Lorentzian quantum cosmology with $R^2$ correction

Understand

Quantum mechanical transition amplitudes directly tells the probability of each transition and which one is more favourable.

• Path-integrals offers a systematic methodology to compute this quantum mechanical process in a consistent manner.
• Although it is not complicated in simple quantum mechanical system but defining path-integral legitimately becomes highly nontrivial in the context of quantum-gravity, where apart from usual issues of renormalizability, regularisation, measure, gauge-fixing, boundary conditions, one still has to define the sensible integration contour for convergence.
• Picard-Lefschetz (PL) theory offers a unique way to find a contour of integration based on the analysis of saddle points and the steepest descent/ascent flow lines in the complex plane.