The New Ekpyrotic Ghost

TL;DR

The paper analyzes the viability of the new ekpyrotic ghost scenario, which aims to resolve the cosmological singularity through NEC violation by coupling ekpyrotic dynamics to a ghost condensate with a stabilizing higher-derivative term. Through both Hamiltonian and Lagrangian quantization, the authors reveal an additional negative-energy ghost mode (an Ostrogradski ghost) and derive the full dispersion relations, showing that the stabilization term introduces fundamental vacuum instabilities that cannot be simply cured by treating it as a UV correction. They compute the energy-momentum tensor and FRW dynamics, demonstrating that Y, related to the higher-derivative term, dynamically decouples only in a strict limit, and that the bounce becomes fragile or unachievable in generic evolution. Moreover, the study argues that vacuum decay induced by ghost–particle production is catastrophically divergent, and proposed UV completions or field-redefinition tricks do not resolve the core inconsistencies, casting serious doubt on the viability of the ghost-augmented ekpyrotic framework for solving the singularity problem.

Abstract

The new ekpyrotic scenario attempts to solve the singularity problem by involving violation of the null energy condition in a model which combines the ekpyrotic/cyclic scenario with the ghost condensate theory and the curvaton mechanism of production of adiabatic perturbations of metric. The Lagrangian of this theory, as well as of the ghost condensate model, contains a term with higher derivatives, which was added to the theory to stabilize its vacuum state. We found that this term may affect the dynamics of the cosmological evolution. Moreover, after a proper quantization, this term results in the existence of a new ghost field with negative energy, which leads to a catastrophic vacuum instability. We explain why one cannot treat this dangerous term as a correction valid only at small energies and momenta below some UV cut-off, and demonstrate the problems arising when one attempts to construct a UV completion of this theory.

Figures (5)

• Figure 1: The "new ekpyrotic potential," see Fig. 3 in Buchbinder:2007ad and Fig. 6 in Buchbinder:2007tw. The cosmological evolution in this model results in a universe with a permanently growing rate of expansion after the bounce, which is unacceptable.
• Figure 2: An improved potential which leads to a bounce followed by a normal cosmological evolution. We do not know whether this extremely fine-tuned potential can be derived from any realistic theory.
• Figure 3: The behavior of the Hubble constant $H(t)$ near the bounce, which occurs near $t = 18$. To verify the stability of the universe during the bounce, one would need to perform an additional investigation taking into account the ghost field oscillations shown in Fig. \ref{['fig:Figb2']}.
• Figure 4: Ekpyrotic ghost field oscillations.
• Figure 5: Vacuum decay with production of ghosts $\xi$ and usual particles $\gamma$ interacting with each other by the graviton exchange.