A theoretical model is proposed in order to explain, via ordinary physics, fundamental aspects of the cold fusion phenomena experimentally observed. These phenomena include unexpected high fusion reaction rates at low temperatures, the paradox of low neutron emission compared to the energy release observed, the cold fusion dependence on critical temperature, neutronic stimulation, and the constitution of nuclei with high electric charge. This theory is based on the hypothesis that a degenerate, cold D12+e- plasma may be created inside lattice defects through a sudden deuteron discharge from a saturated metal lattice. The proposed method is based on the perturbative solution of Vlasov-Poisson kinetic-electric equations. A Fourier transformation of such equations proves that the plasma behaves like an ideal Bose gas of electronically screened deuterons. This approach shows that a high particle density can exist with no pressure increase above the limiting value reached at Bose-Einstein condensation (BEC) and that the electrical repulsion field between positive ions disappears below the critical temperature for BEC. Inside the voids created by defects, the behavior of the cold degenerate plasma below critical temperature suppresses the Coulomb barrier between any pair of ions, in particular those that will fuse. The absence of Coulomb barrier allows one to simply predict fusion reaction rates of the order of those found experimentally and the particle trapping in high-density condensate causing fusion chains. The main reactions involved are D12-T13 and D12-He23. Subsequent fusions of the main reaction products lead to nuclei of greater complexity. A high neutron multiplication factor via deuteron disintegrations is calculated. Neutron bursts, temperature, and pressure excursions are also predicted. Finally, new procedures for inducing such reactions outside metal lattices are suggested.