  The covariant canonical transformation theory applied to the relativistic
Hamiltonian theory of classical matter fields in dynamical space-time yields a
novel (first order) gauge field theory of gravitation. The emerging field
equations necessarily embrace a quadratic Riemann term added to Einstein's
linear equation. The quadratic term endows space-time with inertia generating a
dynamic response of the space-time geometry to deformations relative to (Anti)
de Sitter geometry. A "deformation parameter" is identified, the inverse
dimensionless coupling constant governing the relative strength of the
quadratic invariant in the Hamiltonian, and directly observable via the
deceleration parameter $q_0$. The quadratic invariant makes the system
inconsistent with Einstein's constant cosmological term, $\Lambda =
\mathrm{const}$. In the Friedman model this inconsistency is resolved with the
scaling ansatz of a "cosmological function", $\Lambda(a)$, where $a$ is the
scale parameter of the FLRW metric. %Moreover, the strain generated by the
quadratic term turns out to act as a geometrical stress. The cosmological
function can be normalized such that with the $\Lambda$ CDM parameter set the
present-day observables, the Hubble constant and the deceleration parameter,
can be reproduced. %We analyze the asymptotics of the such normalized Friedman
equations with respect to both, the fundamental parameters (coupling constants)
and the scale $a$. With this parameter set we recover the dark energy scenario
in the late epoch. The proof that inflation in the early phase is caused by the
"geometrical fluid" representing the inertia of space-time is yet pending,
though.
