Affine quantisation of the Brans-Dicke theory: Smooth bouncing and the equivalence between the Einstein and Jordan frames

Abstract

In this work, we present a complete analysis of the quantisation of the classical Brans-Dicke Theory using the method of affine quantisation in the Hamiltonian description of the theory. The affine quantisation method is based on the symmetry of the phase-space of the system, in this case the (positive) half-plane, that is identified with the affine group. We consider a FLRW-type spacetime, and since the scale factor is always positive, the affine method seems to be more suited than the canonincal quantisation for our Quantum Cosmology. We find the wave function of the Brans-Dicke universe, and its energy spectrum. A smooth bounce is expected at the semi-classical level in the quantum phase-space portrait. We also adress the problem of equivalence between the Jordan and Einstein frames.

28 pages, 8 figures

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• Quantum Mixmaster as a model of the Primordial Universe
• Primordial Magnetogenesis in a Bouncing Universe
• Canonical Analysis of Brans-Dicke Theory Addresses Hamiltonian Inequivalence between Jordan and Einstein Frames
• Fluid-gravity correspondence in the scalar-tensor theory of gravity: (in)equivalence of Einstein and Jordan frames
• Dynamical black hole in a bouncing universe
• Regular Bouncing Solutions, Energy Conditions and the Brans-Dicke Theory
• Stochastic collapse
• Jordan and Einstein Frames from the perspective of $\omega =-3/2$ Hamiltonian Brans-Dicke theory
• Survival of black holes through a cosmological bounce
• Black hole in asymmetric cosmological bounce
• Fifth forces and frame invariance
• Solving oscillations problems through affine quantization
• Quantum Newtonian cosmology revisited
• Quantum formalism on the plane: POVM-Toeplitz quantization, Naimark theorem and linear polarisation of the light
• Quantization of a Black-Hole Gravity: geometrodynamics and the quantum phase-space formalism
• Affine Quantization of the Harmonic Oscillator on the Semi-bounded domain $(-b,\infty )$ for $b:0\to \infty$
• What can we learn from the conformal noninvariance of the Klein-Gordon equation?
• Affine quantization of the dynamical Reissner--Nordström region