Dark energy scaling from dark matter to acceleration

The dark sector of the Universe need not be completely separable into distinct dark matter and dark energy components. We consider a model of early dark energy in which the dark energy mimics a dark matter component in both evolution and perturbations at early times. Barotropic aether dark energy scales as a fixed fraction, possibly greater than one, of the dark matter density and has vanishing sound speed at early times before undergoing a transition. This gives signatures not only in cosmic expansion but in sound speed and inhomogeneities, and in number of effective neutrino species. Model parameters describe the timing, sharpness of the transition, and the relative abundance at early times. Upon comparison with current data, we find viable regimes in which the dark energy behaves like dark matter at early times: for transitions well before recombination the dark energy to dark matter fraction can equal or exceed unity, while for transitions near recombination the ratio can only be a few percent. After the transition, dark energy goes its separate way, ultimately driving cosmic acceleration and approaching a cosmological constant in this scenario.

Figure 1

For the barotropic aether we plot the ratio of the total dark energy density to the matter density ${\rho }_{de}/{\rho }_m$, the total dark energy equation of state parameter $w$, the dark energy sound speed squared $c_s^2$, and the aether equation of state parameter $w_{ae}$. Thick curves take $\tau =0.5$, thin curves $\tau =0.25$, with both having $a_t=10^{-4}$ and $R={\rho }_{de}/{\rho }_m(a\ll a_t)=1.5$.

Figure 2

The total dark energy equation of state $w(a)$ is plotted for several values of the transition scale factor $a_t$ and early dark energy-dark matter density ratio $R$ (for fixed $\tau =0.5$). The location of the transition away from dark matter behavior $w=0$ is determined by $a_t$ and the length of aether dominated behavior ($w=1$) by $R$, but at late times all curves go to the dark energy attractor with $w=-1$.

Figure 3

The effective number of extra neutrino species equivalent to the early dark energy density is plotted vs scale factor for different cases of the transition scale factor $a_t$ and width $\tau$, with fixed $R=1.5$.

Figure 4

The CMB temperature power spectrum for $\mathrm{\Lambda }\mathrm{CDM}$ and several barotropic aether models are shown (top panel) along with the relative deviations from $\mathrm{\Lambda }\mathrm{CDM}$ (bottom panel). Postrecombination transitions can be readily distinguished while subpercent level prerecombination models are consistent with data. For this plot we fix the other cosmological parameters and set $\tau =1$.

Figure 5

Assuming a bound on the dark energy to dark matter density at recombination imposes constraints on the dark energy parameters. Here for an upper bound of 0.4%, only the parameter space below the respective $\log a_t$ curves is allowed.

Figure 6

Two-dimensional joint confidence contours at 68% C.L. (dark) and 95% C.L. (light) are shown for the dark energy and dark matter parameters, marginalized over all other parameters. The fully marginalized one-dimensional PDFs are shown on the diagonal.

Figure 7

As Figure 6, but restricted to $R>0.02$.

Figure 8

As Figure 6, but restricted to $0.01<R<0.02$.