Isotropic LQC and LQC--inspired Models with a massless scalar field as Generalised Brans--Dicke theories

TL;DR

This paper investigates how generalized Brans-Dicke theories can serve as effective models for Loop Quantum Cosmology (LQC) and LQC-inspired models with a massless scalar field, establishing specific relations between their functions.

Contribution

It demonstrates the conditions under which generalized Brans-Dicke theories can replicate LQC effective equations in isotropic cosmology and relates their defining functions.

Findings

Near the bounce, the scalar field $\

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Abstract

We explore whether generalised Brans -- Dicke theories, which have a scalar field $\Phi$ and a function $\omega(\Phi)$, can be the effective actions leading to the effective equations of motion of the LQC and the LQC--inspired models, which have a massless scalar field $\sigma$ and a function $f(m) \;$. We find that this is possible for isotropic cosmology. We relate the pairs $(\sigma, f)$ and $(\Phi, \omega)$ and, using examples, illustrate these relations. We find that near the bounce of the LQC evolutions for which $f(m) = sin \; m$, the corresponding field $\Phi \to 0$ and the function $\omega(\Phi) \propto \Phi^2 \;$. We also find that the class of generalised Brans -- Dicke theories, which we had found earlier to lead to non singular isotropic evolutions, may be written as an LQC--inspired model. The relations found here in the isotropic cases do not apply to the anisotropic cases, which perhaps require more general effective actions.