Cosmology of a Scalar Field Coupled to Matter and an Isotropy-Violating Maxwell Field

TL;DR

This work introduces Doubly Coupled Quintessence (DCQ), a cosmological model where a scalar field φ is coupled both to matter and to a Maxwell-type vector field, with the background spacetime allowed to be anisotropic via a Bianchi I geometry. Using a dynamical-systems approach, the authors identify seven isotropic and six anisotropic fixed points, including novel scaling solutions like AφMDE(a4) and AφDE(a6) that can drive matter- and dark-energy-dominated epochs with small shear. In the strong-vector-coupling regime they show viable cosmologies closely approaching ΛCDM and delineate four representative trajectories connecting radiation, matter, and acceleration phases; CMB quadrupole bounds imply very tight constraints on the coupling ratios and potential slopes. The results demonstrate that late-time isotropy is achievable across a wide parameter range, while still allowing anisotropic epochs that could yield distinctive observational signatures, motivating further perturbative studies. Overall, DCQ provides a rich, testable framework linking high-energy couplings to cosmological evolution with both isotropic and anisotropic phases.

Abstract

Motivated by the couplings of the dilaton in four-dimensional effective actions, we investigate the cosmological consequences of a scalar field coupled both to matter and a Maxwell-type vector field. The vector field has a background isotropy-violating component. New anisotropic scaling solutions which can be responsible for the matter and dark energy dominated epochs are identified and explored. For a large parameter region the universe expands almost isotropically. Using that the CMB quadrupole is extremely sensitive to shear, we constrain the ratio of the matter coupling to the vector coupling to be less than 10^(-5). Moreover, we identify a large parameter region, corresponding to a strong vector coupling regime, yielding exciting and viable cosmologies close to the LCDM limit.

Figures (3)

• Figure 1: Figure a) shows the parameter space ($\lambda$,$Q_{\! A}$) of the model for the slice $Q_{\! M}=0.1$. Each region is labeled by the fix-point that is an attractor in that region. The green shaded region is the accelerated part of the attractors. For $Q_{\! M}=-0.1$ the plot is similar except that (i6) is the stable fix-point also in the regions labeled (i5) and (a4). Figure b) shows the the same for the slice $Q_{\! M}=-3.3$, a case to be discussed in section \ref{['chpresent']}.
• Figure 2: The phase flow and dynamics for four different sets of parameters (written in the figure), but with the same initial conditions close to the concordance radiation saddle $\text{RDE(i2)}$. The four set of parameters give examples on each of the four different types of trajectories described in section \ref{['chdynamics']}. In each simulation (labeled a-d) the first figure in the corresponding column shows the phase flow (displaying the relevant fix-points that exists there), the second figure is a logarithmic plot of the time evolution of the dynamical variables, the third figure is similar with linear y-axis (it is then no point to plot the vector and shear since they are too small visually), and the fourth figure compares $\Omega_m$, $\Omega_r$ and $\Omega_V$ to a $\Lambda$CDM simulation that starts with the same initial conditions ($\delta_i = |\Omega_i / \Omega_i^{\lambda\text{CDM}} -1|$ ). In the phase flow diagram the shear axis is normalized such that the fix-point that has the largest shear is positioned at $x=1$ (for instance a4$\Sigma$ is the shear at $\text{A}\phi\text{MDE(a4)}$ which can be looked up in table \ref{['case1']}).
• Figure 3: Simulation where the present universe is a a global attractor represented by $\text{(i6)}_{\!\phi m}$ with $\Omega_\phi\simeq 0.7$ and $\Omega_m\simeq 0.3$. The parameters used are $Q_{\! M}=-3.3$, $\lambda=2.2$ and $Q_{\! A}=-100$.