In search of the dark matter dark energy interaction: a kinematic approach

TL;DR

This paper investigates whether an interaction between dark matter and dark energy can be inferred from the cosmic expansion history by adopting a purely kinematic approach with a constant jerk parameter $j$. It derives a two-parameter model for the dimensionless Hubble rate, $h^2(z)=A(1+z)^{(3+\sqrt{9-8(1+j)})/2}+(1-A)(1+z)^{(3-\sqrt{9-8(1+j)})/2}$, where $A$ plays the role of $\Omega_{m0}$ only in the $j=-1$ limit; for $j\neq -1$ the non-standard exponent signals potential dark matter–dark energy interaction, quantified by the interaction term $Q(z)$. Fits to observational data (OHD, SNe, BAO) yield $j$ values very close to $-1$, implying proximity to $\Lambda$CDM, with $Q(z)$ near zero at $z=0$ but possibly nonzero at higher redshift, and a transition redshift around $z\sim0.6-0.8$ signaling possible early-universe interaction. Overall, the study demonstrates that a kinematic reconstruction based on the jerk parameter can constrain DM–DE interactions and remains consistent with $\Lambda$CDM while highlighting sensitivity to the chosen data sets.

Abstract

The present work deals with a kinematic approach to the modelling the late time dynamics of the universe. This approach is based upon the assumption of constant value of cosmological jerk parameter, which is the dimensionless representation of the 3rd order time derivative of the scale factor. For the $Λ$CDM model, the value of jerk parameter is -1 throughout the evolution history. Now any model dependent estimation of the value of the jerk parameter would indicate the deviation of the model from the cosmological constant. In the present work, it has also been shown that for a constant jerk parameter model, any deviation of its value from -1 would not allow the dark matter to have an independent conservation, thus indicating towards an interaction between dark matter and dark energy. Statistical analysis with different observational data sets (namely the observational Hubble parameter data (OHD), the type Ia supernova data (SNe), and the baryon acoustic oscillation data (BAO)) lead to a well constrained values of the jerk parameter and the model remains at a very close proximity of the $Λ$CDM. The possibility of interaction is found to be more likely at high redshift rather than at present epoch.

Figures (5)

• Figure 1: Confidence contours on the 2D parameter space of the reconstructed model. The 1$\sigma$, 2$\sigma$ and 3$\sigma$ confidence regions have been presented from inner to outer area and the central black dots represent the corresponding best fit point. The left panel shows the confidence contours obtained for the statistical analysis using OHD+SNe data, the middle panel is obtained SNe+BAO and the right panel is for OHD+SNe+BAO.
• Figure 2: Plots of marginalized likelihood functions of the reconstructed model. The dotted curves represents the likelihood obtained for OHD+SNe, dashed curves represents the likelihood for SNe+BAO and the solid curves represents the likelihood for OHD+SNe+BAO.
• Figure 3: The plots of the deceleration parameter ($q(z)$) (left panel) and the effective equation of state parameter ($w_{eff}(z)$) (right panel) for the reconstructed model. The corresponding 1$\sigma$ and 2$\sigma$ confidence regions and the best fit curves obtained in the analysis combining OHD, SNe and BAO data sets, are presented.
• Figure 4: The plots of the dark energy equation of state parameter ($w_{DE}(z)$), obtained from the analysis with different combination of the data sets are presented. The corresponding 1$\sigma$ and 2$\sigma$ confidence regions and the best fit curves are shown.
• Figure 5: The plots of interaction term $Q(z)$, obtained from the analysis with different combination of the data sets are presented. The corresponding 1$\sigma$ and 2$\sigma$ confidence regions and the best fit curves are shown. The Q=0 straight line represents the $\Lambda$CDM model.