| Abstract: |
We propose a solution to the cosmological constant problem using non-linear quantum mechanics. The gravitation of the vacuum energy in linear quantum mechanics is due to the fact that the volume element of the theory is an operator. This non-trivial operator multiplies the energy density, resulting in the gravitation of the vacuum energy. We propose to change the volume element from an operator to the volume element constructed from the expectation value of the metric on the full quantum state of the universe. In this theory, the vacuum energy density multiplies the expectation value which is a c-number function. Thus the vacuum energy no longer gravitates. Despite being a big change to General Relativity, this theory is in concordance with precision tests of gravitation such as tests of the equivalence principle. It also reproduces the observed dynamics of non-linear gravitational systems such as Schwarschild solutions and the evolution of the universe during radiation domination. The simple proposal does not reproduce the observed evolution during matter domination, requiring ad-hoc but realizable fixes to the theory. The theory can potentially be tested in measurements of the expansion history of the universe during matter domination and probes of black hole space-times. This proposal also automatically solves the black hole information problem by creating a firewall at the horizon of a black hole. |
