Astrophysics > Cosmology and Nongalactic Astrophysics
[Submitted on 16 Mar 2015 (v1), last revised 27 Apr 2015 (this version, v2)]
Title:Lyth bound revisited
View PDFAbstract:Imposing that the excursion distance of inflaton in field space during inflation be less than the Planck scale, we derive an upper bound on the tensor-to-scalar ratio at the CMB scales, i.e. $r_{*,max}$, in the general canonical single-field slow-roll inflation model, in particular the model with non-negligible running of the spectral index $\alpha_s$ and/or the running of running $\beta_s$. We find that $r_{*,max}\simeq 7\times 10^{-4}$ for $n_s=0.9645$ without running and running of running, and $r_{*,max}$ is significantly relaxed to the order of ${\cal O}(10^{-2}\sim 10^{-1})$ in the inflation model with $\alpha_s$ and/or $\beta_s\sim +{\cal O}(10^{-2})$ which are marginally preferred by the Planck 2015 data.
Submission history
From: Qing-Guo Huang [view email][v1] Mon, 16 Mar 2015 03:55:25 UTC (143 KB)
[v2] Mon, 27 Apr 2015 04:05:41 UTC (228 KB)
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