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 $\sim5\sigma$ to $\sim3\sigma$ and the $S_{8}$ tension from $\sim3\sigma$ to $\sim1\sigma$. 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 $\sim2$ greater in this model than what is expected from the standard model $\Lambda$CDM. These results extend to other degenerate models of dark matter, such as unified or interacting dark matter and dark energy models.