From Causal Dynamical Triangulations To Astronomical Observations

TL;DR

This paper explores the phenomenological implications of dimensional reduction in quantum gravity via Causal Dynamical Triangulations, reconstructs related dispersion relations, and compares predictions with astronomical observations, finding significant constraints.

Contribution

It connects CDT quantum gravity predictions with observational data, deriving bounds on the energy scale of dimensional reduction and analyzing effects on cosmological perturbations.

Findings

Lower bound on the energy scale of dimensional reduction: $E_* > 0.7 imes 10^{10}$ GeV.

Predicted deviations in the scalar spectral index are incompatible with Planck and BICEP2 data.

The model constrains the UV spectral dimension based on observational limits.

Abstract

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.