Vertex Expansion for the Bianchi I model

Understand

A perturbative expansion of Loop Quantum Cosmological transitions amplitudes of Bianchi I models is performed.

• Following the procedure outlined in [1,2] for isotropic models, it is shown that the resulting expansion can be written in the form of a series of amplitudes each with a fixed number of transitions mimicking a spin foam expansion.
• This analogy is more complete than in the isotropic case, since there are now the additional anisotropic degrees of freedom which play the role of `colouring' of the spin foams.
• Furthermore, the isotropic expansion is recovered by integrating out the anisotropies.