Effects of Anisotropic Stress in Interacting Dark Matter - Dark Energy Scenarios

TL;DR

This work extends the interacting dark matter–dark energy framework by including matter-sourced anisotropic stress and a coupling form $Q=3H\xi(1+w_x)\rho_x$. Using Planck CMB data, SNIa (JLA), BAO, cosmic chronometers, weak lensing, and local $H_0$ measurements with CAMB/CosmoMC, it constrains the perturbative dynamics and finds that a nonzero interaction is allowed but the data prefer a near-$\Lambda$CDM background with a small perturbative deviation. The anisotropic stress is constrained to be small, and $w_x$ remains close to $-1$, though ratios of CMB TT spectra hint at mild deviations from $\Lambda$CDM in some cases. Bayesian evidence consistently favors $\Lambda$CDM over the interacting scenarios, though allowing phantom $w_x$ can modestly ease the $H_0$ tension in specific data combinations, highlighting the potential value of next-generation surveys for discriminating these models.

Abstract

We study a novel interacting dark energy $-$ dark matter scenario where the anisotropic stress of the large scale inhomogeneities is considered. The dark energy has a constant equation of state and the interaction model produces stable perturbations. The resulting picture is constrained using different astronomical data aiming to measure the impact of the anisotropic stress on the cosmological parameters. Our analyses show that a non-zero interaction in the dark sector is allowed while a non-interaction scenario is recovered within 68\% CL. The anisotropic stress is also constrained to be small, and its zero value is permitted within 68\% CL. The dark energy equation of state, $w_x$, is also found to be close to `$-1$' boundary. However, from the ratio of the CMB TT spectra, we see that the model has a mild deviation from the $Λ$CDM cosmology while such deviation is almost forbidden from the CMB TT spectra alone. Although the deviation is not much significant, but from the present data, we cannot exclude such deviation. Overall, at the background level, the model is close to the $Λ$CDM cosmology while at the level of perturbations, a non-zero but a very small interaction in the dark sector is permitted. Perhaps, a more accurate conclusion can be made with the next generation of surveys. We also found that the region $w_x < -1$, is found to be effective to release the tension on $H_0$. Finally, from the Bayesian analysis, we find that $Λ$CDM remains in still preferred over the interacting scenarios.

Figures (9)

• Figure 1: The plots show the one-dimensional posterior distributions for various cosmological parameters using different combined analysis of the observational data as displayed in Table \ref{['tab:results']}.
• Figure 2: 68% and 95% confidence-level contour plots in the two-dimensional $(H_0, w_x)$, $(\Omega_{m0}, w_x)$ and $(\xi, w_x)$ planes for different combined analyses have been shown. Left Panel: This shows that higher values of $H_0$ allow more phantom nature in the dark energy equation of state $w_x$, while the quintessence nature is favoured in $w_x$ for lower values of $H_0$. Middle Panel: Higher values of $\Omega_{m0}$ favor the quintessence character in the dark energy equation of state while the phantom character of $w_x$ is increased with the lower values of $\Omega_{m0}$. Right panel: The parameters $w_x$ and $\xi$ are almost uncorrelated with each other.
• Figure 3: 68% and 95% confidence-level contour plots in $(e_{\pi}, H_0)$, $(e_{\pi}, \xi)$, and $(e_{\pi}, w_x)$ planes have been shown for several observational combinations. Left Panel: This shows the $(H_0, e_{\pi})$ plane. One can see that the combination CMB+ext (where 'ext' is the other data sets, for instance BAO, RSD,.. etc) decreases the error bars on the parameters. Although, one cannot find a clear relation between $e_{\pi}$ and the Hubble parameter values, but the plots for different combinations (except CMB) slightly show that $e_{\pi}$ has a very weak tendency to increase its values for lower values of $H_0$. We repeat that such tendency is extremely weak according to the current data we employ. Middle Panel: This actually infers a low interaction scenario with a small anisotropic stress. However, one can clearly notice that the parameters ($e_{\pi}$, $\xi$) are almost uncorrelated with each other. Right Panel: One can see that the phantom dark energy allows lower values of $e_{\pi}$ while for quintessence dark energy one may expect slightly higher values of $e_{\pi}$, although, it is clear that the observational data do not allow a large $e_{\pi}$.
• Figure 4: 68% and 95% confidence-level contour plots in ($\sigma_8$, $e_{\pi}$), ($\sigma_8$, $\xi$) and ($H_0$, $\sigma_8$) planes for several observational combinations. Left Panel: From the plot, we do not observe any significant effect on $\sigma_8$ for anisotropic stress. In fact, one may see that a small value of $\pi$ is allowed in agreement with the estimated value of $\sigma_8$ from Planck Ade et al. (2016). Middle Panel: One may notice that $\sigma_8$ has a slight dependence on $\xi$, although such dependence is weak but this is not null. One can see that $\sigma_8$ has a tendency to take lower values for increasing strength of the interaction. Right Panel: A weakly dependence between $H_0$ and $\sigma_8$ is reflected from this plot.
• Figure 5: The figure shows the CMB TT power spectra (Left Panel) and the ratio (also known as the relative deviation) of the CMB TT power spectra (Right Panel) for the present interacting dark-energy scenario $Q = 3 H \xi (1+w_x) \rho_x$ with and without the presence of anisotropic stress that we consider in this work (see section \ref{['sec-bg+per']} for details). Here, $\Delta C_l^{TT} =C_{l}^{TT}\bigl|_{model} \, -\, C_{l}^{TT}\bigl|_{LCDM}$ and $C_l^{TT} = C_{l}^{TT}\bigl|_{LCDM}$. From the Left Panel, one may notice that at low angular scales, with the increase of $|e_{\pi}|$, the deviation from the non-interacting $\Lambda$CDM becomes high, but however, at high angular scales, no such deviation in the CMB TT spectra for $|e_{\pi}|$ is observed. The similar behaviour is reflected from the Right Panel, although a non-zero deviation from the $\Lambda$CDM even at high angular scales is observed here.