Would the presence of B-modes in the CMB provide evidence for quantum gravity?

The question whether primordial B-mode detection says something about quantum gravity or not may be subjective, but one can give an unambiguous and objective answer why people were even bringing up quantum gravity in connection with B-modes (and BICEP2). Here, I will try to answer that question.

My answer is mostly based on an excellent (guest) blog post by Liam McAllister, a researcher from Cornell who has published several papers on inflation, and is currently writing a textbook called String theory and inflation together with Daniel Baumann from Cambridge (part of the draft is freely available here).

In the post, McAllister explains that a generic prediction of inflationary models is that the tensor-to-scalar ratio $r$ of the primordial gravitational wave perturbation spectrum is related to the energy density $\rho$ at the time during which inflation occurred:

$$\rho^{1/4}=2.2\times 10^{18}\;\text{GeV}\left(\frac{r}{0.2}\right)^{1/4} $$

Thus, if a detection like BICEP2 determines that $r$ is on the scale of $0.1$, this tells us that we can hope to gain insights into physics that occurred at energy scales that we could have never dreamed of achieving here on Earth (for comparison, the LHC runs at $\sim 10^{4}\;\text{GeV}$). In fact, this energy density is reasonably close to the Planck scale, which is where it is generally expected that quantum gravitational effects should start kicking in. Reminding ourselves that these gravitational waves are theorized to have originated from quantum mechanical fluctuations, we seem to be tantalizingly close to realizing the dream of experimentally accessing regimes where quantum gravity can be probed!

...this, of course, all under the assumption that BICEP2-like results have been demonstrated which, at the moment, seems dubitable at best.