Extended Effective Field Theory of Dark Energy: Ghost Condensate Dark Energy with Sextic Dispersion Relation in de Sitter Spacetime

TL;DR

This paper extends the effective field theory of dark energy by analyzing ghost condensates with sixth-order dispersion relations, revealing modifications to gravitational potential and wave speed in de Sitter spacetime.

Contribution

It introduces a sixth-order dispersion relation for ghost condensates and explores its implications on gravitational potential and wave speed modifications.

Findings

Newtonian potential correction depends on matter density evolution

Oscillatory behavior occurs at specific distance and time scales

Gravitational wave speed becomes frequency-dependent near certain momenta

Abstract

We continue our studies of the ghost condensate (GC) with sixth-order dispersion relation. Contrary to the GC with quartic dispersion relation, we find that the correction to the Newtonian potential explicitly depends on the space and time dependence of matter density. At late times when the Newtonian potential becomes time-independent, one obtains similar oscillatory behavior at the distance $\frac{M_\textrm{Pl}}{M^2}$, but this time at the time scale $\frac{M^4}{M_\textrm{Pl}^3}$, where $M^2$ is the ghost field velocity. We also show that the speed of gravitational wave is modified in a frequency dependent manner at momenta close to $\frac{M_\textrm{Pl}}{\sqrt{|\sigma_1|}}$, where $\sigma_1$ is the coefficient of $\gamma^{ij} \nabla_i K_{lr} \nabla_j K^{lr}$ operator in the unitary gauge action.