(b,v)-type variables for black to white hole transitions in effective loop quantum gravity

Understand

Quantum gravity effects in effective models of loop quantum gravity, such as loop quantum cosmology, are encoded in the choice of so-called polymerisation schemes.

• Physical viability of the models, such as an onset of quantum effects at curvature scales near the Planck curvature, severely restrict the possible choices.
• An alternative point of view on the choice of polymerisation scheme is to choose adapted variables so that the scheme is the simplest possible one, known as $\mu_0$-scheme in loop quantum cosmology.
• There, physically viable models with $\mu_0$-scheme polymerise the Hubble rate $b$ that is directly related to the Ricci scalar and the matter energy density on-shell.