  Quantum cosmology based on Lorentzian path integrals is a promising avenue.
However, many previous works allow non-Lorentzian configurations by integrating
the squared scale factor over the whole real line. Here we show that
restricting the minisuperspace path integral to Lorentzian configurations with
positive squared scale factor can significantly change the expectation values.
In addition, this enables the study of causal horizons and their quantum
fluctuations, and achieves singularity avoidance trivially by excluding
singular minisuperspace geometries as non-Lorentzian. The results indicate that
semiclassical saddle point approximation is not always valid in truly
Lorentzian quantum cosmology. As a consequence, related works on the tunnelling
and no-boundary proposals, bouncing cosmology, and the quantum origin of
inflation etc. need to be reexamined.
