Anisotropic Dark Energy: Dynamics of Background and Perturbations

TL;DR

This work investigates cosmologies with anisotropic dark energy in a Bianchi I universe by introducing two skewness parameters $\\delta$ and $\\gamma$ that quantify directional pressure differences. It develops a dynamical-system treatment of the background through variables $U$, $R$, and $S$, identifying fixed points such as FLRW, Kasner, and anisotropic $\\Lambda$-dominated or scaling solutions, and analyzes two classes of anisotropic cosmological-constant models. Observational bounds are derived from the CMB quadrupole and SNIa data, showing tight constraints from the quadrupole but admitting sizable late-time anisotropy in certain regions of parameter space; a covariant perturbation framework is then constructed to study inhomogeneities and structure formation, revealing direction-dependent growth and potential connections to CMB/LSS anomalies and Lorentz-violating theories. Together, these results suggest that anisotropic stresses could play a role in linking early- and late-time cosmology and motivate further work to compute the full-sky signatures and their observational implications.

Abstract

We investigate cosmologies where the accelerated expansion of the Universe is driven by a field with an anisotropic equation of state. We model such scenarios within the Bianchi I framework, introducing two skewness parameters to quantify the deviation of pressure from isotropy. We study the dynamics of the background expansion in these models. A special case of anisotropic cosmological constant is analyzed in detail. The anisotropic expansion is then confronted with the redshift and angular distribution of the supernovae type Ia. In addition, we investigate the effects on the cosmic microwave background (CMB) anisotropies for which the main signature appears to be a quadrupole contribution. We find that the two skewness parameters can be very well constrained. Tightest bounds are imposed by the CMB quadrupole, but there are anisotropic models which avoid this bound completely. Within these bounds, the anisotropy can be beneficial as a potential explanation of various anomalous cosmological observations, especially in the CMB at the largest angles. We also consider the dynamics of linear perturbations in these models. The covariant approach is used to derive the general evolution equations for cosmological perturbations taking into account imperfect sources in an anisotropic background. The implications for the galaxy formation are then studied. These results might help to make contact between the observed anomalies in CMB and large scale structure and fundamental theories exhibiting Lorentz violation.

Figures (6)

• Figure 1: Phase portraits in the cases $\delta=-0.25$ (right) and $\delta=0.25$ (left) when $w=-1$. The solution (\ref{['flrw_s']}) is at $R=U=0$, and the fixed points (\ref{['empty']}) and (\ref{['cigar']}) are at the four corners of the portraits. In both cases the fixed point (\ref{['domi_s']}) attracts trajectories from everywhere.
• Figure 2: Phase portraits in the cases $\delta=-2$ (right) and $\delta=2$ (left) when $w=-1$. The solution (\ref{['flrw_s']}) is at $R=U=0$, and the fixed points (\ref{['empty']}) and (\ref{['cigar']}) are at the four corners of the portraits. In right panel all trajectories lead to the scaling solution all (\ref{['scal_s']}). The left panel shows isotropizations in the example with $w+\delta>w_m$.
• Figure 3: The asymptotic state of the universe starting 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']}) where $U=0$) continues forever. Otherwise, the universe will end up expanding anisotropically and either dominated by dark energy (solution (\ref{['domi_s']}) where $U=1$) or exhibiting a scaling property (solution (\ref{['scal_s']}) where $0<U<1$). Fig. (\ref{['phases1']}) showed phase portraits of two $U=1$ models, the right panel of Fig. (\ref{['phases2']}) showed an example of the $0<U<1$ case, and finally the left panel of Fig. (\ref{['phases2']}) showed isotropizations in the $U=0$ (here we refer to the asymptotic value of $U$).
• Figure 4: The asymptotic state of the universe starting from an Einstein-deSitter stage for the anisotropic generalization of cosmological constant having constant $\delta$ and $\gamma$ (case II, section \ref{['case2']}). The $R$ (blue, solid lines) and $S$ (red, dashed lines) are given as function of $\delta$. The thick lines depict the cases $\gamma=1,2,3,4,5$, and the thin lines depict the case that $\gamma=0,-1,-2,-3,-4,-5$. The analytic solution (\ref{['alambda_s2']}) is recovered in the case $\gamma=0$. These curves show how this generalizes non-axisymmetric cases.
• Figure 5: Limits on the skewness of dark energy arising from the SNIa data when $\Omega_m=0.3$. In the LHS, $w=-1$ and RHS $w=-1.2$. The contours correspond to 68.3, 90, and 95.4 percent confidence limits. The crosses mark the location of the best-fit models (there are two in each figure since, because we marginalize over the direction of the coordinates, there is a symmetry of projections about the $\delta+\gamma=0$ line).