Testing the Direction of Dark Sector Interaction Using Late-Time Datasets

Technical Summary: Testing the Direction of Dark Sector Interaction Using Late-Time Datasets

Problem Statement
The standard $\Lambda$CDM cosmological model, while empirically successful, faces significant theoretical and observational challenges. These include the cosmological constant problem, the cosmic coincidence problem, and the "Hubble tension"—a persistent discrepancy between the Hubble constant ($H_0$) inferred from early-universe Cosmic Microwave Background (CMB) data and local distance-ladder measurements. Recent observational data, particularly from the Dark Energy Spectroscopic Instrument (DESI), have suggested evidence for dynamical dark energy and time-dependent evolution, challenging the static nature of the cosmological constant.

To address these issues, this work investigates the phenomenological interacting dark energy ($\xi$IDE) model. In this framework, dark matter (DM) and dark energy (DE) exchange energy via a non-gravitational coupling. The specific model posits that the ratio of dark energy to dark matter densities evolves as $\rho_{DE}/\rho_{DM} \propto a^\xi$, where $\xi$ is a parameter quantifying the severity of the coincidence problem. The study aims to constrain the parameters of this model, specifically determining the existence and direction of energy transfer within the dark sector, and assessing whether such interactions can alleviate the Hubble tension.

Methodology
The authors perform a Bayesian statistical analysis using the SimpleMC cosmological inference framework. Parameter space exploration is conducted via the dynamic nested sampling algorithm implemented in the dynesty package. The analysis utilizes a Markov Chain Monte Carlo (MCMC) approach to derive marginalized posterior distributions and 2D confidence regions for the model parameters.

The study employs a multi-probe observational dataset combining:

• Baryon Acoustic Oscillations (BAO): Measurements from DESI Data Release 1 (DR1) and Data Release 2 (DR2).
• Cosmic Chronometers (CC): 15 direct $H(z)$ measurements derived from massive, passively evolving galaxies.
• Type Ia Supernovae (SNe Ia): Three distinct compilations: Pantheon+, the recalibrated DES-Dovekie sample, and Union3.
• Compressed CMB Likelihood: A 3 $\times$ 3 Gaussian likelihood based on the CamSpec data, constraining the angular scale of the sound horizon and physical matter densities.

The analysis compares the $\xi$IDE model against the standard $\Lambda$CDM model. Model selection is performed using the logarithmic Bayes factor ($\ln B_{i,j}$) based on the revised Jeffreys' scale and the $N_\sigma$ statistic derived from the maximum-a-posteriori (MAP) goodness-of-fit difference ($\Delta\chi^2_{MAP}$).

Key Contributions and Results
The paper presents constraints on the $\xi$IDE parameters ($\xi$, $w_X$, and the interaction combination $\xi + 3w_X$) across various dataset combinations.

1. Hubble Tension: The $\xi$IDE model favors slightly higher values of the Hubble constant ($h$) compared to $\Lambda$CDM. For instance, with the CMB + DESI DR1 + CC dataset, $h$ shifts from $0.676 \pm 0.005$ in $\Lambda$CDM to $0.694 \pm 0.016$ in $\xi$IDE. This shift reduces the tension with local $R22$ measurements (e.g., from $4.71\sigma$ to $1.91\sigma$ for the DR1 combination). However, the tension is not completely resolved for any dataset combination, and the inclusion of DESI DR2 data weakens the preference for higher $h$ values compared to DR1.

2. Parameter Constraints:

   • $\xi$ (Coincidence Parameter): The parameter is consistently constrained to values close to the $\Lambda$CDM prediction of $\xi = 3$ (ranging roughly from $2.7$ to $3.05$). This indicates no statistically significant deviation from the standard cosmological evolution.
   • $w_X$ (Equation of State): Except for the CMB + DESI DR1 + CC combination, the dark energy equation-of-state parameter prefers values $w_X > -1$, suggesting a mild preference for quintessence-like behavior. However, the cosmological constant value ($w_X = -1$) remains consistent within $1\text{--}2\sigma$ confidence levels.
   • Interaction Direction ($\xi + 3w_X$): The combination $\xi + 3w_X$ is found to be negative for all dataset combinations, corresponding to an energy transfer from dark energy to dark matter ($Q > 0$). The strongest indication is found in the CMB + DESI DR2 + CC + Union3 combination, yielding $\xi + 3w_X = -0.035 \pm 0.023$. This represents a deviation of only $1.52\sigma$ from the non-interacting limit ($\xi + 3w_X = 0$).

3. Model Comparison:

   • Frequentist Significance ($N_\sigma$): The preference for the $\xi$IDE model over $\Lambda$CDM ranges from $1.10\sigma$ to $2.06\sigma$ across all datasets. All values fall within the "weak evidence" category ($1 \le N_\sigma < 2.5$), failing to reach the threshold for moderate evidence ($2.5\sigma$).
   • Bayesian Evidence: The logarithmic Bayes factors consistently favor the $\Lambda$CDM model. For DESI DR1 combinations, evidence ranges from moderate to strong ($\ln B_{i,j} \approx 4.18\text{--}5.38$) in favor of $\Lambda$CDM. For DESI DR2 combinations, the preference remains moderate ($\ln B_{i,j} \approx 2.60\text{--}4.16$).

Significance and Conclusion
The paper concludes that while the $\xi$IDE model offers a viable phenomenological extension that can mildly alleviate the Hubble tension and suggests a direction of energy transfer (from DE to DM), current cosmological observations do not provide compelling evidence for a non-zero dark-sector interaction.

The authors emphasize that the parameter constraints remain largely consistent with the standard $\Lambda$CDM scenario. The slight preference for dynamical dark energy ($w_X > -1$) and energy transfer is statistically weak, with the strongest deviation from the non-interacting limit reaching only $1.52\sigma$. Furthermore, Bayesian model comparison consistently prefers the simpler $\Lambda$CDM model. Thus, the study asserts that while the interaction scenario remains a possible mechanism, the current data do not necessitate a departure from the standard non-interacting cosmological model.