Quantized Brans Dicke Theory: Phase Transition and Strong Coupling (Large $\omega$) Limit & General Relativity

Abstract

We show that Friedmann-Robertson-Walker (FRW) geometry with flat spatial section in quantized (Wheeler deWitt quantization) Brans Dicke (BD) theory reveals a rich phase structure owing to anomalous breaking of a classical symmetry, which maps the scale factor $a\mapsto \lambda a$ for some constant $\lambda$. In the weak coupling ($\omega$) limit, the theory goes from a symmetry preserving phase to a broken phase. The existence of phase boundary is an obstruction to another classical symmetry [arXiv:gr-qc/9902083] (which relates two BD theory with different coupling) admitted by BD theory with scale invariant matter content i.e $T^{\mu }{}_{\mu }=0$. Classically, this prohibits the BD theory to reduce to General Relativity (GR) for scale invariant matter content. We show that strong coupling limit of BD and GR both preserves the symmetry involving scale factor. We also show that with a scale invariant matter content (radiation i.e $P=\frac{1}{3}\rho$), the quantized BD theory does reduce to GR as $\omega \to \infty$, which is in sharp contrast to classical behavior. This is a first known illustration of a scenario, where quantized BD theory provides example of anomalous symmetry breaking and resulting binary phase structure. We make a conjecture regarding strong coupling limit of BD theory in generic scenario.

v1: 5 Pages and a lonely line ; 1 figure; v2: 5.7 Pages, a note added, ref. added; emphasized cross-disciplinary interest v3: published version, graph mended

References in corpus (31)

• 4D Gravity on a Brane in 5D Minkowski Space
• The galileon as a local modification of gravity
• From k-essence to generalised Galileons
• The (pseudo)issue of the conformal frame revisited
• Singular Potentials and Limit Cycles
• Renormalization in Quantum Mechanics
• Renormalization of the Inverse Square Potential
• Collapse to Black Holes in Brans-Dicke Theory: II. Comparison with General Relativity
• The Behaviour Of Cosmological Models With Varying-G
• Illusions of general relativity in Brans-Dicke gravity
• Limit cycles in quantum theories
• The omega-tends-to-infinity limit of Brans-Dicke theory
• Anisotropic Scalar-Tensor Cosmologies
• A question mark on the equivalence of Einstein and Jordan frames
• Russian Doll Renormalization Group and Superconductivity
• Russian Doll Renormalization Group, Kosterlitz-Thouless Flows, and the Cyclic sine-Gordon model
• Extended Inflation with a Curvature-Coupled Inflaton
• On limits of spacetimes -- a coordinate-free approach
• On the limit cycle for the 1/r^2 potential in momentum space
• Universality, marginal operators, and limit cycles
• Log-periodic behavior of finite size effects in field theories with RG limit cycles
• On the limits of Brans-Dicke spacetimes: a coordinate-free approach
• On the Asymptotic Behaviour of Cosmological Models in Scalar-Tensor Theories of Gravity
• A comparison between Jordan and Einstein frames of Brans-Dicke gravity a la loop quantum cosmology
• Graceful Exit in Extended Inflation and Implications for Density Perturbations
• Restoring unitarity in anisotropic quantum cosmological models
• Addressing the issue of non-unitarity in anisotropic quantum cosmology
• Renormalization group limit-cycles and field theories for elliptic S-matrices
• Unitary evolution for a quantum Kantowski-Sachs cosmology
• Physical Aspects of Unitary evolution of Bianchi-I Quantum Cosmological Model
• Spin-fermion mappings for even Hamiltonian operators

Cited by in corpus (11)

• Fresh look at the scalar-tensor theory of gravity in Jordan and Einstein frames from undiscussed standpoints
• Affine quantisation of the Brans-Dicke theory: Smooth bouncing and the equivalence between the Einstein and Jordan frames
• Symmetry of Brans-Dicke gravity as a novel solution-generating technique
• Two new approaches to the anomalous limit of Brans-Dicke to Einstein gravity
• Dynamics of a perfect fluid through velocity potentials with aplication in quantum cosmology
• Signatures of Quantum Gravity in the Gravitational Self-Interaction of Photons
• Scalar-tensor gravity from thermodynamic and fluid-gravity perspective
• Quantum cosmology in an anisotropic n-dimensional universe
• Quantum cosmology of scalar-tensor theories and self-adjointness
• Renormalization Group-Improved Gravitational Action: A Lagrangian Framework
• Anisotropic n-dimensional quantum cosmological model with fluid