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

Understand

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.