Rainbow metric from quantum gravity: anisotropic cosmology

TL;DR

This paper develops effective anisotropic cosmological models with rainbow metrics, revealing a unique deformation parameter that induces isotropic dispersion relations, and connects these findings to loop quantum cosmology.

Contribution

It introduces a novel construction of effective anisotropic models with rainbow metrics, identifying a unique deformation parameter under certain conditions, and relates it to isotropic cases in loop quantum cosmology.

Findings

Discovery of a unique deformation parameter $eta$ in anisotropic models.

Recovery of isotropic dispersion relations under symmetry constraints.

Estimation of the deformation parameter within loop quantum cosmology.

Abstract

In this paper we present a construction of effective cosmological models which describe the propagation of a massive quantum scalar field on a quantum anisotropic cosmological spacetime. Each obtained effective model is represented by a rainbow metric in which particles of distinct momenta propagate on different classical geometries. Our analysis shows that upon certain assumptions and conditions on the parameters determining such anisotropic models, we surprisingly obtain a unique deformation parameter $\beta$ in the modified dispersion relation of the modes. Hence inducing an isotropic deformation despite the general starting considerations. We then ensure the recovery of the dispersion relation realized in the isotropic case, studied in [arXiv:1412.6000], when some proper symmetry constraints are imposed, and we estimate the value of the deformation parameter for this case in loop quantum cosmology context.