_{DE}^0$ allows us to use the current observational bounds on $n_s$ to
further constrain the dark energy equation of state to $0< 1+\omega_{DE}^0<
0.02$, which is to be confronted with future dark energy surveys.
