Testing coupled dark energy models with their cosmological background evolution

TL;DR

The authors explore a cosmology in which dark matter interacts with a quintessence field through conformal and disformal couplings, emphasizing background evolution. They formulate the model in the Einstein frame with $ ilde{g}_{\mu\nu}= C() g_{\mu\nu} + D()\partial_{\mu}\u0003\partial_{\nu}\u0003$, adopting an exponential potential and constant disformal coupling, and derive the modified Klein-Gordon and Friedmann equations along with an effective equation of state $w_{\rm eff}$. Using $H(z)$, BAO, and SNIa data (plus BBN and HST priors), they perform a global MCMC analysis with CLASS and MontePython for three coupling scenarios: purely conformal, purely disformal, and mixed, finding that disformal terms relax conformal constraints and can be preferred by the background evolution. The main conclusions are that a nonzero disformal coupling is favored over ΛCDM at the background level, and that future work should incorporate perturbations to tighten constraints and compare with Planck-era data. Overall, the work highlights the viability and testability of dark-sector interactions beyond standard ΛCDM using background cosmology alone, setting the stage for growth-rate analyses.

Abstract

We consider a cosmology in which dark matter and a quintessence scalar field responsible for the acceleration of the Universe are allowed to interact. Allowing for both conformal and disformal couplings, we perform a global analysis of the constraints on our model using Hubble parameter measurements, baryon acoustic oscillation distance measurements, and a Supernovae Type Ia data set. We find that the additional disformal coupling relaxes the conformal coupling constraints. Moreover we show that, at the background level, a disformal interaction within the dark sector is preferred to both $Λ$CDM and uncoupled quintessence, hence favouring interacting dark energy.

Figures (8)

• Figure 1: These figures show the evolution of the effective equation of state (solid) and the corresponding evolution of the scalar field equation of state parameter (dashed). We show a conformal case with $\alpha=0.02$ (left), a disformal case with $D_M=0.34\,\text{meV}^{-1}$ (right), and a conformal disformal case with $\alpha=0.02$ and $D_M=0.34\, \text{meV}^{-1}$ (bottom). In all cases we set $\lambda=1.2$.
• Figure 2: In this figure we show the distance modulus for three different models together with the supernova Union2.1 data set Suzuki:2011hu. We illustrate a conformal case with $\alpha=0.02$, a disformal case with $D_M=0.4\,\text{meV}^{-1}$, and a mixed conformal disformal case with $\alpha=0.18$ and $D_M=0.4\, \text{meV}^{-1}$. In all cases we set $\lambda=1.1$.
• Figure 3: Confidence--level contours of the cosmological parameters for the conformally coupled DM case. We compare the $68.3\%$ (dark shaded) and $95.4\%$ (light shaded) constraints arising from $H+$SNIa+BAO observations with $H+$SNIa+BAO+BBN and $H+$SNIa+BAO+BBN+HST observations. The marginalized one--dimensional posterior distributions are also shown for comparison.
• Figure 4: Confidence--level contours of the model parameters for the conformally coupled DM case. We compare the $68.3\%$ (dark shaded) and $95.4\%$ (light shaded) constraints arising from $H+$SNIa+BAO observations with $H+$SNIa+BAO+BBN and $H+$SNIa+BAO+BBN+HST observations. The marginalized one--dimensional posterior distributions are also shown for comparison.
• Figure 5: Confidence--level contours of the cosmological parameters for the disformally coupled DM case. We compare the $68.3\%$ (dark shaded) and $95.4\%$ (light shaded) constraints arising from $H+$SNIa+BAO observations with $H+$SNIa+BAO+BBN and $H+$SNIa+BAO+BBN+HST observations. The marginalized one--dimensional posterior distributions are also shown for comparison.