The perfect Planck spectrum of the observed cosmic microwave background radiation indicates that our universe must be in thermal equilibrium. The dark sector of the universe should also be in the same equilibrium state with dark matter and dark energy coupled to each other and emits gravitational phonon blackbody radiation which is the main component of the cosmic background radiation. In the radiation-dominated era such gravitational radiation should be the majority species of the cosmic medium. Instead of the ideal fluid assumed by the standard cosmological model ΛCDM, the universe has to be taken as a thermodynamic system consisting of gravitationally connected dark energy and matter. Besides particle dynamics, statistical thermodynamics is also necessary for understanding the cosmological constitution and evolution history. As an alternative to ΛCDM we constructed a dark-energy-matter-coupled (DEMC) cosmological model. Based on the relativistic mass-energy relation, conservation law of energy, Lagrange's equation with variable potential function, mean-field theory of continuous phase transition, and the symmetry principle of the kinetic coefficients, we deduced dynamic equations of the expansion of a DEMC universe with three parameters. These equations reproduce the observed history of the rate of expansion of our universe.