Dust of Dark Energy

TL;DR

This work introduces the λφ-fluid, a two-scalar theory in which a Lagrange multiplier enforces a constraint between a scalar field and its derivative, so fluid elements move along timelike geodesics while carrying nonzero pressure and, crucially, with zero sound speed. The authors derive two first-order dynamical equations and show the absence of wave-like propagating modes, enabling a dust-like perturbation behavior even with pressure; they compute the Newtonian potential evolution and show it reduces to standard dust growth in the ΛCDM limit. They present explicit cosmological realizations, including a Dusty Dark Energy model that unifies dark matter and dark energy in a single degree of freedom, with a rich set of background evolutions and perturbation dynamics, including scalable attractor solutions and phantom-crossing within a stable classical regime. The model yields potentially observable deviations from ΛCDM in the growth of structure and ISW effects, offering a novel framework for exploring the dark sector and guiding future theoretical and observational studies.

Abstract

We introduce a novel class of field theories where energy always flows along timelike geodesics, mimicking in that respect dust, yet which possess non-zero pressure. This theory comprises two scalar fields, one of which is a Lagrange multiplier enforcing a constraint between the other's field value and derivative. We show that this system possesses no wave-like modes but retains a single dynamical degree of freedom. Thus, the sound speed is always identically zero on all backgrounds. In particular, cosmological perturbations reproduce the standard behaviour for hydrodynamics with vanishing sound speed. Using all these properties we propose a model unifying Dark Matter and Dark Energy in a single degree of freedom. In a certain limit this model exactly reproduces the evolution history of Lambda-CDM, while deviations away from the standard expansion history produce a potentially measurable difference in the evolution of structure.

Figures (3)

• Figure 1: Time evolution of the total effective equation of state for the dark sector. The black solid line represents the evolution in $\Lambda$CDM which is identical to that of the $w_{\text{fin}}=-1$ model. Models with final equations of state $1+w_{\text{fin}}>0$ begin to deviate from matter domination earlier and the transition is slower than $\Lambda$CDM. The opposite is true in phantom models. The evolution is normalised such that the equation of state at $a=1$ matches the best-fit result for the $\Lambda$CDM cosmology as determined by WMAP7 results, $w_{0}=-0.74$Komatsu:2010fb.
• Figure 2: Comparison of the derivative of the effective equation of state for Dusty Dark Energy (Eq. \ref{['LambdaEvolutionWeqConst']}) with that for a dark matter plus dark energy with a constant equation of state, $w$CDM, (Eq. \ref{['WevolutionMixture']}). The magnitude of the derivative determines the duration of the transition between matter domination and the acceleration era. The left panel shows that for $w_{\text{fin}}>-1$, the transition in the DDE model is more rapid than the corresponding $w$CDM model. On the other hand, for phantom $w_{\text{fin}}$ this transition is slower than for the corresponding $w$CDM model, as shown in the panel on the right.
• Figure 3: The comparison of the total growth of perturbation amplitude between Dusty Dark Energy and $\Lambda$CDM. The evolution of the Newtonian potential, $\Phi$, is determined by Eq. \ref{['PhiN']} and deviates by a few percent from its $\Lambda$CDM values by a few percent. This evolution will affect the strength of the ISW signal in the CMB. On the other hand, the evolution of the density perturbation on subhorizon scales is determined by Eq. \ref{['dotRelativeDeltaE']} and is affected much more strongly.