A comparison between Jordan and Einstein frames of Brans-Dicke gravity a la loop quantum cosmology

Abstract

It is well known that the Jordan and Einstein frames are equivalent to each other in classical Brans-Dicke theory, provided that one and the same metric is employed for the physical space-time. Nevertheless, it is shown in this paper by cosmological models that the loop quantisation in the two different frames will lead to inequivalent effective theories. Analytical solutions have been found in both frames for the effective loop quantum Brans-Dicke cosmology without potential in: (i) vacuum case, (ii) additional massless scalar field case. In Einstein frame the analytical solution for the Brans-Dicke potential $\propto {\phi }^2$ has been found. In all of those solutions the bouncing evolution of the scale factor has been obtained around Planck regime. The differences between the loop quantisation of the two frames are reflected by: (i) the evolution of the scale factor around the bounce, (ii) the scale of the bounce in the physical Jordan frame.

13 pages, 2 figures

References in corpus (8)

• Quantum Nature of the Big Bang: Improved dynamics
• Inflation scenario via the Standard Model Higgs boson and LHC
• Loop Quantum Cosmology: An Overview
• Extension of loop quantum gravity to $f(R)$ theories
• Loop quantum Brans-Dicke cosmology
• Inflation from non-minimally coupled scalar field in loop quantum cosmology
• Loop cosmological implications of a non-minimally coupled scalar field
• Loop quantum modified gravity and its cosmological application

Cited by in corpus (27)

• Invariant quantities in the scalar-tensor theories of gravitation
• Pre-inflationary universe in loop quantum cosmology
• Higgs inflation with the Holst and the Nieh-Yan term
• Quantum Gravity in the Sky: Interplay between fundamental theory and observations
• A question mark on the equivalence of Einstein and Jordan frames
• Non-adiabatic Evolution of Primordial Perturbations and non-Gaussinity in Hybrid Approach of Loop Quantum Cosmology
• Affine quantisation of the Brans-Dicke theory: Smooth bouncing and the equivalence between the Einstein and Jordan frames
• Pre-inflationary dynamics of Starobinsky inflation and its generization in Loop Quantum Brans-Dicke Cosmology
• The effective dynamics of loop quantum $R^2$ cosmology
• Background dynamics of pre-inflationary scenario in Brans-Dicke loop quantum cosmology
• Strong Dynamics and Inflation: a review
• Quantized Brans Dicke Theory: Phase Transition and Strong Coupling (Large $\omega$) Limit & General Relativity
• Alternative dynamics in loop quantum Brans-Dicke cosmology
• Connection Dynamics for Higher Dimensional Scalar-Tensor Theories of Gravity
• Banks-Zaks Cosmology, Inflation, and the Big Bang Singularity
• Saddle point inflation from $f(R)$ theory
• Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame
• Einstein and Jordan frame correspondence in quantum cosmology: Expansion-collapse duality
• Novel symmetries in Weyl-invariant gravity with massive gauge field
• Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term
• Conservation Law for Massive Scale-Invariant Photons in Weyl-Invariant Gravity
• Bouncing and collapsing universes dual to late-time cosmological models
• Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime
• Nonclassical cosmological dynamics in the low-energy limit of loop quantum scalar-tensor theory
• Aspects of Quantum Cosmology
• Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology
• Mechanics of Isolated Horizons in Scalar-Tensor Theories