Constraints on the interaction strength in the model of interacting dynamical dark energy with linear and non-linear interacting terms

In this work the observational constraints on interaction coupling parameter between dynamical dark energy and cold dark matter were obtained using CMB, BAO and SN Ia data. The dark energy in considered models is dynamical and evolution of its equation of state parameter depends on dark coupling and internal properties of the dark energy. Such model is believed to be more physically consistent than models of interacting dark energy considered in previous works. Constraints were made for three types of interaction. The first two are the types which are often considered in other works on interacting dark energy. The third type has the non-linear dependence on densities of dark components and is studied for the first time. Observational constraints on Hubble constant $H_{0}$ for the first two models are in strong disagreement with so called local measurements of $H_{0}$. And the third model is in better agreement with local measurements than $Λ$CDM model. Also for the last non-linear model existence of non-zero interaction was found at greater than $1σ$ significance level.

💡 Research Summary

This research presents a sophisticated investigation into the interaction between Dark Energy (DE) and Cold Dark Matter (CDM), aiming to resolve the long-standing “Hubble Tension” and the inherent instabilities found in previous Interacting Dark Energy (IDE) models. The core innovation of this paper lies in the transition from a static equation of state ($w$) to a dynamical one, where the evolution of $w$ is coupled with the interaction strength, thereby ensuring physical stability during the cosmic perturbation phase.

The authors propose and evaluate three distinct interaction models based on the energy-momentum exchange four-vector $J^0$. Models I and II represent traditional linear interactions, where the interaction strength is proportional to either the CDM density ($\rho_c$) or the total density ($\rho_{de} + \rho_c$). In contrast, Model III introduces a novel non-linear interaction term, proportional to the product of the densities of the two dark components ($\rho_{de}\rho_c / (\rho_{de}+\rho_c)$). This third model is inspired by the Coulomb-like interaction seen in electromagnetism and represents a significant departure from previous linear frameworks.

To test these models, the researchers employed a rigorous statistical approach using a modified version of the CAMB code (IDECAMB) and the Parameterized Post-Friedmann (PPF) framework. The analysis integrated high-precision datasets, including the Planck 2018 CMB temperature and polarization spectra, Baryon Acoustic Oscillation (BAO) data from 6dF, SDSS, and BOSS, and the Pantheon supernova sample of 1048 Type Ia supernovae. The parameter estimation was conducted via MCMC (Markov Chain Monte Carlo) simulations, ensuring high convergence standards.

The findings reveal a stark contrast between the models. Models I and II, despite being widely studied, failed to alleviate the Hubble tension; instead, they yielded $H_0$ values around $68\text{ km/s/Mpc}$, widening the discrepancy with local measurements of $H_0 \approx 73\text{ km/s/Mpc}$. However, the non-linear Model III emerged as a superior candidate. It provided evidence for a non-zero interaction ($\beta \neq 0$) at a significance level greater than $1\sigma$ and yielded $H_0$ values that are more consistent with local observations than the standard $\Lambda$CDM model.

Furthermore, the study highlights the physical implications of the interaction direction. When $\beta < 0$, indicating an energy flow from CDM to DE, the model predicts an increase in the growth rate of structures at small scales and a decrease in uniformity at large scales. This research concludes that non-linear interactions in the dark sector are not only more physically stable but also offer a promising pathway to reconciling the conflicting measurements of the universe’s expansion rate, potentially reshaping our understanding of cosmic evolution.