Dark matter solution to the $H_0$ and $S_8$ tensions, and the integrated Sachs-Wolfe void anomaly

We consider a phenomenological model of dark matter with an equation-of-state $w$ that is negative and changing at late times. We show this couples the $H_0$ and $S_8$ tensions, alleviating them both simultaneously, reducing the $H_0$ tension from $\sim 5\sigma$ to $\sim 3\sigma$ and the $S_8$ tension from $\sim 3\sigma$ to $\sim 1\sigma$. Furthermore, the model provides an explanation for the anomalously large integrated Sachs-Wolfe (ISW) effect from cosmic voids, a unique consequence of the changing and negative equation-of-state. Observations of high ISW from cosmic voids may therefore be evidence that dark matter plays a significant role in both the $H_0$ and $S_8$ tensions. We predict the ISW from cosmic voids to be a factor of up to $\sim 2$ greater in this model than what is expected from the standard model $\mathrm{\Lambda }$CDM. These results extend to other degenerate models of dark matter, such as unified or interacting dark matter and dark energy models.