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Spinfoam transition amplitudes only depend lightly on cosmological constant. This is looking good (especially in view of the Hamber Toriumi paper that just appeared.)

==quote Aldo Riello's new paper, page 4==

The ERPL-FK model can also be extended to the case of General Relativity

**with cosmological constant**in a non-trivial way, both in its Euclidean [25, 26, 27] and Lorentzian [28, 27] versions. Such an extension uses the q-deformed Lorentz group, with the q-deformation parameter related to the cosmological constant, and turns out to be (perturbatively) finite. The existence of a finite model does not mean that the issue of large radiative corrections can be ignored: it may still happen that some higher order graphs have large amplitudes and therefore drive a renormalization flow, possibly even through phase transitions. Qualitatively, the scale which imposes the infrared

^{8}finiteness of the theory is given by the cosmological constant, which is of the order of the radius of the Universe; therefore, at our - or smaller - length scales, it can be considered as infinite for practical purposes (but see comments in the conclusions).

In this paper, in order to study the simplest EPRL-FK divergence, we introduce a cut-off Λ to the SU (2) representations j . The physical meaning of such a cut-off is that of imposing a maximal value for the area operator, which can be thought as the introduction of a finite size for the Universe itself. A bound to the area operator is typical of the q-deformed version of the EPRL-FK model. Therefore the introduction of such a cut-off can be hoped to be a simple implementation of the main feature of the q-deformed EPRL-FK model within the much more manageable non-deformed version. At the light of this (qualitative) correspondence, the cal- culation of this paper can be also given a more physical, though possibly naive, interpretation in which the cut-off Λ is a physical quantity and corresponds - at least in order of magnitude - to the cosmological constant Λ

_{CC}expressed in Planck units of area: Λ ≈ Λ

_{CC}/l

_{P}

^{2}∼ 10

^{120}.

The goal of this work is to calculate the most divergent contribution to the self-energy of the EPRL-FK spin foam model...

Footnote 8: Here, the term “infrared” must be understood as relating to large physical distances; analogously, an “ultraviolet” cut-off, in the sense of a short distance cut-off, is naturally present in any spin foam models, via the existence of the area gap [29]. It must however be kept in mind, that the roles of the words “infrared” and “ultraviolet” are interchanged