Recovering P(X) from a canonical complex field

Abstract

We study the correspondence between models of a self-interacting canonical complex scalar field and P (X)-theories/shift-symmetric k-essence. Both describe the same background cosmological dynamics, provided that the amplitude of the complex scalar is frozen modulo the Hubble drag. We compare perturbations in these two theories on top of a fixed cosmological background. The dispersion relation for the complex scalar has two branches. In the small momentum limit, one of these branches coincides with the dispersion relation of the P (X)-theory. Hence, the low momentum phase velocity agrees with the sound speed in the corresponding P (X)-theory. The behavior of high frequency modes associated with the second branch of the dispersion relation depends on the value of the sound speed. In the subluminal case, the second branch has a mass gap. On the contrary, in the superluminal case, this branch is vulnerable to a tachyonic instability. We also discuss the special case of the P (X)-theories with an imaginary sound speed leading to the catastrophic gradient instability. The complex field models provide with a cutoff on the momenta involved in the instability.

Dark Matter and Baryon Asymmetry from the very Dawn of Universe

“…Thus, for M H we end up with the adiabatic perturbations of the complex field by the end of inflation. Note that the results of the present section are generic and stay valid for fairly arbitrary steep potentials V [11].…”

“…First assume that it is sterile, and thus serves as a DM candidate. In that case, the energy density (11) should correspond to the observed abundance of DM. Namely,…”

Critical collapse in K-essence models

“…For example, considering K = (αX 1/2β − A) β , the EoS is P = Aρ (β−1)/β , a polytropic law similar to various models describing neutron stars (without the anisotropic stress tensor). Notice also that K(X) models can be related to canonical complex scalar field theories [30] where the potential of the complex scalar field is defined by K(X). More than an equivalence between these theories, it is an extension or UV completion.…”

“…But in all cases, it was claimed in [53] that the solution would be infinitely strongly coupled and therefore could not be trusted within the regime of validity of this effective field theory. It would be interesting to see if the recent extension [30] of these theories suffer from the same problem.…”

Emergence of ghosts in Horndeski theory

“…Note that one can construct an extension of the k-essence theory to include a second dynamical field, so that the formation of caustics can be avoided[15,16]. For such a theory, the low-energy modes effectively behave as k-essence, while at high energy the kinetic structure becomes canonical and thus caustic-free.…”