B-modes and the Nature of Inflation
  Observations of the cosmic microwave background do not yet determine whether
inflation was driven by a slowly-rolling scalar field or involved another
physical mechanism. In this paper we discuss the prospects of using the power
spectra of scalar and tensor modes to probe the nature of inflation. We focus
on the leading modification to the slow-roll dynamics, which entails a sound
speed $c_s$ for the scalar fluctuations. We derive analytically a lower bound
on $c_s$ in terms of a given tensor-to-scalar ratio $r$, taking into account
the difference in the freeze-out times between the scalar and tensor modes. We
find that any detection of primordial B-modes with $r > 0.01$ implies a lower
bound on $c_s$ that is stronger than the bound derived from the absence of
non-Gaussianity in the Planck data. For $r \gtrsim 0.1$, the bound would be
tantalizingly close to a critical value for the sound speed, $(c_s)_\star =
0.47$ (corresponding to $(f_{\rm NL}^{\rm equil})_\star = -0.93$), which we
show serves as a threshold for non-trivial dynamics beyond slow-roll. We also
discuss how an order-one level of equilateral non-Gaussianity is a natural
observational target for other extensions of the canonical paradigm.
