# From causal dynamical triangulations to astronomical observations

Abstract : This essay discusses phenomenological aspects of the diffusion time dependence of the spectral dimension predicted by the Causal Dynamical Triangulations (CDT) approach to quantum gravity. The deformed form of the dispersion relation for the fields defined on the CDT space-time is reconstructed. Using the \emph{Fermi} satellite observations of the GRB 090510 source we find that the energy scale of the dimensional reduction is $E_* > 6.7 \cdot 10^{10}$ GeV at (95 $\%$ CL). By applying the deformed dispersion relation to the cosmological perturbations it is shown that, for a scenario when the primordial perturbations are formed in the UV region, the scalar power spectrum $\mathcal{P}_S \propto k^{n_S-1}$ where $n_S-1\approx \frac{3r(d_{\rm UV}-2)}{r+48(d_{\rm UV}-3)}$. Here, $d_{\rm UV} \approx 2$ is obtained from the CDT value of the spectral dimension in the UV limit and $r$ is the tensor-to-scalar ratio. We find that, the predicted deviation from the scale-invariance ($n_S=1$) is in contradiction with the up to date \emph{Planck} and \emph{BICEP2} results.
Type de document :
Pré-publication, Document de travail
LPSC15089. 10 pages, 1 figure. 2015
Domaine :

http://hal.in2p3.fr/in2p3-01138052
Contributeur : Emmanuelle Vernay <>
Soumis le : mercredi 1 avril 2015 - 08:42:20
Dernière modification le : jeudi 11 janvier 2018 - 06:13:08

### Identifiants

• HAL Id : in2p3-01138052, version 1
• ARXIV : 1503.08794

### Citation

J. Mielczarek. From causal dynamical triangulations to astronomical observations. LPSC15089. 10 pages, 1 figure. 2015. 〈in2p3-01138052〉

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