Sub-Planckian two-field inflation consistent with the Lyth bound

The BICEP2 observation of a large tensor-to-scalar ratio, r = 0.20(-0.05)(+0.07), implies that the inflaton phi in single-field inflation models must satisfy phi similar to 10 M-Pl in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound phi less than or similar to M-Pl. Here we consider whether it is possible to have successful sub-Planckian inflation in the case of two-field inflation. The trajectory in field space cannot be radial if the effective single-field inflaton is to satisfy the Lyth bound. By considering a complex field Phi, we show that a near circular but aperiodic modulation of a vertical bar Phi vertical bar(4) potential can reproduce the results of phi(2) chaotic inflation for n(s) and r while satisfying vertical bar Phi vertical bar less than or similar to 0.01 M-Pl throughout. More generally, for models based on a vertical bar Phi vertical bar(4) potential, the simplest sub-Planckian models are equivalent to phi(2) and phi(4/3) chaotic inflation.