Amjad Ashoorioon (IPM)

Ghost Condensate Dark Energy with Sextic Dispersion Relation in de Sitter Spacetime

We study the ghost condensate (GC) with a sixth-order dispersion relation $\omega^2 \sim k^6$, within the effective field theory framework of dark energy. Unlike the GC with a quartic dispersion relation, we find that in the sextic case, the correction to the Newtonian potential depends explicitly on the space and time variations of the matter density. At very late times, the resulting modification exhibits oscillatory behavior at distances of order $\frac{M_{\rm Pl}}{M^2}$, at the timescale $\frac{M^4}{M_{\rm Pl}^3}$, where $M^2$ corresponds to the scale of the ghost condensate. We analyze scalar and tensor perturbations in both FLRW and de Sitter backgrounds, and show that the gravitational potential receives non-trivial, scale-dependent modifications arising from the inclusion of higher-derivative operators in the effective action. In the FLRW background, we compute the effective gravitational constant $G_{\rm eff}$ and the gravitational slip parameter, $\gamma$, in the sub-horizon limit $k/a \gg H$, revealing their explicit dependence on spatial scales.  Additionally, we demonstrate that the speed of gravitational waves becomes frequency dependent, with significant deviations from luminal propagation arising at momenta near $\frac{M_{\rm Pl}}{\sqrt{|\sigma_1|}}$, where $\sigma_1$ is the coefficient of the operator $\gamma^{ij} \nabla_i K_{lr} \nabla_j K^{lr}$ in the unitary gauge action.