The Quantization Conditions in Curved Spacetime and Uncertainty Driven Inflation

Abstract

An alternative inflationary model is proposed predicated upon a consideration of the form of the uncertainty principle in a curved background spacetime. An argument is presented suggesting a possible curvature dependence in the correct commutator relations for a quantum field in a classical background which cannot be deduced by simply extrapolation from the flat spacetime theory. To assess the possible consequences of this dependence, we apply the idea to a scalar field in a closed Friedmann-Robertson-Walker background, using a simple model for the curvature dependence (along the way, a previous result obtained by Bunch (1980) for the adiabatically expanded wave function is corrected). The result is a time-dependent cosmological constant, producing a vast amount of inflation that is independent of the mass of the matter field or its effective potential. Furthermore, it is seen that the field modes are initially zero for all wavelengths and come into being as the universe evolves. In this sense, the universe creates its contents out of its own expansion. At the end of the process, the matter field is far from equilibrium and essentially reproduces the initial conditions for the New Inflationary Model.