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.