On the Lyth bound and single field slow-roll inflation

Abstract

We take a pragmatic, model independent approach to single field slow-roll inflation by imposing conditions to the slow-roll parameter $\epsilon$ and its derivative ${\epsilon }^{\prime }.$ To accommodate the recent (large) values of $r$ reported by the BICEP2 collaboration we advocate for a decreasing $\epsilon$ during most part of inflation. However because at ${\varphi }_{\mathrm{H}}$, at which the perturbations are produced, some $50$ $-$ $60$ e-folds before the end of inflation, $\epsilon$ is increasing we thus require that $\epsilon$ develops a maximum for $\varphi >{\varphi }_{\mathrm{H}}$ and then decrease to small values where most e-folds are produced. The end of inflation might occur trough a hybrid field and a small $\Delta \varphi$ is obtained with a sufficiently thin $\epsilon$ which, however, should not conflict with the curvature of the potential measured by the second slow-roll parameter $\eta$. The conclusion is that under these circumstances $\Delta \varphi$ and the spectral index $n_{\mathrm{s}}$ are restricted to narrow windows of values.

5 pages, 2 figures; V2: added discussion on power spectrum constraints, 3 new references

References in corpus (1)

• BICEP2 implications for single-field slow-roll inflation revisited

Cited by in corpus (2)

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