Viability of phantom dark energy as a quantum field in first-order perturbation theory of FLRW spacetime

Abstract

In the standard cosmological framework of the 0th-order FLRW metric and the use of perfect fluids in the stress-energy tensor, dark energy with an equation-of-state parameter $w < -1$ (known as phantom dark energy) implies negative kinetic energy and vacuum instability when modeled as a scalar field. However, the accepted values for present-day $w$ from Planck and WMAP9 include a significant range of values less than $-1$. A flip of the sign in front of the kinetic energy term in the Lagrangian remedies the negative kinetic energy but introduces ghostlike instabilities, which perhaps may be rendered unobservable, but certainly not without great cost to the theory. Staying within the confines of observational constraints and general relativity, we treat dark energy as a quantum scalar field in the background of this 1st-order FLRW space-time, find an approximation for the Green's function, and calculate the expectation value of the field's kinetic energy for $w<-1$ using adiabatic expansion to renormalize and obtain a finite value. We find that the kinetic energy is positive for values of $w$ less than $-1$ in 0th- or 1st-order FLRW space, thus giving more theoretical credence to observational values of $w<-1$ and demonstrating that phantom dark energy does not categorically have negative kinetic energy. For a nonminimal coupling parameter $\xi=0$, kinetic energy is positive for $w \gtrsim -1.22$, which includes virtually all values of constant $w$ allowed by cosmological data constraints, and more negative values of $w$ give positive kinetic energy for non-zero values of $\xi$. Also, our results are generally applicable for a massive free field or a field with a small potential in a 0th- or 1st-order FLRW background dominated by a fluid with a constant $w$. [abridged]