Generalizing the Swampland: Embedding $P(X,\phi )$ Inflationary Theories in a Curved Multi-field Space

Abstract

We study the general embedding of a $P(X,\phi )$ 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 $P(X,\phi )$ 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.

17 pages. (V2: typos corrected and references added.)

References in corpus (8)

• On the Geometry of the String Landscape and the Swampland
• The Effective Field Theory of Inflation
• Observational Signatures and Non-Gaussianities of General Single Field Inflation
• Mass hierarchies and non-decoupling in multi-scalar field dynamics
• Heavy fields, reduced speeds of sound and decoupling during inflation
• Strongly Coupled Perturbations in Two-Field Inflationary Models
• Effective field theory of weakly coupled inflationary models
• A Positive Energy Theorem for P(X,phi) Theories

Cited by in corpus (1)

• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme