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

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 $f(m)=sinm$, 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.

Version 3. 33 pages. Minor change. To appear in General Relativity and Gravitation

References in corpus (10)

• Modified Gravity Theories on a Nutshell: Inflation, Bounce and Late-time Evolution
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Bouncing Cosmologies in Palatini $f(R)$ Gravity
• Effective loop quantum cosmology as a higher-derivative scalar-tensor theory
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• Covariant Effective Action for Loop Quantum Cosmology from Order Reduction
• Effective Actions from Loop Quantum Cosmology: Correspondence with Higher Curvature Gravity
• Variety of $(d+1)$ dimensional Cosmological Evolutions with and without bounce in a class of LQC -- inspired Models
• A Class of LQC--inspired Models for Homogeneous, Anisotropic Cosmology in Higher Dimensional Early Universe

Cited by in corpus (1)

• Non singular M theory Universe in Loop Quantum Cosmology -- inspired Models