Spin foam propagator: A new perspective to include a cosmological constant

Abstract

In recent years, the calculation of the first non-vanishing order of the metric 2-point function or graviton propagator in a semiclassical limit has evolved as a standard test for the credibility of a proposed spin foam model. The existing results of spinfoam graviton propagator rely heavily on the so-called double scaling limit where spins $j$ are large and the Barbero-Immirzi parameter $\gamma$ is small such that the area $A\propto j\gamma$ is approximately constant. However, it seems that this double scaling limit is bound to break down in models including a cosmological constant. We explore this in detail for the recently proposed model by Haggard, Han, Kaminski and Riello and discuss alternative definitions of a graviton propagator, in which the double scaling limit can be avoided.

15 pages, 1 figure

References in corpus (10)

• LQG vertex with finite Immirzi parameter
• Flipped spinfoam vertex and loop gravity
• The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex
• Area-angle variables for general relativity
• The complete LQG propagator: II. Asymptotic behavior of the vertex
• Gauge-invariant coherent states for Loop Quantum Gravity I: Abelian gauge groups
• Gauge-invariant coherent states for Loop Quantum Gravity II: Non-abelian gauge groups
• Einstein Equation from Covariant Loop Quantum Gravity in Semiclassical Continuum Limit
• A note on the geometrical interpretation of quantum groups and non-commutative spaces in gravity
• Loop-Quantum-Gravity Simplicity Constraint as Surface Defect in Complex Chern-Simons Theory

Cited by in corpus (4)

• Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator
• Semiclassical Limit of New Path Integral Formulation from Reduced Phase Space Loop Quantum Gravity
• Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-${\Delta }_3$ complex
• A saddle-point finder and its application to the spin foam model