Interacting Dark Sectors in Anisotropic Universe: Observational Constraints and $H_{0}$ Tension

TL;DR

This study constrains the interaction between dark matter and dark energy within an anisotropic Bianchi type I universe, exploring both constant and redshift-dependent couplings. By performing a Bayesian MCMC analysis on a joint data set that includes OHD, CMB, BAO, SNIa, and an $H_{0}$ prior, the authors derive analytic (constant coupling) and numerical (variable coupling) solutions for the cosmic evolution, incorporating an anisotropy density term. The results indicate that the present Universe is consistent with uncoupled $Λ$CDM in this anisotropic setting, with the dark-energy equation of state $ ilde{ω}^{X}$ near $-1$ and the coupling $ ilde{δ}$ consistent with zero; however, the constant coupling case can yield a higher $H_{0}$ when using the $H_{0}$ prior, while the varying coupling case does not alleviate the $H_{0}$ tension. Overall, the data prefer negligible anisotropy and nearly standard cosmology, suggesting limited evidence for dark-sector coupling in this BI framework and showing that $H_{0}$ tension persists in the variable-coupling scenario.

Abstract

The present study reveals observational constraints on the coupling between dark components of anisotropic Bianchi type I universe. We assume interaction between dark matter and dark energy and split the continuity equation with inclusion of interaction term $Γ$. Two scenarios have been considered (i) when coupling between dark components is constant and (ii) when it is a function of redshift ($z$). Metropolis-Hasting algorithm has been used to perform Monte Carlo Markov Chain (MCMC) analysis by using observational Hubble data obtained from cosmic chronometric (CC) technique, cosmic microwave background (CMB) baryon acoustic oscillation (BAO), Pantheon compilation of Supernovae type Ia (SNIa), their joint combination and a Gaussian prior on the Hubble parameter $H_{0}$. It is obtained that the combination of all databases plus $H_{0}$ prior marginalized over a present dark energy density gives stringent constraints on the current value of coupling as $-0.001<δ<0.041$ in constant coupling model and $-0.042<δ<0.053$ in varying coupling model at 68\% confident level. In general, for both models, we found $ω^{X}\approx -1$ and $δ(δ_{0})\approx 0$ which indicate that still recent data favor uncoupled $Λ$CDM model. Our estimations show that in constant coupling model $(H_{0}=73.9^{+1.5}_{-0.95}, δ=0.023^{+0.017}_{-0.024})$ which naturally leads to consistent value of the Hubble constant. This result is interesting because the previous works show that such a high value of Hubble constant requires the significant value of coupling parameter $δ$. It has been also observed that in the constant coupling model, we do not find any disagreement between the estimated $H_{0}$ and those reported by Hubble space telescope (HST) and large scale structure (LSS) experiments.

Figures (5)

• Figure 1: The contour plots of (a) $H_{0}-\delta$ plane, (b) $H_{0}-\omega^{X}$ plane, and (c) $\delta-\omega^{X}$ plane at $1\sigma$-$3\sigma$ confidence levels. The dashed horizontal and vertical lines in (a)& (b) show the mean value of Hubble constant obtained from HST project and the mean values of $\delta$ & $\omega^{X}$ obtained in this work respectively. In (c), the mean estimated values of $\delta$ and $\omega^{X}$ are shown by horizontal and vertical lines respectively.
• Figure 2: The contour plots of (a) $H_{0}-\delta_{0}$ plane, (b) $H_{0}-\omega^{X}$ plane, (c) $\delta_{0}-\omega^{X}$ and (d) $\delta_{0}-\gamma$ planes at $1\sigma$-$3\sigma$ confidence levels. The dashed vertical, in figure (a) , and horizontal, in figures (c) and (d), lines stand for $\delta_{0}=0$. In (b) and (c), the dashed vertical lines stand for $\omega^{X}=-1$.
• Figure 3: Plots of correlation matrix of parameter space ${\bf\Theta_{1}}$ using combinations of different data for constant coupling model. The color bars share the same scale.
• Figure 4: Whisker plot with the $1\sigma$ confidence level on the Hubble constant for varying coupling case. Pink and gray vertical bands correspond to the value for the Hubble constant estimate by the Planck 2018 release Aghanim/2018aand the HST in Riess/2019 respectively.
• Figure 5: Plots of correlation matrix of parameter space ${\bf\Theta_{1}}$ using combinations of different data for varying coupling model. The color bars share the same scale.