Crossing the Phantom Divide: Dark Energy Internal Degrees of Freedom

TL;DR

The paper addresses the stability problem that arises when dark energy crosses the phantom divide at $w=-1$, showing that single-field models are prone to gravitational instabilities during crossing. It introduces a two-field dark energy construction that preserves energy-momentum conservation and reproduces the predictions of a canonical single-field model to sub-percent accuracy across observables. This approach demonstrates that the dark energy can remain smooth to horizon scales even as $w(a)$ evolves, enabling robust cosmological constraints and likelihood analyses for crossing scenarios. The authors argue that if future data require crossing, it would point to hidden internal degrees of freedom in the dark energy sector, rather than a simple canonical field.

Abstract

Dark energy constraints have forced viable alternatives that differ substantially from a cosmological constant Lambda to have an equation of state w that evolves across the phantom divide set by Lambda. Naively, crossing this divide makes the dark energy gravitationally unstable, a problem that is typically finessed by unphysically ignoring the perturbations. While this procedure does not affect constraints near the favored cosmological constant model it can artificially enhance the confidence with which alternate models are rejected. Similar to the general problem of stability for w< 0, the solution lies in the internal degrees of freedom in the dark energy sector. We explicitly show how to construct a two scalar field model that crosses the phantom divide and mimics the single field behavior on either side to substantially better than 1% in all observables. It is representative of models where the internal degrees of freedom keep the dark energy smooth out to the horizon scale independently of the equation of state.

Figures (2)

• Figure 1: Target versus 2 field model behavior of $w$ and the dark energy observables relative to a fiducial $\Lambda$ model (dotted line, see text). Even in this nearly worst case scenario where $w$ crosses the phantom divide near the pivot point $a \sim 3/4$ or $z\sim 0.3$, the model reproduces the observables to $0.1\%$ accuracy for $w_a>0$ and only a factor of a few larger for $w_a<0$.
• Figure 2: Model predictions for the CMB anisotropy power spectrum relative to a fiducial $\Lambda$CDM model. For models that do not cross the phantom divide, e.g. $w_0=-1$, $w=0.5$, the 2 field model matches the single field predictions to $0.1\%$. For crossing models that mimic a cosmological constant by having $w_n\approx -1$, e.g. $w_0=-1.15$, $w=0.5$, the deviations are essentially indistinguishable.