# Riello: EPRL radiative corrections only logarithmic in cosmo constant

1. Feb 7, 2013

### marcus

http://arxiv.org/abs/1302.1781
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 infrared8 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 ΛCC expressed in Planck units of area: Λ ≈ ΛCC/l P2 ∼ 10120 .
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

2. Feb 8, 2013

### John86

Re: Riello: EPRL radiative corrections only logarithmic in cosmo const

Is this paper in favour of the Hamber Toriumi result ?

3. Feb 8, 2013

### marcus

Re: Riello: EPRL radiative corrections only logarithmic in cosmo const

Hi John!
I didn't yet get around to posting the abstract of Aldo Riello's paper. I'll do that now.
The reason I mentioned the Hamber Toriumi paper in post #1 in this thread has to do with the fact that a running cosmological constant could turn out to be a liability for a major rival theory (namely Asym Safe QG) if the Hamber Toriumi result holds.

This would presumably NOT pose any inconvenience for LQG, because it does NOT involve Lambda running in any essential way. Riello's paper tentatively suggests that in LQG the dependence on Lambda is comparatively weak (logarithmic).

The paper focuses on a salient case and makes approximations (which are explained in one of the sections). More work could certainly be done along these same lines! Here's the abstract:
http://arxiv.org/abs/1302.1781
Self-Energy in the Lorentzian ERPL-FK Spin Foam Model of Quantum Gravity
Aldo Riello
(Submitted on 7 Feb 2013)
We calculate the most divergent contribution to the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK Spin Foam model of Quantum Gravity. We find that such a contribution is logarithmically divergent in the cut-off over the SU(2)-representation spins when one chooses the face amplitude guaranteeing the face-splitting invariance of the foam.We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the non-commutativity of the EPRL-FK Y-map with the projector onto SL(2,C)-invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, its geometrical interpretation as well as the physical consequences of our result.
55 pages, 8 figures

4. Feb 9, 2013

### MTd2

Re: Riello: EPRL radiative corrections only logarithmic in cosmo const

Hamber Toriumi also considers an effective running lambda.

5. Feb 15, 2013

### marcus

Re: Riello: EPRL radiative corrections only logarithmic in cosmo const

In his ILQGS talk this week, Haggard cited Riello's paper (slide #33, conclusions) in a way that puts it in larger context and notes the paper's significance.

The ILQGS talk set out 3 main questions at the beginning
• Gravitational divergences under control?
• Volume gap robust?
• How does thermalization proceed?
and in the wind-up addressed each of them.

==quote slide #33==
Gravitational divergences
Loop gravity continues to indicate physical cutoffs at the Planck scale:

Robust volume gap due to: chaos & low density of states at low volume

Meanwhile, Riello is finding divergences at large j (large distance) are tamer than first indicated,
only logarithmic: gr-qc/1302.1781

Loop gravity has a coherent and, so far, consistent view of gravitational divergences.
==endquote==
http://relativity.phys.lsu.edu/ilqgs/haggard021213.pdf