Lyth Bound, eternal inflation and future cosmological missions

摘要

In this paper we provide a new expression for the variation of the inflatonfield $\Delta\phi$ during the horizon crossing epoch in the context of singlefield slow roll inflationary models. Such an expression represents ageneralization of the well-know Lyth bound. We also explore the consequences ofa detection of permille order of the tensor-to-scalar ratio amplitude, $r$, aswell as an improvement on the estimation of the scalar spectral index, $n_s$and its running $\alpha_s$, by the upcoming CMB polarization experiments thatwill provide plausible constraints on the quantity $\Delta\phi$ during thehorizon exit moment. In addition we discuss the relation between the localvariation of the field and the possibilities of an eternal inflation. Theresults of the analysis are completely model independent.