Lorentzian quantum cosmology

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Using Picard-Lefschetz theory we show that the Lorentzian path integral forms a good starting point for quantum cosmology which avoids the conformal factor problem present in Euclidean gravity. We study the Lorentzian path integral for a homogeneous and isotropic model with a positive cosmological constant. Applied to the “no-boundary” proposal, we show that this leads to the inverse of the result obtained by Hartle and Hawking. Including a inflation field, the Lorentzian path integral prefers to start at the 'top of the hill' leading to good initial conditions for slow roll inflation. However, when including gravitons the fluctuations seem to be unstable.