Post-Planck dark energy constraints

We constrain plausible dark energy models using the recently published cosmic microwave background (CMB) temperature anisotropy data from Planck together with WMAP9 low-$\ell$ polarization data and the data from low redshift surveys. To circumvent the limitations of any particular equation of state toward describing all existing dark energy models, we work with three different equations of state covering a wider class of dark energy models and hence provide more robust and generic constraints on the dark energy behavior. We show that a possible tension exists between constraints from CMB and non-CMB observations when one allows for both phantom and nonphantom behavior for the dark energy. Further, we reconstruct the equation of state of dark energy as a function of redshift using the combined CMB and non-CMB data and show that cosmological constant behavior is disallowed at the 68.3% confidence level. A fully nonphantom history is also disallowed at the 68.3% confidence level, and a considerable fine-tuning is also needed to keep it inside the 95.5% confidence limit. This result might motivate one to construct phantom models for dark energy, which may be achievable in the presence of higher derivative operators as in string theory. However, for a theoretical model that allows only nonphantom behavior, both CMB and non-CMB data sets agree on the dark energy constraint with the mean equation of state being very close to the cosmological constant.

Figure 1

The one-dimensional marginalized likelihoods for different parameters of the equation of state. The parametrizations are mentioned at the top of each plot. The color codes are for different analyses with different observational data and are described in the plot. Note here that for GCG, $-A$ corresponds to the equation of state of dark energy today, i.e., $w_0$.

Figure 2

Marginalized likelihoods in the $w_0-w_{\mathrm{a}}$ plane for CPL and the $A-\alpha$ plane for the GCG parametrization. Inward to outward the black bounding lines represent 68.3%, 95.5%, and 99.7% confidence contours, respectively. For CPL we have marked the cosmological constant with the intersection of two black lines, and for GCG we have marked the $1+\alpha =0$ line to distinguish between the freezing and thawing regions. Note here that for GCG, $-A$ corresponds to the equation of state of dark energy today, i.e., $w_0$.

Figure 3

Marginalized likelihoods in $w_0-H_0$ parameter plane for CPL (left), SS (middle), and GCG (right) parametrizations. The red horizontal lines represent the best-fit value for $H_0$ obtained from Planck for $\mathrm{\Lambda }\mathrm{CDM}$ case. Inward to outward the black bounding lines represent 68.3%, 95.5%, and 99.7% confidence contours, respectively.

Figure 4

Marginalized likelihoods in ${\mathrm{\Omega }}_{\mathrm{m}}-H_0$ parameter plane for CPL (left), SS (middle), and GCG (right) parametrizations. The red lines represent the best-fit values for $H_0$ and ${\mathrm{\Omega }}_{\mathrm{m}}$ obtained from Planck for $\mathrm{\Lambda }\mathrm{CDM}$ model. Inward to outward the black bounding lines represent 68.3%, 95.5%, and 99.7% confidence contours, respectively.

Figure 5

Behavior of equation of state $w$ as a function of redshift $z$ for CPL (left), SS (middle), and GCG (right) parametrization for 68.3% and 95.5% confidence levels. The red solid and the blue dashed lines correspond to $w=-1$ and the mean $w$, respectively.