Could dark energy be vector-like?

TL;DR

This work examines whether a vector field can drive the current phase of cosmic acceleration while preserving the observed isotropy, by introducing a cosmic triad of three orthogonal vector fields with a self-interaction V(A^a^2). The background dynamics exhibit tracking attractors and a de Sitter attractor when the triad dominates, enabling w_A to approach -1 and potentially fall below -1 for tachyonic potentials, though the onset of acceleration requires tuning of model parameters. A key finding is that the perturbation theory in the presence of a triad violates the decomposition theorem: scalar, vector, and tensor modes couple, and the triad can source vector and tensor perturbations, with stability remaining robust during inflation, radiation, and matter domination but potentially unstable during late-time acceleration. The results suggest vector dark energy via a triad is a viable phenomenological candidate, but quantum stability of tachyonic vectors and full metric-perturbation analysis remain essential for assessing viability and possible links to CMB anomalies.

Abstract

In this paper I explore whether a vector field can be the origin of the present stage of cosmic acceleration. In order to avoid violations of isotropy, the vector has be part of a ``cosmic triad'', that is, a set of three identical vectors pointing in mutually orthogonal spatial directions. A triad is indeed able to drive a stage of late accelerated expansion in the universe, and there exist tracking attractors that render cosmic evolution insensitive to initial conditions. However, as in most other models, the onset of cosmic acceleration is determined by a parameter that has to be tuned to reproduce current observations. The triad equation of state can be sufficiently close to minus one today, and for tachyonic models it might be even less than that. I briefly analyze linear cosmological perturbation theory in the presence of a triad. It turns out that the existence of non-vanishing spatial vectors invalidates the decomposition theorem, i.e. scalar, vector and tensor perturbations do not decouple from each other. In a simplified case it is possible to analytically study the stability of the triad along the different cosmological attractors. The triad is classically stable during inflation, radiation and matter domination, but it is unstable during (late-time) cosmic acceleration. I argue that this instability is not likely to have a significant impact at present.

Figures (6)

• Figure 1: A plot of $w_A$, equation (\ref{['eq:wattractor']}), for (from top to bottom) $\beta=1/2$ (radiation domination), $\beta=2/3$ (dust domination) and $\beta=15$ (nearly de Sitter inflation).
• Figure 2: A phase diagram of the system (\ref{['eq:xandy']}) for $n=1/2$. The units are arbitrary. The diagram clearly shows that all phase trajectories converge to the single de Sitter attractor at constant $A$ and $H$.
• Figure 3: Triad energy density (in units of today's critical energy density) versus $\log_{10} (1+z)$ for the interaction (\ref{['eq:interaction1']}). Shown is the energy density of vector dark energy for four sets of initial conditions (continuous lines). For reference, the energy densities of radiation (dash-dotted) and dust (dotted) are also displayed. Note that despite the big difference in the initial value of the energy density (50 orders of magnitude), the present value of the dark energy density parameter still is $\Omega_{DE}\approx 0.72$.
• Figure 4: A plot of the triad equation of state for the same initial conditions and interaction as in figure \ref{['fig:rho']}. The attractors are easily identified by their constant value of $w_A$, which can be read off figure \ref{['fig:wattractor']}. For one set of initial conditions, the system reaches first the radiation attractor, then proceeds to the dust attractor and finally to the de Sitter attractor. For another, the system does not reach the radiation attractor, but does reach the dust one before continuing to the de Sitter solution. And lastly, for yet a different one the universe barely reaches the transition to the de Sitter attractor just in time. For all initial conditions, $w_{A}\approx -0.87$ today.
• Figure 5: Triad energy density (in units of today's critical energy density) versus $\log_{10} (1+z)$ for the second model (\ref{['eq:interaction2']}). For reference, the energy densities of radiation (dash-dotted) and dust (dotted) are also displayed. The shown trajectories share the same initial value of $A$, though the initial values of $B$ are different. The present value of the dark energy density parameter is $\Omega_{DE}\approx 0.72$.