From Causal Dynamical Triangulations To Astronomical Observations.

This letter discusses phenomenological aspects of dimensional reduction 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 Fermi satellite observations of the GRB 090510 source we find that the energy scale of the dimensional reduction is $E_* > 0.7 \sqrt{4-d_{\rm UV}} \cdot 10^{10}$ GeV at (95 $\%$ CL), where $d_{\rm UV}$ is the value of the spectral dimension in the UV limit. 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 $n_S-1\approx \frac{3 r (d_{\rm UV}-2)}{(d_{\rm UV}-1)r-48}$. Here, $r$ is the tensor-to-scalar ratio. We find that within the considered model, the predicted from CDT deviation from the scale-invariance ($n_S=1$) is in contradiction with the up to date Planck and BICEP2 data.