Birth of an Isotropic and Homogeneous Universe with a Running Cosmological Constant

The present work discusses the birth of the Universe via quantum tunneling through a potential barrier, based on quantum cosmology, taking into account a running cosmological constant. We consider the Friedmann-Lemaître-Robertson-Walker (FLRW) metric with positively curved spatial sections ($k = 1$) and the matter content is a dust perfect fluid. The model was quantized by the Dirac formalism, leading to a Wheeler-DeWitt equation. We solve that equation both numerically and using a WKB approximation. We studied the behavior of tunneling probabilities $TP_{WKB}$ and $TP_{int}$ by varying the energy $E$ of the dust perfect fluid, the phenomenological parameter $\nu$, the present value of the Hubble function $H_0$ and the constant energy density $\rho^0_\Lambda$, all the last three parameters associated with the time-varying cosmological constant.