Topological Induced Gravity

We propose a topological model of induced gravity (pregeometry) where both Newton's coupling constant and the cosmological constant appear as integration constants in solving field equations. The matter sector of a scalar field is also considered, and by solving field equations it is shown that various types of cosmological solutions in the FRW universe can be obtained. A detailed analysis is given of the meaning of the BRST transformations, which make the induced gravity be a topological field theory, by means of the canonical quantization analysis, and the physical reason why such BRST transformations are needed in the present formalism is clarified. Finally, we propose a dynamical mechanism for fixing the Lagrange multiplier fields by following the Higgs mechanism. The present study clearly indicates that the induced gravity can be constructed at the classical level without recourse to quantum fluctuations of matter and suggests an interesting relationship between the induced gravity and the topological quantum field theory.