Higgs-Dilaton cosmology: Universality vs. criticality
  The Higgs-Dilaton model is able to produce an early inflationary expansion
followed by a dark energy dominated era responsible for the late time
acceleration of the Universe. At tree level, the model predicts a small
tensor-to-scalar ratio ($0.0021\leq r \leq 0.0034$), a tiny negative running of
the spectral tilt ($-0.00057 \leq dn_s/d\ln k \leq -0.00034$) and a nontrivial
consistency relation between the spectral tilt of scalar perturbations and the
dark energy equation of state, which turns out to be close to a cosmological
constant ($0 \leq 1+w_{DE} \leq 0.014$). We reconsider the validity of these
predictions in the vicinity of the critical value of the Higgs self-coupling
giving rise to an inflection point in the inflationary potential. The value of
the inflationary observables in this case strongly depends on the parameters of
the model. The tensor-to-scalar ratio can be large [$r\sim {\cal O}(0.1)$] and
notably exceed its tree-level value. If that happens, the running of the scalar
tilt becomes positive and rather big [$dn_s/d\ln k \sim {\cal O}(0.01)$] and
the equation-of-state parameter of dark energy can significantly differ from a
cosmological constant [$1+w_{DE}\sim {\cal O}(0.1)$].
