Asymptotically de Sitter universe inside a Schwarzschild black hole

Abstract

Extending our previous analysis, we study the interior of a Schwarzschild black hole derived from a partial gauge fixing of the full Loop Quantum Gravity Hilbert space, this time including the inverse volume and coherent state subleading corrections. Our derived effective Hamiltonian differs crucially from the ones introduced in the minisuperspace models. This distinction is reflected in the class of homogeneous bouncing geometries that replace the classical singularity and are labeled by a set of quantum parameters associated with the structure of coherent states used to derive the effective Hamiltonian. By fixing these quantum parameters through geometrical considerations, the post-bounce interior geometry reveals a high sensitivity to the value of the Barbero-Immirzi parameter $\gamma$. Surprisingly, we find that $\gamma\approx 0.274$ results in an asymptotically de Sitter geometry in the interior region, where now a cosmological constant is generated purely from quantum gravitational effects. The striking fact is the exact coincidence of this value for $\gamma$ with the one derived from the SU(2) black hole entropy calculations in Loop Quantum Gravity. The emergence of this value in two entirely unrelated theoretical frameworks and computational setups is strongly suggestive of deep ties between the area gap in Loop Quantum Gravity, black hole physics, and the observable Universe. In connection to the latter, we point out an intriguing relation between the measured value of the cosmological constant and the observed mass in the Universe from a proposal for a spin quantum number renormalization effect associated to the microscopic dynamics.