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

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