Generalizing the swampland: Embedding P(X,φ) inflationary theories in a curved multifield space

Wei-Chen Lin,Rance M Solomon

doi:10.1103/physrevd.103.063533

Abstract

We study the general embedding of a $ P(X, \varphi) $ inflationary theory into a two-field theory with curved field space metric, which was proposed as a possible way to examine the relation between de Sitter Swampland conjecture and \textit{k}-inflation. We show that this embedding method fits into the special type of two-field model in which the heavy field can be integrated out at the full action level. However, this embedding is not exact due to the upper bound of the effective mass of the heavy field. We quantify the deviation between the speed of sound calculated via the $ P(X, \varphi) $ theory and the embedding two-field picture to next leading order terms. We especially focus on the first potential slow roll parameter defined in the two-field picture and obtain an upper bound on it.

Highlights

In inflationary cosmology [1,2,3,4,5,6,7], scalar fields have been extensively used for modeling the inflaton field causing an exponential expansion in the very early universe which sets up the initial condition of the hot big bang
Over the past several years, a series of so-called swampland conjectures have been proposed concerning the consistency of effective scalar field models with a UV completion in a theory of quantum gravity [10], including the de Sitter swampland conjecture
We conclude that to have a small deviation between the speed of sound derived from the PðX; φÞ theory and the corresponding two-field model, those two terms must be small compared to a leading term proportional to Λ6 in Eq (95)

Summary

INTRODUCTION

In inflationary cosmology [1,2,3,4,5,6,7], scalar fields have been extensively used for modeling the inflaton field causing an exponential expansion in the very early universe which sets up the initial condition of the hot big bang. The two-field extension has to satisfy the energy conditions where this embedding is valid This requirement gives an upper bound of the parameter Λ in the action (3). We conclude that to have a small deviation between the speed of sound derived from the PðX; φÞ theory and the corresponding two-field model, those two terms must be small compared to a leading term proportional to Λ6 in Eq (95). We obtain εV and the speed of sound cS derived from the embedded two-field model in terms of quantities defined in PðX; φÞ to the leading order. From the condition that the two-field model and PðX; φÞ should give a similar speed of sound, we conclude that the εV can only be dominated by the leading term proportional to Λ6 in a large turning scenario.

Multifield models with nontrivial field space metric

The gelaton scenario

NEXT TO THE LEADING ORDER CALCULATION AND εV

CONCLUSION