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Fractal Space-Time from Spin-Foams

Elena Magliaro
(
- Marseille, CPT
)
,
Claudio Perini
(
- Marseille, CPT and
- Rome III U.
)
,
Leonardo Modesto
(
- Perimeter Inst. Theor. Phys.
)

Nov, 2009

5 pages

e-Print:

0911.0437 [gr-qc]

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Abstract: (arXiv)

In this paper we perform the calculation of the spectral dimension of spacetime in 4d quantum gravity using the Barrett-Crane (BC) spinfoam model. We realize this considering a very simple decomposition of the 4d spacetime already used in the graviton propagator calculation and we introduce a boundary state which selects a classical geometry on the boundary. We obtain that the spectral dimension of the spacetime runs from

\approx 2

to 4, across a

\approx 1.5

phase, when the energy of a probe scalar field decreases from high

E \lesssim E_P/25

to low energy. The spectral dimension at the Planck scale

E \approx E_P

depends on the areas spectrum used in the calculation. For three different spectra

l_P^2 \sqrt{j(j+1)}

,

l_P^2 (2 j+1)

and

l_P^2 j

we find respectively dimension

\approx 2.31

, 2.45 and 2.08.

space-time: fractal
spin: foam
dimension: spectrum

References(22)

Figures(3)

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(
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(
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)
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(
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)
,
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- Perimeter Inst. Theor. Phys.
)

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Eugenio Bianchi
(
- Marseille, CPT
)
,
Elena Magliaro
(
- Marseille, CPT and
- Rome III U.
)
,
Claudio Perini
(
- Marseille, CPT and
- Rome III U.
)

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(
- Rome U. and
- Marseille, CPT
)
,
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(
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)

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Emanuele Alesci
(
- Marseille, CPT and
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)
,
Eugenio Bianchi
(
- Pisa, Scuola Normale Superiore and
- Marseille, CPT
)
,
Carlo Rovelli
(
- Marseille, CPT
)

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Eugenio Bianchi
(
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)
,
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(
- Bologna U. and
- INFN, Bologna and
- Marseille, CPT
)

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•
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