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The attractive behaviour of ultra-slow-roll inflation

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It is often claimed that the ultra-slow-roll regime of inflation, where the dynamics of the inflaton field are friction dominated, is a non-attractor and/or transient. In this work we carry out a phase-space analysis of ultra-slow roll in an arbitrary potential, V(). We show that while standard slow roll is always a dynamical attractor whenever it is a self-consistent approximation, ultra-slow roll is stable for an inflaton field rolling down a convex potential with MPl V''>|V'| (or for a field rolling up a concave potential with MPl V''<−|V'|). In particular, when approaching a flat inflection point, ultra-slow roll is always stable and a large number of \efolds may be realised in this regime. However, in ultra-slow roll,  is not a unique function of  as it is in slow roll and dependence on initial conditions is retained. We confirm our analytical results with numerical examples.
Original languageEnglish
Article number048
JournalJournal of Cosmology and Astroparticle Physics
Issue number08
Publication statusPublished - 31 Aug 2018


  • 1806.09553v2

    Rights statement: This is an author-created, un-copyedited version of an article published in Journal of Cosmology and Astroparticle Physics. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at

    Accepted author manuscript (Post-print), 3.21 MB, PDF document

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