Distinguishing interacting dark energy from wCDM with CMB, lensing, and baryon acoustic oscillation data

TL;DR

This paper investigates whether Planck 2013 CMB data, including lensing and BAO, can distinguish interacting dark energy from a non-interacting $w$CDM model by introducing a phenomenological background coupling $Q_c=-\Gamma\rho_c$ and a time-varying dark-energy equation of state $w_{\mathrm{de}}(t)$. Using full perturbation theory and MCMC with CosmoMC, the authors find that non-phantom models ( $w_{\mathrm{de}}> -1$ ) show no evidence for interaction, with $-0.14<\Gamma/H_0<0.02$ at 95% CL after CMB+BAO+lensing; BAO is crucial to break the CMB degeneracy. In phantom models ($w_{\mathrm{de}}<-1$), energy transfer from DE to DM is modestly favored by CMB+BAO data ($-0.57<\Gamma/H_0<-0.10$), and lensing shifts this to $-0.46<\Gamma/H_0<-0.01$, while also inducing strong shifts in $\omega_c$ and $\Omega_{\mathrm{de}}$. Overall, lensing data enhance the ability to discriminate between interacting and non-interacting scenarios, highlighting the potential of future surveys to probe dark-sector couplings through growth and ISW-related observables.

Abstract

We employ the Planck 2013 CMB temperature anisotropy and lensing data, and baryon acoustic oscillation (BAO) data to constrain a phenomenological $w$CDM model, where dark matter and dark energy interact. We assume time-dependent equation of state parameter for dark energy, and treat dark matter and dark energy as fluids whose energy-exchange rate is proportional to the dark-matter density. The CMB data alone leave a strong degeneracy between the interaction rate and the physical CDM density parameter today, $ω_c$, allowing a large interaction rate $|Γ| \sim H_0$. However, as has been known for a while, the BAO data break this degeneracy. Moreover, we exploit the CMB lensing potential likelihood, which probes the matter perturbations at redshift $z \sim 2$ and is very sensitive to the growth of structure, and hence one of the tools for discerning between the $Λ$CDM model and its alternatives. However, we find that in the non-phantom models ($w_{\mathrm{de}}>-1$), the constraints remain unchanged by the inclusion of the lensing data and consistent with zero interaction, $-0.14 < Γ/H_0 < 0.02$ at 95\% CL. On the contrary, in the phantom models ($w_{\mathrm{de}}<-1$), energy transfer from dark energy to dark matter is moderately favoured over the non-interacting model; $-0.57 < Γ/H_0 < -0.10$ at 95\% CL with CMB+BAO, while addition of the lensing data shifts this to $-0.46 < Γ/H_0 < -0.01$.

Figures (5)

• Figure 1: The $w_e$ volume effect in the non-phantom models ($w_{\mathrm{de}} > -1$). The points indicate samples from our Monte Carlo Markov Chains with the data combination CMB+BAO. The colour scale shows the value of $w_0$ for each sample. Whilst marginalizing (integrating) over the $w_e$ direction, the models with a positive $\Gamma$ (energy transfer from CDM to dark energy) receive much less weight than the ones with a negative $\Gamma$ (energy transfer from dark energy to CDM).
• Figure 2: The non-phantom interacting model ($w_{\mathrm{de}} > -1$). 68% and 95% CL regions with CMB (gray), CMB+BAO (red), and CMB+BAO+lensing (blue) data.
• Figure 3: Comparison of the non-phantom models ($w_{\mathrm{de}} > -1$). 1d marginalized posterior probability densities for the interacting dark-sector model (solid lines) and for the non-interacting "standard" $w$CDM model (dashed lines). In the non-interacting model, with the CMB and CMB+BAO data, we allow the early-time dark energy equation of state parameter, $w_e$, to vary between -1 and +1/3, whereas with the CMB+BAO+lensing data we allow only the same range, $w_e\in(-0.8,+1/3)$, which is possible in the interacting model (see figure \ref{['w0_we_Gamma_CMBandBAO_3D']}), in order to provide a different perspective for comparing the models.
• Figure 4: The phantom interacting model ($w_{\mathrm{de}} < -1$) with CMB, BAO, and lensing data.
• Figure 5: The phantom model ($w_{\mathrm{de}} < -1$) with CMB, BAO, and lensing data.