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# Dark energy and matter interacting scenario can relieve $H_0$ and $S_8$ tensions

Dec 2022

In this work, we consider a new cosmological model (named $\tilde\Lambda$CDM)in which the vacuum energy interacts with matter and radiation, and test thismodel using the current cosmological observations. We find that this model cansignificantly relieve the $H_0$ tension, and at the same time it can alsoslightly reduce the $S_8$ tension, which cannot be easily observed in othercosmological models. Using the CMB+BAO+SN (CBS) data to constrain the model, weobtain the results of $H_0=70.6^{+1.4}_{-1.7}~\rm{km~s^{-1} Mpc^{-1}}$ and$S_8=0.820\pm 0.011$, and thus the $H_0$ and $S_8$ tensions are relieved to$1.28\sigma$ and $2.67\sigma$, respectively. However, in this case the$\tilde\Lambda$CDM model is not favored by the data, compared with$\Lambda$CDM. We find that when the $H_0$ and $S_8$ data are added into thedata combination, the situation is significantly improved. In the CBS+$H_0$case, we obtain the result of $H_0=72.2\pm 1.2$ ${\rm km~s^{-1}~Mpc^{-1}}$,which relieves the $H_0$ tension to $0.53\sigma$, and in this case the model isfavored over $\Lambda$CDM. In the CBS+$H_0$+$S_8$ case, we get a syntheticallybest situation, $H_0=71.9\pm 1.1$ ${\rm km~s^{-1}~Mpc^{-1}}$ and $S_8=0.8071\pm0.0099$, in which the $H_0$ and $S_8$ tensions are relived to $0.75\sigma$ and$2.09\sigma$, respectively. In this case, the model is most favored by thedata. Therefore, such a cosmological model can greatly relieve the $H_0$tension, and at the same time it can also effectively alleviate the $S_8$tension.

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