Effective spin foams provide the most computationally efficient spin foam models yet and are therefore ideally suited for applications, e.g., to quantum cosmology. Here, we provide the first effective spin foam computations of a finite time evolution step in a Lorentzian quantum de Sitter universe. We will consider a setup that computes the no-boundary wave function and a setup describing the transition between two finite scale factors. A key property of spin foams is that they implement discrete spectra for the areas. We therefore study the effects that are induced by the discrete spectra. To perform these computations, we had to identify a technique to deal with highly oscillating and slowly converging or even diverging sums. Here, we illustrate that high-order Shanks transformation works very well and is a promising tool for the evaluation of Lorentzian (gravitational) path integrals and spin foam sums.
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Albert Einstein Inst, Max Planck Inst Gravitat Phys, D-14476 Potsdam, GermanyAlbert Einstein Inst, Max Planck Inst Gravitat Phys, D-14476 Potsdam, Germany
Di Tucci, Alice
Lehners, Jean-Luc
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Albert Einstein Inst, Max Planck Inst Gravitat Phys, D-14476 Potsdam, GermanyAlbert Einstein Inst, Max Planck Inst Gravitat Phys, D-14476 Potsdam, Germany
Lehners, Jean-Luc
Sberna, Laura
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Perimeter Inst, 31 Caroline St N, Waterloo, ON N2L 2Y5, CanadaAlbert Einstein Inst, Max Planck Inst Gravitat Phys, D-14476 Potsdam, Germany