Partial UV Completion of $P(X)$ from a Curved Field Space

Abstract

The $k$-essence theory is a prototypical class of scalar-field models that already gives rich phenomenology and has been a target of extensive studies in cosmology. General forms of shift-symmetric $k$-essence are known to suffer from formation of caustics in a planar-symmetric configuration, with the only exceptions of canonical and DBI-/cuscuton-type kinetic terms. With this in mind, we seek for multi-field caustic-free completions of a general class of shift-symmetric $k$-essence models in this paper. The field space in UV theories is naturally curved, and we introduce the scale of the curvature as the parameter that controls the mass of the heavy field(s) that would be integrated out in the process of EFT reduction. By numerical methods, we demonstrate that the introduction of a heavy field indeed resolves the caustic problem by invoking its motion near the would-be caustic formation. We further study the cosmological application of the model. By expanding the equations with respect to the curvature scale of the field space, we prove that the EFT reduction is successfully done by taking the limit of infinite curvature, both for the background and perturbation, with gravity included. The next leading-order computation is consistently conducted and shows that the EFT reduction breaks down in the limit of vanishing sound speed of the perturbation.

arXiv comment24 pages, 4 figures (10 plots)

Cited by in corpus (9)

• Stability of the fundamental quasinormal mode in time-domain observations against small perturbations
• UV completions, fixing the equations and nonlinearities in $k$-essence
• DeWitt wave function in Hořava-Lifshitz cosmology with tensor perturbation
• Some disquisitions on cosmological 2-form dualities
• A new nonlinear instability for scalar fields
• Cuscuton Bounce Beyond the Linear Regime: Bispectrum and Strong Coupling Constraints
• Generalizing the Swampland: Embedding $P(X,\phi )$ Inflationary Theories in a Curved Multi-field Space
• A Bit Rate Bound on Superluminal Communication
• Positivity vs. Lorentz-violation: an explicit example