Can the dark energy equation-of-state parameter w be less than -1?

TL;DR

This work investigates whether dark-energy models with $w<-1$ (phantom energy) can be internally consistent. By treating phantom fields as effective field theories with a momentum cutoff, the authors analyze classical energy conditions, cosmological evolution, and linear perturbations, finding that transient phantom phases can be phenomenologically viable but stability beyond linear order is challenging. A quantum-field-theory decay-rate calculation shows that, without a cutoff, phantom states exhibit catastrophic vacuum decay; with a cutoff and mild symmetry, decay can be sufficiently slow only if the cutoff is $\lesssim 100$ MeV. Overall, the results cast doubt on many naive phantom constructions and emphasize the need for explicit, low-energy new physics to ensure stability, otherwise observers should be cautious about interpreting $w<-1$ from data.

Abstract

Models of dark energy are conveniently characterized by the equation-of-state parameter w=p/ρ, where ρis the energy density and p is the pressure. Imposing the Dominant Energy Condition, which guarantees stability of the theory, implies that w \geq -1. Nevertheless, it is conceivable that a well-defined model could (perhaps temporarily) have w<-1, and indeed such models have been proposed. We study the stability of dynamical models exhibiting w<-1 by virtue of a negative kinetic term. Although naively unstable, we explore the possibility that these models might be phenomenologically viable if thought of as effective field theories valid only up to a certain momentum cutoff. Under our most optimistic assumptions, we argue that the instability timescale can be greater than the age of the universe, but only if the cutoff is at or below 100 MeV. We conclude that it is difficult, although not necessarily impossible, to construct viable models of dark energy with w<-1; observers should keep an open mind, but the burden is on theorists to demonstrate that any proposed new models are not ruled out by rapid vacuum decay.

Figures (8)

• Figure 1: Shaded regions in the $\rho$-$p$ plane are those which obey the designated energy conditions. Illustrated are the Weak Energy Condition (WEC), Null Energy Condition (NEC), Dominant Energy Condition (DEC), Null Dominant Energy Condition (NDEC), the Strong Energy Condition (SEC), and the condition $w\geq -1$. Definitions of each condition are found in the text.
• Figure 2: The gaussian potential energy of (\ref{['potential']}). The phantom scalar will evolve to the top of the hill and oscillate around the maximum.
• Figure 3: Evolution of the density parameters in radiation ($\Omega_{\rm R}$), matter ($\Omega_{\rm M}$), and the phantom field ($\Omega_\phi$).
• Figure 4: Evolution of the phantom field $\phi$ as a function of the scale factor.
• Figure 5: Evolution of the equation of state parameter $w$ for the phantom field as a function of the scale factor.