Constraining the quintessence equation of state with SnIa data and CMB peaks

TL;DR

The paper tackles distinguishing Quintessence from a cosmological constant by constraining a broad class of Quintessence potentials using Type Ia supernovae and CMB peak positions in a flat universe. It employs a Bayesian likelihood framework over potential parameters $\alpha$, $\beta$ and the present dark-energy density $Ω_Q$, marginalizing over nuisance parameters, to extract constraints from SN Ia and acoustic-peak data, including the pivotal third CMB peak. The main finding is that, when all data are considered, the present-day equation of state is tightly constrained to $-1 \le w_Q^0 \le -0.93$ (2σ) for $Ω_Q \approx 0.75$, implying Quintessence must mimic a cosmological constant for these models. This result disfavors simple inverse-power-law potentials under minimal coupling and highlights the discriminating power of the third CMB peak, while leaving room for more complex exponential-type potentials.

Abstract

Quintessence has been introduced as an alternative to the cosmological constant scenario to account for the current acceleration of the universe. This new dark energy component allows values of the equation of state parameter $w_{Q}^0\geq-1$, and in principle measurements of cosmological distances to Type Ia supernovae can be used to distinguish between these two types of models. Assuming a flat universe, we use the supernovae data and measurements of the position of the acoustic peaks in the Cosmic Microwave Background (CMB) spectra to constrain a rather general class of Quintessence potentials, including inverse power law models and recently proposed Supergravity inspired potentials. In particular we use a likelihood analysis, marginalizing over the dark energy density $Ω_{Q}$, the physical baryon density $Ω_{b}h^2$ and the scalar spectral index $n$, to constrain the slopes of our Quintessence potential. Considering only the first Doppler peak the best fit in our range of models gives $w_{Q}^0\sim-0.8$. However, including the SnIa data and the three peaks, we find an upper limit on the present value of the equation of state parameter, $-1\leq w_{Q}^0\leq-0.93$ at $2σ$, a result that appears to rule out a class of recently proposed potentials.

Figures (6)

• Figure 1: In (a) the evolution of $w_{Q}$ against the red-shift is plotted for different values of $\alpha$ and $\beta$. In (b) the behaviour of the deceleration parameter, $q$, is plotted against the red-shift. The acceleration starts ($q<0$) earlier for models with an equation of state close to that of a true cosmological constant.
• Figure 2: Fractional Quintessence energy density likelihoods, (a) for SnIa, (b) for the combined CMB peaks and (c) for the combined data sets.
• Figure 3: Likelihood contour plots for SnIa, I, II and III acoustic peaks. The blue region is the $68\%$ confidence region while the $90\%$ is the light blue one. For the SnIa the white region correspond to $2\sigma$. The position of the third CMB acoustic peak strongly constrains the acceptable parameter space.
• Figure 4: One-dimensional likelihood for $n$ and $\Omega_{b}h^2$.
• Figure 5: Two-dimensional likelihood for SnIa and CMB with $1$ (dark blue) and $2\sigma$ (light blue) contours.