WMAP constraints on low redshift evolution of dark energy

TL;DR

The paper addresses whether dark energy evolves at low redshift by jointly analyzing type Ia supernovae and the full WMAP angular power spectrum. It models $w(z)$ with two parameterizations, $w(z)=w_0 + w_1 \frac{z}{(1+z)^p}$ for $p=1,2$, and assesses constraints on $w_0$, $w_1$, and the derived $w_{\rm eff}$ under fixed priors. Using CMBFAST and the WMAP likelihood alongside SN data, the study finds that WMAP tightens the constraints far more than SN data alone, reducing the viable region in parameter space and highlighting the role of $w_{\rm eff}$ in shaping the angular-diameter distance. The results largely favor a cosmological-constant–like behavior ($w=-1$) within the explored space, though nontrivial evolution remains allowed for some parameter choices, underscoring ongoing degeneracies and the need to consider dark-energy perturbations in future work.

Abstract

The conceptual difficulties associated with a cosmological constant have led to the investigation of alternative models in which the equation of state parameter, $w=p/ρ$, of the dark energy evolves with time. We show that combining the supernova type Ia observations {\it with the constraints from WMAP observations} restricts large variation of $ρ(z)$ at low redshifts. The combination of these two observational constraints is stronger than either one. The results are completely consistent with the cosmological constant as the source of dark energy.

Figures (3)

• Figure 1: The top panel shows the allowed region at $99\%$ confidence level in the $w'(0)-w(0)$ plane for $\Omega_{nr} = 0.3$ for the parameterization in Eq.(\ref{['taylor']}) with $p=1$. The purple region is excluded by supernova observations. WMAP constraints rule out the region in green at the same confidence level. The thick dotted line divides models that violate the strong energy condition from those that do not. Models which preserve strong energy condition are on the top right of the dotted lines. The lower panel shows the same plot for $p=2$.
• Figure 2: The top panel shows those values of $\rho(z)$ for $2 \geq z \geq 0$ that are disallowed by the supernova and WMAP constraints for $\Omega_{nr}=0.3$. The purple region is ruled out by supernova observations and WMAP constraints limit the allowed region by also ruling out the green region. The remaining region contains allowed models that are parameterized by Eq.(\ref{['taylor']}) with $p=1$. The allowed region for models that do not violate the condition $(\rho+p)\geq0$ is smaller and lies between the dotted lines. The lower panel shows the same plot for $p=2$.
• Figure 3: The figure shows confidence levels in $\Omega_{nr}-w_0$ plane for supernova and WMAP constraints (for both parameterisations) with $w'(z=0)=0$. $99\%$ confidence levels are plotted for both observational constraints. The bold solid contour is $99\%$ confidence level for WMAP. It is clear that the region allowed by the combination of two observational constraints is much smaller than the one allowed by supernova data.