  The Higgs-Dilaton model is a scale-invariant extension of the Standard Model
non-minimally coupled to gravity and containing just one additional degree of
freedom on top of the Standard Model particle content. This minimalistic
scenario predicts a set of measurable consistency relations between the
inflationary observables and the dark-energy equation-of-state parameter. We
present an alternative derivation of these consistency relations that
highlights the connections and differences with the $\alpha$-attractor
scenario. We study in how far these constraints allow to distinguish the
Higgs-Dilaton model from $\Lambda$CDM and $w$CDM cosmologies. To this end we
first analyze existing data sets using a Markov Chain Monte Carlo approach.
Second, we perform forecasts for future galaxy surveys using a Fisher matrix
approach, both for galaxy clustering and weak lensing probes. Assuming that the
best fit values in the different models remain comparable to the present ones,
we show that both Euclid- and SKA2-like missions will be able to discriminate a
Higgs-Dilaton cosmology from $\Lambda$CDM and $w$CDM.
