  The discovery of dark energy (DE) as the physical cause for the accelerated
expansion of the Universe is the most remarkable experimental finding of modern
cosmology. However, it leads to insurmountable theoretical difficulties from
the point of view of fundamental physics. Inflation, on the other hand,
constitutes another crucial ingredient, which seems necessary to solve other
cosmological conundrums and provides the primeval quantum seeds for structure
formation. One may wonder if there is any deep relationship between these two
paradigms. In this work, we suggest that the existence of the DE in the present
Universe could be linked to the quantum field theoretical mechanism that may
have triggered primordial inflation in the early Universe. This mechanism,
based on quantum conformal symmetry, induces a logarithmic,
asymptotically-free, running of the gravitational coupling. If this evolution
persists in the present Universe, and if matter is conserved, the general
covariance of Einstein's equations demands the existence of dynamical DE in the
form of a running cosmological term whose variation follows a power law of the
redshift.
