Sub-Planckian Two-Field Inflation Consistent with the Lyth Bound

The BICEP2 observation of a large tensor-to-scalar ratio, $r = 0.20^{+0.07}{-0.05}$,impliesthattheinflaton$\phi$ in single-field inflation models must satisfy $\varphi \sim 10M_{Pl}$ in order to produce sufficient inflation. This is a problem if interaction terms suppressed by the Planck scale impose a bound $\varphi {}_{\sim }^{<}{M}_{Pl}$. 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 $\mathrm{\Phi }$, we show that a near circular but aperiodic modulation of a $\mathrm{\mid }\mathrm{\Phi }{\mathrm{\mid }}^4$ potential can reproduce the results of ${\varphi }^2$ chaotic inflation for $n_s$ and $r$ while satisfying $|\Phi|; ^{<}{\sim} ; 0.01 M_{Pl}$throughout\mathrm{.}Moregenerally,formodelsbasedona$|\Phi|^{4}$potential,thesimplestsub-Planckianmodelsareequivalentto$\phi^{2}$and$\phi^{4/3}$ chaotic inflation.