  We present a cosmological model of an early-time scenario that incorporates a
relaxation process of the would-be large vacuum energy, followed by a reheating
era connecting to the standard hot big bang universe. Avoiding fine-tuning the
cosmological constant is achieved by the dynamics of a scalar field whose
kinetic term is modulated by an inverse power of spacetime curvature. While it
is at work against radiative corrections to the dark energy, this mechanism
alone would wipe out not only the vacuum energy but also all other matter
contents. Our present work aims to complete the scenario by exploiting a
null-energy-condition violating sector whose energy is eventually transferred
to a reheating sector. We provide an explicit example of this process and thus
a concrete scenario of the cosmic onset that realizes the thermal history of
the Universe with a negligible cosmological constant.
