Using torsion two-form we present a new Lorentz gauge invariant U(1)topological field theory in Riemann–Cartan space–time manifold U4.By virtue of the decomposition theory of U(1) gauge potential and theϕ-mapping topological current theory, it is proven that theU(1) complex scalar field ϕ(x) can be looked upon as theorder parameter field in our Universe, and a set of zero pointsof ϕ(x) create the cosmic strings as the space–time defectsin the early Universe. In the standard cosmology, this complexscalar order parameter field possesses negative pressure, providesan accelerating expansion of Universe, and be able to explain theinflation in the early Universe. Therefore this complex scalarfield is not only the order parameter field created the cosmicstrings in the early universe, but also reasonably behaves as the quintessence, the darkenergy.