We consider a minimal scale-invariant extension of the Standard Model of particle physics combined with Unimodular Gravity formulated in ( ) .
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 .