Curvature perturbations and anomaly explain dark energy

We investigate the history of dark energy to explain the present magnitude. We assume the dark energy is the residual cosmological constant. The most important channel in the reheating process is gluon pair production by the quantumchromodynamic trace anomaly. We argue that dark energy decays rapidly by gluon pair emissions during the reheating and after the big bang. The reheating temperature is determined by the decay width of dark energy, $\Gamma$, and the Planck mass, $M_\mathrm{p}$, as $\sqrt{M_\mathrm{P}\Gamma} \sim 10^6 \, GeV$. This is a consequence of Friedmann’s equation and the equilibrium condition $\Gamma\sim H$. As the Universe cools below the hadronic scale, the dark energy density is almost frozen. Nevertheless, the dark energy further decreases by emitting two photons. We have estimated the current decay rate of dark energy from the quantum electrodynamic trace anomaly. The consistent solution of the Friedmann equation is in excellent agreement with the observations. The suppression factor of the dark energy scale is the product of the fine structure constant, $\alpha$, and the curvature perturbation, $P$: $10^{-30}=(\alpha^2P/4\pi)^2$. We argue that the conformal symmetry breaking in both ultraviolet and infrared are necessary unless dark energy is subtracted. We also investigate leptogenesis by adding massive right-handed neutrinos: realistic leptogenesis takes place during the reheating process.