Cor Bobeldijk (1936–2014), Emeritus Scientific Editor of Nuclear Fusion

[摘要] We examine the third quantization of f(R)-type gravity, based on its effectiveLagrangian in the case of a flat Friedmann–Lemaitre–Robertson–Walkermetric. Starting from the effective Lagrangian, we make a suitable changeof variable and the second quantization, and we obtain the Wheeler–DeWittequation. The third quantization of this theory has been considered. Theuncertainty relation of the universe has been investigated in the example off(R)-type gravity, where f(R) = R2. It has been shown that, at late timesnamely the scale factor of the universe is large, the spacetime does not contradictto become classical, and, at early times namely the scale factor of the universeis small, the quantum effects dominate.