  We demonstrate that there exists a large class of action functionals of the
scalar curvature and of the Gauss-Bonnet invariant which are able to relax
dynamically a large cosmological constant (CC), whatever it be its starting
value in the early universe. Hence, it is possible to understand, without
fine-tuning, the very small current value of the CC as compared to its
theoretically expected large value in quantum field theory and string theory.
In our framework, this relaxation appears as a pure gravitational effect, where
no ad hoc scalar fields are needed. The action involves a positive power of a
characteristic mass parameter, M, whose value can be, interestingly enough, of
the order of a typical particle physics mass of the Standard Model of the
strong and electroweak interactions or extensions thereof, including the
neutrino mass. The model universe emerging from this scenario (the "Relaxed
Universe") falls within the class of the so-called LXCDM models of the cosmic
evolution. Therefore, there is a "cosmon" entity X (represented by an effective
object, not a field), which in this case is generated by the effective
functional and is responsible for the dynamical adjustment of the cosmological
constant. This model universe successfully mimics the essential past epochs of
the standard (or "concordance") cosmological model (LCDM). Furthermore, it
provides interesting clues to the coincidence problem and it may even connect
naturally with primordial inflation.
