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

Abstract

The BICEP2 observation of a large tensor-to-scalar ratio, $r=0.20_{-0.05}^{+0.07}$, implies that the inflaton $\varphi$ 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 $\Phi$, we show that a near circular but aperiodic modulation of a $|\Phi {|}^4$ potential can reproduce the results of ${\varphi }^2$ chaotic inflation for $n_s$ and $r$ while satisfying $|\Phi |{}_{\sim }^{<}0.01M_{Pl}$ throughout. More generally, for models based on a $|\Phi {|}^4$ potential, the simplest sub-Planckian models are equivalent to ${\varphi }^2$ and ${\varphi }^{4/3}$ chaotic inflation.

7 pages, 2 figures. Some additional references and discussion. Version published in JCAP

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