Dynamical relaxation of cosmological constant
  A special class of conformal gravity theories is proposed to solve the long
standing problem of the fine-tuned cosmological constant. In the proposed model
time evolution of the inflaton field leaves behind a nearly vanishing, but
finite value of dark energy density of order (a few meV)$^4$ to explain the
late-time accelerating universe. A multiple scalar inflaton field is assumed to
have a conformal coupling to the Ricci scalar curvature in the lagrantian,
which results in, after a Weyl rescaling to the Einstein metric frame,
modification of inflaton kinetic and potential terms along with its coupling to
Higgs fields in the standard model. One may define an effective cosmological
$\Lambda$ function in the Einstein metric frame, which controls, when the
potential is added, a slow-roll inflation and subsequent oscillation at the
potential minimum of a spontaneous symmetry breaking phase. The inflaton
oscillation accompanies particle production towards thermalized hot big-bang
universe. At the same time zero-point quantum fluctuation of second inflaton
field is generated,and its accumulated fluctuation gives rise to a symmetry
restoration, pushing back the inflaton field towards the infinity. This gives a
dynamical relaxation of vanishing effective cosmological constant. Both
inhomogeneous inflaton modes and their collapsed black holes of primordial
origin are good candidates of cold dark matter.
