Dark matter solution to the H0 and S8 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 H₀ and S₈ tensions, alleviating them both simultaneously, reducing the H₀ tension from 5 to 3 and the S₈ tension from 3 to 1. 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 H₀ and S₈ tensions. We predict the ISW from cosmic voids to be a factor of up to 2 greater in this model than what is expected from the standard model. These results extend to other degenerate models of dark matter, such as unified or interacting dark matter and dark energy models.