Accelerating Cosmologies with an Anisotropic Equation of State

TL;DR

The paper investigates cosmologies with an anisotropic dark energy equation of state in a Bianchi type I background, parameterized by the equation of state $w$ and skewness parameters $(\delta,\gamma)$ with possible coupling $Q$ to matter. It analyzes the resulting dynamical system, identifies late-time attractors including isotropic and anisotropic accelerating solutions, and develops a vector-field realization as a proof of concept. It then derives observational signatures in the CMB quadrupole via the background anisotropy and in the SNIa luminosity-distance relation, highlighting tight quadrupole constraints and potential degeneracies with time-varying skewness. The work shows that anisotropic dark energy can be cosmologically viable, may explain some CMB anomalies, and provides concrete predictions for future SNIa surveys to differentiate between isotropic and anisotropic late-time expansion.

Abstract

If the dark energy equation of state is anisotropic, the expansion rate of the universe becomes direction-dependent at late times. We show that such models are not only cosmologically viable but that they could explain some of the observed anomalies in the CMB, and shed some light into the coincidence problem. The possible anisotropy can then be constrained by studying its effects on the luminosity distance-redshift relation inferred from several observations. A vector field action for dark energy is also presented as an example of such possibility.

Figures (4)

• Figure 1: Asymptotic state from an Einstein-deSitter stage. The future fate depends on the dark energy properties $w$ and $\delta$ and is classified into three possibilities. If $\delta+w > 0$, the isotropically expanding dust domination (solution (\ref{['flrw_s']}) for which $U=0$) continues forever. Otherwise, the universe will end up expanding anisotropically and either dominated by dark energy (solution (\ref{['domi_s']}) for which $U=1$) or exhibiting a scaling property (solution (\ref{['scal_s']}) for which $0<U<1$).
• Figure 2: A minimally coupled vector field satisfying the quadrupole constraint. The solid (black) line is the dark energy density fraction $U$, the dashed (red) line is the effective equation of state of the universe $w_{eff}$, and the dash-dotted (blue) line describes the evolution of eccentricity, $E=500e_y^2$. The potential is a double-power law $V = m A^2 + \lambda A^{-4}$. The dynamics of the field is such that though there are significant anisotropies, the eccentricity at the present is close to zero. This may be achieved with different power-law potentials, but requires fine-tuning of the mass scales $m$ and $\lambda$.
• Figure 3: Limits on the (constant) skewness parameters of dark energy arising from the SNIa data, when when $\Omega_m=0.3$ and $w=-1$. The contours correspond to 68.3, 90, 95.4 and 99 percent confidence limits.
• Figure 4: Constraints arising from the SNIa in the axisymmetric case $\gamma=0$. Inside the darker isosurface, the fit is as good as in the $\Lambda$CDM model, $\chi^2 < 158$. Inside the lighter isosurface, one has $\Delta\chi^2 < 8.02$. One notes that larger skewness $\delta$ would typically be compatible with the SNIa data for phantom equations of state $w<-1$ and large matter densities.