Tracking and coupled dark energy as seen by WMAP

TL;DR

This paper uses WMAP first-year data, in combination with pre-WMAP CMB measurements, to constrain tracking dark energy models, including uncoupled inverse power-law potentials and models with a dark-matter coupling. By solving the perturbation equations with a modified code and performing a likelihood analysis in a flat universe, it derives bounds on the present equation of state w_phi and on the potential slope alpha, as well as on the coupling parameter beta. The results show WMAP alone constrains w_phi to about -0.67 (68%) or -0.49 (95%) with alpha bounded accordingly, while allowing a beta coupling yields alpha < 2.08 and beta < 0.13 (95%), with w_e during phiMDE near zero. Including SN Ia data tightens the w_phi bound to below -0.76 and yields Omega_m ≈ 0.67, while the coupling constraint remains, suggesting Planck-era observations could tighten beta further (to ~0.05) and test equivalence-principle violations more stringently.

Abstract

The satellite experiment WMAP has produced for the first time a high-coverage, high resolution survey of the microwave sky, releasing publicly available data that are likely to remain unrivalled for years to come. Here we compare the WMAP temperature power spectrum, along with an exhautive compilation of previous experiments, to models of dark energy that allow for a tracking epoch at the present, deriving updated bounds on the dark energy equation of state and the other cosmological parameters. Moreover, we complement the analysis by including a coupling of the dark energy to dark matter. The main results are: a) the WMAP data alone constrains the equation of state of tracking dark energy to be w_φ<-0.67(-0.49) to 68%(95%) (confining the analysis to w_φ>-1), which implies for an inverse power law potential an exponent α<0.99(2.08); b) the dimensionless coupling to dark matter is |β|<0.07(0.13). Including the results from the supernovae Ia further constrains the dark energy equation of state.

Figures (7)

• Figure 1: Behavior of the energy densities for the coupled ($\beta =0.1$, top) and uncoupled ($\beta =0$, bottom) model. Notice, in the coupled case, the $\phi$MDE in which $\Omega _{\phi }$ is almost constant and dominated by the kinetic energy of the scalar field. The label $T$ denotes the tracking behavior, the label $A$ denotes the final future attractor.
• Figure 2: Likelihood functions for uncoupled dark energy models, in arbitrary units. In each panel the other parameters have been marginalized. The dotted lines are for the HST prior on the Hubble constant. The horizontal long-dashed lines are the confidence levels at 68% and 95%. The vertical long-dashed lines in the panel for $w_{\phi }$ mark the upper bounds at 68% and 95% confidence levels.
• Figure 3: Likelihood contour plots in the space $w_{\phi (tracking)}$,$w_{e(\phi MDE)}$ (or $\alpha ,\beta$) marginalizing over the other parameters at the 68,95 and 99% c.l..
• Figure 4: Marginalized likelihood for tracking trajectories. The solid curves are for the WMAP data, the short-dashed curves are for the HST prior, and the dotted curves in the panels for $w_{\phi }$ and $\beta$ for the pre-WMAP compilation . The horizontal long-dashed lines are the confidence levels at 68% and 95%. The vertical long-dashed lines in the panel for $w_{\phi }$ mark the upper bounds at 68% and 95% confidence levels.
• Figure 5: Likelihood for $\beta ,\, h$. This shows the residual degeneracy between the two parameters due to the geometric degeneracy in the angular diameter distance to last scattering.