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Since electromagnetic gauge theory and its generalization (Yang-Mills gauge field theory) have succeeded in quantum field theory and particle physics, it requires that the theory of gravitation also be a gauge field theory under certain local gauge symmetries, e.g., local Lorentz or Poincaré invariance. The discrepancy between unusually large quantum vacuum energy density and observational cosmology may indicate that the generic gravity theory of Einstein is a low-energy phenomenological theory, and a more fundamental theory of gravity might be hidden behind it. A new spin-connection gauge theory for gravitational interaction at high energies (close to the Planck energy scale) is introduced. In such a gravitational gauge field theory, the local Lorentz group is the gauge symmetry group, and the spin-affine connection serves as a non-Abel gauge field (fundamental dynamical variable). A third-order differential equation of metric can be obtained as the gravitational gauge field equation, where the Einstein field equation of gravitation is a first-integral solution. As the vacuum energy density is a constant, the covariant derivative of its energy-momentum tensor unavoidably vanishes. Therefore, the quantum vacuum energy term disappears in the gravitational gauge field equation, and the anomalously large vacuum energy density does not make a practical contribution to gravity. This would enable us to seek for a new route to the longstanding vacuum-energy cosmological constant problem. Some topics relevant to gravitational gauge theory and its applications in cosmology are also addressed. For example, the five-dimensional cosmology within the framework of the present gravitational gauge theory, in which a quasi fluid is emergent, can exhibit the effects of equivalent dark matter and dark energy.

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Swedish physicist Oskar Klein (1894-1977) suggested a vectorial gauge theory and a unified model of electromagnetic and nuclear forces in a conference of physics held in Warsaw, Poland in 1938. These theoretical prescriptions are reviewed in this paper and we shall show that Klein's theory of vectorial gauge field theory is actually a standard Yang-Mills gauge theory, rectifying a conventional viewpoint that Klein's 1938 theory was simply "a bit like the Yang-Mills gauge theory, but it is really not the one". Though Klein did not employ the gauge symmetry concept and Lie group theoretical tool, which were used by Pauli and Yang-Mills in 1953 and 1954, respectively, Klein has adopted covariant derivative, neutrino-electron isospin doublet state and isospin conservation. All these have enabled Klein to be brought to the SU(2) non-Abelian gauge theory. We can, therefore, draw a conclusion that it was Klein who first established the correct formalism of the non-Abelian gauge theory, 15 or 16 years before Pauli or Yang-Mills did. Unfortunately, Klein's work has been misinterpreted by other physicists in the literature. Though Klein was actually the first one to put forward the non-Abelian gauge theory (1938), he has been deprived of such an honor. Instead, in the literature, he was merely acting as a foil in the history of the non-Abelian gauge theory. As a result, even though his unified model of electromagnetic and nuclear forces has included the basic components and framework (except for the Higgs mechanism) of the later electroweak unified model, it has been ignored by physical community. We shall comment on the issues relevant to Klein's vectorial gauge theory, its significance in physics as well as remarks made by other physicists.