Consistency Relation for multifield inflation scenario with all loop contributions

TL;DR

This paper derives a comprehensive all-loop order inequality relating non-Gaussianity parameters in multifield inflation, extending previous loop-corrected relations and providing a more robust test for inflationary models.

Contribution

It extends the Suyama-Yamaguchi inequality to include all loop corrections, offering a more complete consistency relation for multifield inflation scenarios.

Findings

Derived an all-loop order inequality for non-Gaussianity parameters.

Confirmed the inequality reduces to the original in single-field models.

Provides a new tool to test inflationary models against observational data.

Abstract

The consistency relation between non-linear parameters $f_{NL}$ and $\tau_{NL}$ characterizing Non-Gaussianity generated during the inflationary period have been emerged as a useful tool which have a possibility to rule out a large class of inflationary models all at once. In our previous work, we extended the Suyama-Yamaguchi inequality up to 1-loop corrections. In this paper, we derive an inequality extended up to {\it all} loop corrections which has the same expression with the original Suyama-Yamaguchi inequality, $\tau_{NL} \geq (6/5f_{NL})^2$, where the equality is not satisfied in the case of single field models any more.