Null Impact of the Null Energy Condition in Current Cosmology

TL;DR

This paper clarifies the role of the Null Energy Condition (NEC) in cosmology by emphasizing that NEC concerns the total stress-energy via $\rho_{tot}+P_{tot}\ge 0$ and does not constrain individual components. It shows that current cosmological data do not indicate NEC violation, even though the dark-energy equation of state can cross the phantom boundary $w_{de}=-1$, and it presents a toy model of 'dark-sector confusion' where misestimating a subdominant component can mimic phantom crossing without NEC violation. The authors categorize crossing scenarios into 'elephant' (unified multi-field or modified gravity models) and 'chimera' (disparate components) and discuss how future probes of $w_0$, $w_a$, growth of structure, and lensing can distinguish these possibilities. Overall, the work clarifies how to interpret phantom crossing in light of NEC and current data and guides the search for viable dark-energy theories.

Abstract

We clarify the role of the oft-misunderstood Null Energy Condition (NEC) in the context of the current cosmological data. In particular, the NEC implies the sum of the total energy density and pressure satisfies $ρ_{tot}+P_{tot} \ge 0$; the energy conditions do not apply separately to individual components of the cosmological fluid. Consequently, we show that under the current best-fit cosmological model no violation of the NEC takes place, past or future. Further, growth in the energy density of an individual component cannot be used to signal violation of the NEC. We illustrate these points with a worked example whereby misestimation of the matter density leads to a phase during which $ρ_{de} + P_{de} < 0$ for the effective dark energy, followed by a phantom crossing and subsequent $ρ_{de} + P_{de} > 0$. At no time is the NEC violated. We also introduce ``elephant'' and ``chimera'' classes of physics for crossing $w_{de}=-1$.

Figures (4)

• Figure 1: The equation of state for various components are shown: total (solid black), thawing quintessence (solid blue), thawing quintessence (X matter -- dashed blue), effective dark energy (solid red), cosmological constant (dot-dashed black). The phantom crossing occurs near $z \sim 0.5$.
• Figure 2: The range of parameters $\Omega_X$ and $w_{Q0}$ that yield a phantom crossing at $z = 0.5 \pm 0.05$ lies between the dashed lines. For simplicity, all other parameters are held fixed.
• Figure 3: Our universe is far from violating NEC, with curves labeled by $w_{\rm tot}$. The current constraints lie roughly along the red line indicating mirage dark energy, with the best fit to current data at $w_0\approx-0.7$, $w_a\approx1$, and hence $w_{\rm tot}\approx-0.53$. Here $\Omega_m=0.3$.
• Figure 4: As Figure \ref{['fig:necpast']}, but covering all times, including the future. Again, NEC will not be violated globally at any time.