KSW criterion in large field models

Abstract We extend the analytic description of complex no-boundary solutions in the context of inflation to large field models. We discuss the Kontsevich–Segal–Witten (KSW) criterion and find it is satisfied in small field models, while in large field models it depends on an integral involving <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mi>V</mml:mi> <mml:mrow> <mml:mi>′</mml:mi> </mml:mrow> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>ϕ</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> over the range of inflation. It follows that although particular models are ruled out, e.g. quadratic inflation, the criterion does not truly constrain inflationary phenomenology since any inflation potential can be completed beyond observable scales so as to satisfy KSW.