Inflation, quintessence, and the origin of mass
  In a unified picture both inflation and present dynamical dark energy arise
from the same scalar field. The history of the Universe describes a crossover
from a scale invariant "past fixed point" where all particles are massless, to
a "future fixed point" for which spontaneous breaking of the exact scale
symmetry generates the particle masses. The cosmological solution can be
extrapolated to the infinite past in physical time - the universe has no
beginning. This is seen most easily in a frame where particle masses and the
Planck mass are field-dependent and increase with time. In this "freeze frame"
the Universe shrinks and heats up during radiation and matter domination. In
the equivalent, but singular Einstein frame cosmic history finds the familiar
big bang description. The vicinity of the past fixed point corresponds to
inflation. It ends at a first stage of the crossover. A simple model with no
more free parameters than $\Lambda$CDM predicts for the primordial fluctuations
a relation between the tensor amplitude $r$ and the spectral index
$n,r=8.19(1-n)-0.137$. The crossover is completed by a second stage where the
beyond-standard-model sector undergoes the transition to the future fixed
point. The resulting increase of neutrino masses stops a cosmological scaling
solution, relating the present dark energy density to the present neutrino
mass. At present our simple model seems compatible with all observational
tests. We discuss how the fixed points can be rooted within quantum gravity in
a crossover between ultraviolet and infrared fixed points. Then quantum
properties of gravity could be tested both by very early and late cosmology.
