Current constraints on the dark energy equation of state

Abstract

We combine complementary datasets from Cosmic Microwave Background (CMB) anisotropy measurements, high redshift supernovae (SN-Ia) observations and data from local cluster abundances and galaxy clustering (LSS) to constrain the dark energy equation of state parameterized by a constant pressure-to-density ratio $w_Q$. Under the assumption of flatness, we find $w_Q < -0.85$ at 68% c.l., providing no significant evidence for quintessential behaviour different from that of a cosmological constant. We then generalise our result to show that the constraints placed on a constant $w_{Q}$ can be safely extended to dynamical theories. We consider a variety of quintessential dynamical models based on inverse power law, exponential and oscillatory scaling potentials. We find that SN1a observations are `numbed' to dynamical shifts in the equation of state, making the prospect of reconstructing $w(z)$, a challenging one indeed.

Figures (6)

• Figure 1: CMB power spectra and the angular diameter distance degeneracy. The models are computed assuming flatness, $\Omega_k=1-\Omega_M-\Omega_Q=0$). The Integrated Sachs Wolfe effect on large angular scale slightly breaks the degeneracy. The degeneracy can be broken with a strong prior on $h$, in this paper we use the results from the HST.
• Figure 2: Contours of constant $R$ (CMB) and $SN-Ia$ luminosity distance in the $w_Q$-$\Omega_M$ plane. The degeneracy between the two distance measures can be broken by combining the two sets of complementary information. The luminosity distance is chosen to be equal to $d_{l}$ at $z=1$ for a fiducial model with $\Omega_{\Lambda}=0.7$, $\Omega_{M}=0.3$,$h=0.65$. (We note that as $\Omega_{Q}=1-\Omega_M$ goes to zero the dependence of $R$ and $d_{L}$ upon $w_{Q}$ also become zero, as there is no dark energy present.)
• Figure 3: The likelihood contours in the ($\Omega_M$, $w_Q$) plane, with the remaining parameters taking their best-fitting values for the joint CMB+SN-Ia+LSS analysis described in the text. The contours correspond to 0.32, 0.05 and 0.01 of the peak value of the likelihood, which are the 68%, 95% and 99% confidence levels respectively.
• Figure 4: The variation of $\Omega_{Q}$ and $w_{Q}$ with redshift for the three models described in section V. The power law potential (full line) $w_{Q}$ shows a steady small variation, the exponential feature potential, (short dashed line) acts remarkably like a cosmological constant at late times, after a deviation from behaving like normal matter with $w_{Q}\sim 0$, whilst the oscillating potential (dot-dash) shows a continual variation in $w_{Q}$.
• Figure 5: Comparison of CMB temperature power spectra for the dynamical quintessence model with an exponential potential with a feature described in section V, and a model with constant $w_{Q}=w_{eff}$ for the dynamical model. In both cases with $\Omega_{Q}=0.7$ and $H_{0}=65$. One can see that the constant model is a remarkably good approximation to the dynamical model, despite the equation of state of the dynamical model varying significantly from the effective value from recombination until nowadays.